@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Community and Regional Planning (SCARP), School of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Chan , Sheung-Ling"@en ; dcterms:issued "2011-05-26T15:47:58Z"@en, "1970"@en ; vivo:relatedDegree "Master of Arts in Planning - MA (Plan)"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """This thesis explores some of the limitations and implications of using multiple regression analysis in transportation models. Specifically it investigates how the problem of multicollinearity, which results from using intercorrelated variables in trip generation models, adversely affects the validation of hypotheses, discovery of underlying relationships and prediction. The research methodology consists of a review of the literature on trip generation analysis and a theoretical exposition on multicollinearity. Secondly, trip generation data for Greater Vancouver (1968) is used for empirical analysis. Factor analysis and multiple regression techniques are employed. The results demonstrate that multicollinearity is both an explanatory and prediction problem which can be overcome by a combined factor analytic and regression method. This method is also capable of identifying and incorporating causal relationships between land use and trip generation into a single model. It is concluded that the distinction between the explanatory, analytic and predictive abilities of a regression model is artificial, and that greater emphasis on theorizing in model-construction is needed. ."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/34904?expand=metadata"@en ; skos:note "MULTICOLLINEARITY IN TRANSPORTATION MODELS by SHEUNG-LING CHAN B . A . , Un iver s i ty of Hong Kong, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF ' THE REQUIREMENT FOR THE DEGREE OF MASTER OF ARTS l in the School of Community & Regional Planning We accept t h i s thes i s as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1970. In presenting this thesis in par t i a l fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shal l make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for f inancial gain sha l l not be allowed without my written permission. School of Community and Regional Planning The University of Br i t i sh Columbia Vancouver 8,' Canada t • Date: A p r i l 1970. i ABSTRACT This thesis explores some of the limitations and implications of using multiple regression analysis in transportation models. Speci f ica l ly i t investigates how the problem of mult icol l inear i ty , which results from using intercorrelated variables in t r i p generation models, adversely affects the validation of hypotheses, discovery of underlying relationships and predict ion. The research methodology consists of a review of the l iterature on t r i p generation analysis and a theoretical exposition on mult ico l l inear i ty . Secondly, t r i p generation data for Greater Vancouver (1968) i s used for empirical analysis . Factor analysis and multiple regression techniques are employed. The results demonstrate that mult icol l ineari ty i s both an explanatory and prediction problem which can be overcome by a combined factor analytic vt and regression method. This method is also capable of identifying and incorporating causal relationships between land use and t r i p generation into a single model. It is concluded that the dist inct ion between the explanatory, analytic and predictive a b i l i t i e s of a regression model i s a r t i f i c i a l , and that greater emphasis on theorizing in model-construction is needed. . • • y. ' i i . TABLE OP CONTENTS PRELIMINARY PAGES PAGE Abstract i Table of Contents i i Acknowledgements v i CHAPTER I . INTRODUCTION 1 ,1.1 J u s t i f i c a t i o n f o r Research 1 1.2 The Problem and General Hypothesis 3 1.3 Postulates 5 1.4 Methodology 5 1.5 Source of Data 6 1.6 Limitation of Data 8 1.7 Organization of the Chapters to Follow 11 1.8 Definitions 11 I I . TRIP GENERATION ANALYSIS - AN OVERVIEW 21 2.1 Trip Generation i n the Transportation Planning Process 21 2.2 Factors Influencing Trip Generation 23 2.3 Approaches to Trip Generation Analysis...... 26 2.4 Some Considerations i n Using Multiple Regression Analysis.....' 33 I I I THEORETICAL EXPOSITION OF MULTICOLLINEARITY AS AN ,. EXPLANATORY AND ANALYTICAL PROBLEM 39 3.1 Model Attributes ' 39 3.2 A Non-mathematical Summary of the Theoretical Implications of M u l t i c o l l i n e a r i t y . . . . . 42 I l l PAGE 3.3 A S t a t i s t i c a l Exposit ion of M u l t i c o l l i n e a r i t y 43 3.4 Conclusion 57 I V . EMPIRICAL VERIFICATION OF HYPOTHESES 60 4.1 Summary of Empir ica l Findings 60 4.2 Formulation of Three Operational H y p o t h e s e s . . . . . . . 61 4.3 Va l ida t ion of Hypothesis 1 62 4.4 Va l ida t ion of Hypothesis 2 68 4.5 Va l ida t ion of Hypothesis 3 79 4.6 Conclusion 91 V . TRANSPORTATION MODELS - A PERSPECTIVE VIEW 94 5.1 Summary of Research Findings 94 5.2 U t i l i t y of Transportation Models 97 5.3 Implications for Model Bu i ld ing i n Transportation Studies 101 5.4 Conclusion 103 BIBLIOGRAPHY . * 108 APPENDICES APPENDIX A. A l i s t of Variables Used i n This Study Il8 , APPENDIX B. S t a t i s t i c a l Test of Autocorrelat ion for Model 2 by Using the \"Contiguity Measure for k-Color Maps \" Technique 119 APPENDIX C. Method of Using Model 3 for Predic t ion 123 APPENDIX D. Input Data and The Corre la t ion Matrix APPENDIX E . Mul t ip le Regression Outputs of Model 1. APPENDIX F . Factor Analysis Outputs for the T r i p Generation Data APPENDIX G. Mul t ip l e Regression Outputs of Model 2. APPENDIX H . Mul t ip l e Regression Outputs of Model 3. iv LIST OF TABLES PAGE TABLE I . TRIPS PER DWELLING UNIT CROSS-CLASSIFIED WITH HOUSEHOLD SIZE AND AUTO-OWNERSHIP. 29 TABLE I I . EXAMPLES OF MULTIPLE CORRELATIONS IN A THREE-VARIABLE PROBLEM WHEN INTERCORRELATIONS VARY. 55 TABLE I I I . SIMPLE AND PARTIAL CORRELATIONS OF MODEL 1. 64 TABLE I V . SIMPLE AND PARTIAL CORRELATIONS OF MODEL 2. 77 TABLE V . LOSS AND GAIN OF COMMUNALITIES IN MODEL 2 COMPARED WITH MODEL 1. 78 TABLE VT. A LIST OF POSSIBLE EXPLANATORY FACTORS OMITTED BY MODEL 2. 84 . ' \\ • .- • FIGURE 1. FIGURE 2.. FIGURE 3. FIGURE 4. FIGURE 5. FIGURE 6. FIGURE 7. FIGURE 8. FIGURE 9. FIGURE 10. FIGURE 11. FIGURE 12. FIGURE 13. FIGURE 14. FIGURE 15. LIST OF ILLUSTRATIONS TRAFFIC DISTRICTS OF GREATER VANCOUVER PAGE 7 GEOMETRIC INTERPRETATION OF MULTIPLE REGRESSION IN A THREE VARIABLE PROBLEM WITH NO INTERCORRELATION BETWEEN INDEPENDENT VARIABLES 44 GEOMETRIC INTERPRETATION OF MULTIPLE REGRESSION • IN A THREE VARIABLE PROBLEM WITH INTERCORRELATION BETWEEN INDEPENDENT VARIABLES . 45 GEOMETRIC INTERPRETATION OF MULTIPLE REGRESSION IN A THREE VARIABLE PROBLEM WITH NEAR PERFECT INTERCORRELATION BETWEEN INDEPENDENT VARIABLES 47 GRAPH SHOWING MULTIPLE R2.. 0 , AS A FUNCTION O F r 2 3 56 COMPOSITION OF SEVEN MAJOR FACTORS OUT OF 29 VARIABLES. .. 70 LOCATION OF THE FIRST AND SECOND COMPONENT VECTORS FOR THE VARIABLES IN TWO-DIMENSIONAL SPACE. 73 LOCATION OF THE SECOND AND THIRD COMPONENT VECTORS FOR THE VARIABLES IN A TWO-DIMENSIONAL SPACE. • 75 LOCATION OF THE THIRD AND FOURTH COMPONENT VECTORS FOR THE VARIABLES IN A TWO-DIMENSIONAL SPACE. 76 OBSERVED AND CALCULATED VALUE OF Y FOR MODEL 1 80 OBSERVED AND CALCULATED VALUE OF Y FOR MODEL 2 8 l MAP SHOWING DISTRIBUTION OF RESIDUALS FOR MODEL 2 83 FACTOR SCORE DISTRIBUTION FOR FACTOR I I (EMPLOYMENT) 85 FACTOR SCORE DISTRIBUTION FOR FACTOR I I I (DENSITY) 86 OBSERVED AND CALCULATED VALUE OF Y FOR MODEL 3 89 ACKNOWLEDGEMENTS Thanks are due to Professor P. 0. Roer for advice and supervision in the preparation of this thes is . I am also much indebted to Dr. N. d . Cherukupalle for inspiration and encouragements. In addition, I am grateful to N. D. Lea & Associates, Vancouver, for permission to use part of their Burnaby Transportation Study data. Financial assistance from the Mellon Foundation is acknowledged. F ina l ly , special words of thanks must be extended to my colleague, How-Yin Leung for his crit icisms and help in proof-reading the manuscript. 1 CHAPTER I INTRODUCTION Multiple regression i s one of the most widely used techniques i n data analysis and model building; i t i s often abused due to a lack of understanding of i t s basic assumptions. This chapter introduces the problem of m u l t i c o l l i n e a r i t y which r e s u l t s from v i o l a t i o n of the assumption that predictors i n the regression equation are independent. The discussion i s conducted within the context of transportation models. 1.1 J u s t i f i c a t i o n for Research Estimation of t r a v e l demand i s an important and i n t e g r a l part of the transportation planning process. Among i t s various phases, t r i p generation and modal s p l i t procedures have generally r e l i e d heavily on s t a t i s t i c a l methodology such as multiple regression. These procedures require a sound knowledge of the s t r u c t u r a l relationship contained i n the basic data set. Yet a survey of the l i t e r a t u r e i n t h i s f i e l d \" indicates that major e f f o r t has so far been i n the direction of s t a t i s t i c a l e f f i c i e n c y and selection of optimal relationships between variables. L i t t l e effort has been devoted to understanding the inferences concerning travel behaviour that are implic i t in these 1 procedures. Stated simply, most model-builders are overly concerned with obtaining a high correlation coeff icient, and hence a good f i t of data, and less attention has been paid to the analytical and explanatory powers of the model. The general view held i s that prediction is not necessarily dependent on explanation. To the extent that the function of a model i s purely predict ive, as opposed to those models that seek to explain certain phenomena or to establish causal relat ionship, a high correlation is seen as an end in i t s e l f . 2 Reacting to the above attitude, Muller and Robertson cautioned that multiple regression equations with a high correlation coefficient, but containing i l l o g i c a l relationships,are s t a t i s t i c a l l y unstable. This i s self-evident as regression, and other mathematical models for that matter, i s only as accurate and as useful as the va l id i ty of the assumptions that are made and the s t a t i s t i c a l significance of the result obtained. It i s ent ire ly possible to produce results meeting a l l of the various s t a t i s t i c a l c r i t e r i a and yet offer no explanation of the causative relationships. In order to forecast, such a causal 3 relationship is essential . The use of intercorrelated variables in regression i s increasingly ' 5 being recognized, by Alonso and Harris among others, as a problem obscuring the causative relationships. Unfortunately variables in the urban context used for transportation models are more often than not spat ia l ly distributed in a correlated fashion, e .g . car ownership i s correlated with income, income with density, density with distance from C .B .D . , e tc . Thus, i f a l l these* intercorrelated variables were 3 used in the model, i t becomes extremely d i f f i c u l t to determine which are the causal factors related to urban t rave l . In other words, i t is not known then'whether tr ips are a function of a l l these variables working independently or whether they are interacting and in effect overlapping. Moreover, the existence of co l l inear i ty among variables casts many doubts on conventional s t a t i s t i c a l analyses and creates 6 severe operating problems. It i s f e l t therefore, that as trans-portation planners are more and more relying on regression as a tool for planning, i t i s perhaps timely to place in perspective this issue which bears on the r e l i a b i l i t y of the model as an explanatory and predictive device. 1.2 The Problem and General Hypothesis , The multiple regression model usually takes the form of Y = a + b,x, + b „ x „ + b~x0 + + b x •LI 2 2 5 5 m m In specifying the model in this form, i t i s assumed that the. various independent variables make independent and additive contribu-tions to the prediction of the variances observed in the dependent variable Y. If the assumption of independence is violated, then the 7 problem of co l l inear i ty is introduced . (in the case of two correlated independent variables) , or mult icol l inear i ty (in the case of three or more correlated variables) . , / ' The term mult icol l ineari ty is the name given to the general problem which arises when some or a l l of the explanatory variables in an equation are so highly correlated that i t becomes very d i f f i c u l t , 4 i f not impossible, to separate their individual influences and obtain 8 a reasonably precise estimate Of their effects. Secondly, since the variables are highly correlated, they reinforce each other's re lat ion-ship with the c r i te r ion , or suppress the true contribution of other variables in the equation. In the former case, the tendency is towards distorting the value of the multiple correlation coefficient beyond i t s true proportion; in the lat ter , some variables of explanatory value may never be able to enter the equation due to the predominance of col l inear sets. As previously stated, this problem i s part icular ly prevalent in transportation models due to the type of variables employed. The objective of this study, therefore, i s to investigate how multi-co l l inear i ty affects the performance of transportation models, in respect to validation of hypotheses, discovery of underlying re lat ion-ships and predict ion. Methods for overcoming the problem w i l l be suggested in the course of investigation. Moreover, the implications of prediction versus explanation in model-building w i l l be discussed. The following general hypothesis i s developed as a focus for the research: \"When co l l inear i ty exists in a regression model, explanatory and analyt ica l powers are decreased, despite the apparently good predictive power shown by a high multiple correlation coef f i c ient . \" / . 5 1.3 Postulates The investigation i s based on the following assumptions: 1) A good s t a t i s t i c a l f i t does not assure a good predictive 9 model. A model's strength l i e s e s s e n t i a l l y i n the sound-ness of i t s t h e o r e t i c a l base. 2) Only variables that can be supported by i n t u i t i v e l y sound arguments should be used i n regression analysis. I t makes l i t t l e sense to throw a l l possible variables into the pot i n a shotgun approach merely to obtain a high correlation c o e f f i c i e n t . 1 0 3) Multiple regression models are b a s i c a l l y concerned with postulates of cause and e f f e c t . Hence t h e i r v a l i d i t y as forecasting tools must r e l y on causative r e l a t i o n s h i p s . 1 1 1.4 Methodology A twofold strategy i s adopted. F i r s t l y , a t h e o r e t i c a l exposition on c o l l i n e a r i t y or m u l t i c o l l i n e a r i t y based on l i t e r a t u r e research i s given. Hopefully t h i s w i l l throw l i g h t on why and how c o l l i n e a r i t y a f fects the v a l i d i t y and u t i l i t y of the model. Secondly, the general hypothesis i s to be v e r i f i e d empirically by: 1) Using multiple regression analysis to examine, i n depth, a t y p i c a l example of transportation models on t r i p generation, ; with s p e c i a l emphasis on the undesirable properties associated with c o l l i n e a r i t y . 6 2) Factor analysis of the data to extract underlying dimensions, and to see i f the model has incorporated the significant factors into the equation.' 3) Formulating a new multiple regression model to eliminate col l inear sets and compare results . Data analysis is carried out by UBC IBM 360 d i g i t a l computer. The 12 13 computer programs used are the TRIP and FACTO packages, the former for regression analysis and the latter for factor analysis . 1.5 Source of Data The t r i p generation model studied here and i t s associated data has been obtained through the courtesy of N. D. Lea & Associates, Vancouver. The.data was collected for thirty-two t ra f f i c d i s t r i c t s of Greater Vancouver in 1968, partly through a telephone survey and partly from census information (See Figure 1). A to ta l of twenty-nine variables are used for computation in this thesis and a l l variables 14 are measured on interval scales. It should be pointed out that the or ig ina l data from N. D. Lea & Associates consisted of ten dependent variables and sixty-nine independent variables. The former is a finer breakdown of the nature 15 of t r i p s . The sixty-nine independent variables include the twenty-16 nine variables selected, in this study, the rest being complex or 17 transgenerated variables. By step regression, a to ta l of about forty ' • • ' • ' • / ' - ' . • equations were developed and f i n a l l y nine were selected, one for each FIG. 1 TRAFFIC DISTRICTS OF GREATER VANCOUVER 8 dependent variable except to ta l t r i p production. The model developed for tota l t r i p generation (total persons tr ips excluding walk tr ips per day) is selected for detailed examination here for two reasons: .1) It is representative of transportation models for t r i p generation. Hence findings w i l l generally be applicable to other models in the f i e l d . 2) It i s a convenient example because data i s available l oca l ly . Famil iari ty with local conditions fac i l i ta tes interpretation and visual izat ion of the issues involved. 1.6 Limitation of the Data Since this i s areal data, i . e . a l l information is grouped on the basis of geographical units , three limitations are recognized: a) The problem of autocorrelation, i . e . measurements obtained in one area are not ent ire ly independent of those obtained in other areas. Certain population and land use characteristics between contiguous areas may exhibit greater s imi lar i ty than non-contiguous areas. If this i s indeed so, then one of the assumptions of correlation analysis, that residuals from regression are mutually . independent random variables w i l l be violated. S t a t i s t i ca l tests are carried out on the residual distr ibution of Model 2 (See Figure 12) using the \"contiguity measures for i k-colour l8 maps technique\". The result reveals that there is no • . / s ignificant autocorrelation in this set of data. Computations can be found in Appendix B. b) The t r a f f i c d i s t r i c t s are not uniform i n s i z e . This gives r i s e to the problem i n i d e n t i f y i n g or e l iminat ing differences i n parameters which may be a t t r ibuted merely to differences i n s ize of area l un i t s from those differences which are owing to 19 \" t r u l y d i f f e r e n t \" r e l a t i o n s h i p s . For example, when comparing two d i s t r i c t s of equal s i z e , the absolute number of people re s id ing w i t h i n them re f l ec t s the i n t e n s i t y of r e s i d e n t i a l use. However, for d i s t r i c t s of unequal s i z e s , there i s no r e a l basis for comparison unless rate var iables are used. As can be seen l a t e r on in t h i s se t .o f data, the var iable \"Area\" i s found to expla in a s i g n i f i c a n t amount of v a r i a t i o n i n t r i p generation (See page 67) . This reveals that the analys is uni t s for t h i s study are d iv ided i n such a way that, the small d i s t r i c t s are found w i t h i n the urban areas wi th the large d i s t r i c t s at the metropolitan f r i ng e ; \"Area\" i n ef fect becomes a proxy for distance from C.B;D. and to some extent r e f l e c t s degree of urbanizat ion of the d i s t r i c t . Hence add i t iona l care must be exercised i n in terpre t ing outputs under these circumstances. c) The h igh ly aggregated data on a d i s t r i c t basis for t h i s set poses some problems of in terpre ta t ion and a p p l i c a t i o n . In general , geographical aggregation of data i s not as e f f i c i e n t • 20 as i t may be. As Fleet and Robertson pointed out, the underlying assumption of a rea l aggregation i s that contiguous households exh ib i t some s i m i l a r i t y In family and t r a v e l c h a r a c t e r i s t i c s . The degree to which these uni t s are not 10 homogenous results in a loss of disaggregated d e t a i l . An example of a detailed household characteristic that does not \"show up\" in explaining the zonal t r i p generation is family-income, which in tu i t ive ly would d i rec t ly ref lect differences in household characteristics and in part icular , differences in trip-making. However,, when this information is averaged for an areal unit composed of a number of households and related to the number of tr ips generated by that unit , almost a l l these differences are los t . This has resulted in the seemingly \"weak\" relationships. Therefore there is an inherent danger in making s t a t i s t i c a l inference from highly aggregated data concerning disaggregated relationships. S imilar ly , because t r i p generation data for this study has been collected at the t ra f f i c d i s t r i c t l eve l , the apparently good results of analysis (the extremely high correlation coefficients obtained) are misleading. This i s in tu i t ive ly obvious since . the larger the unit , the more to ta l variation w i l l be lost within the uni t s . L i t t l e of the to ta l variation is actually left to explain between the units , thus allowing a high propor-tion of the between-group-variance to be unaccounted for . As such i t i s s t a t i s t i c a l l y incorrect to use equations developed at the d i s t r i c t level to calculate tr ips generated at the smaller zonal level because another set of variables may do a better job at this l e v e l . 1 1 Since the primary interes t of t h i s study i s to invest igate t r i p generation charac te r i s t i c s at an a rea l l e v e l , the inferences drawn w i l l not be applicable to i n d i v i d u a l and household t r a v e l behaviour. 1 .7 Organization of the Chapters to Follow Chapter I I presents an overview of current pract ices and develop-ments i n t r i p generation analys is based on l i t e r a t u r e research. Chapter I I I contains a discussion on model a t t r ibutes and a s t a t i s t i c a l exposit ion on the problem of m u l t i c o l l i n e a r i t y . Chapter IV attempts to v a l i d a t e , e m p i r i c a l l y , the general hypothesis through the t e s t ing of three operat ional hypotheses and the development of an a l te rnat ive model. F i n a l l y , Chapter V deals with the planning impl icat ions of the f indings and concludes with a summary and suggestions for future . . . . > research. ' \\i ' -1 . 8 Def in i t ions The fo l lowing i s a b r i e f resume of the terms used in the t e x t . More rigorous and t echnica l exposit ions on regression and factor analys is can be found i n standard textbooks on these subjects . 2 1 ' Linear Mult ip le Regression Analysis Using the least-squares p r i n c i p l e , mult iple regression i s a technique for measuring the influence of some independent var iables (predictors) on a dependent var iable ( c r i t e r i o n ) . In the context of t h i s study, 12 the aim of linear multiple regression is to obtain from land use, t ra f f ic and population data an equation of the form: t ; Y = a + b-jX^ + bgXg + B3X3 + b n X n where Y is the zonal measure of t rave l . A l l the x 's are the independent zonal land use and population factors, each of which has a separate influence on Y with per unit effects given by b^, b^, b^, etc . Since not a l l of the numbers of t r ips per zone may be explained by the x's in the equation, 'a ' is a number put in to represent the unexplained part of the value of Y. It i s often referred to as the 'constant 1 of the equation. A large constant for this reason is undesirable as i t indicates the pos s ib i l i ty of presence of other explanatory variables not taken into account. The b-coefficients are called regression coefficients which in the case of standardized variables are cal led B coeff icients . Beta coefficients indicate the relat ive weights of the different independent\\,variables. Standardized Variables Variable values are transformed into standard or Z scores rather than in raw scores. The Z score expresses the measurement of a variable for an individual in terms of i t s deviation from the mean value of the d i s t r ibut ion . The formula i s Z = x ± - x ' 13 F P r o b a b i l i t y A measure of whether the regression coe f f i c i ent i s s i g n i f i c a n t to the regression equation. Generally when the F P r o b a b i l i t y i s greater than 0.05 the regression coe f f i c ient i s not s i g n i f i c a n t at the 5$ l e v e l . Standard Error of Estimate (Residual Standard Deviation or Root Mean Square Er ror ) I t i s u sua l ly denoted by S . I t i s a summary of a l l the squared d i s -crepencies of ac tua l measurements from the predicted measurements. A general measure of the value of a regression equation i s the standard error of estimate as a percentage of the mean value of the dependent v a r i a b l e ; a good equation has a small standard e r ror of estimate which i s a small percentage of the mean, and v ice ver sa . Corre la t ion Coef f ic ient I t i s possible to measure the degree of associat ion between two var iables by means of a s t a t i s t i c known as coe f f i c ient of simple c o r r e l a t i o n . I t i s general ly represented by ' r / , which can assume values i n the range +1 o n l y . The closer ' r ' i s to +1, the stronger the r e l a t i onsh ip between the two v a r i a b l e s . As a measure of c o r r e l a -t i o n between one dependent var iable and more than one independent v a r i a b l e , the s t a t i s t i c i s known as coe f f i c i ent of mult iple cor re l a t ion or ' R ' . There i s a further property of the coe f f i c ient of cor re l a t ion which i s useful i n in terpre t ing the re su l t s given by the regression equation. The percentage of the t o t a l v a r i a t i o n i n the dependent var iable which i s 'expla ined' by an independent var iable i s approximately equal to 14 one hundred times the square of ' r ' . This s t a t i s t i c i s known as the p coefficient of determination or r_ in case of simple correlation, and 2 R_ for multiple correlat ion. It should be noted that the tendency for one variable to vary with another, as shown by i t s ' r ' , i s no evidence of any causal relationship, since i t may be that both variables are influenced by other variable(s) not examined. Fisher's Transformation A method to transform the value of the correlation coefficient of a regression equation into a s t a t i s t i c known as . Fisher's ' z ' so that the testing of whether ' r ' is s igni f icant ly different from zero or to compare the difference between two r ' s can be carried out by ' t 1 test . The principle involves approximating * r ' into a normal sampling population regardless of the size of sample and population. Par t ia l and Simple Corre la t ions^ A simple correlation expresses the relationship between two variables under consideration, not holding constant any other variables. There-fore, i f there i s any co l l inear i ty between the explanatory variable and other Independent variables, then the simple ' r ' w i l l incorporate this relationship a l so . The par t i a l . 'r 1 expresses the relationship between the Independent variable under consideration and the dependent . variable, holding the effect of other independent variables constant. Factor Analysis A generic term for a v a r i e t y of procedures developed for the analys is of in te rcor re l a t ions w i t h i n a set of va r i ab le s . The most common type of factor analys is i s p r i n c i p a l component ana ly s i s ; i t collapses large masses of data in to basic underlying dimensions, and i s capable of e l iminat ing c o l l i n e a r sets of var iables w i t h i n a set of data to produce an underlying set of independent or orthogonal f ac tor s . Factor Loading The square root of the t o t a l variance of a var iable accounted for by the f ac to r s . In other words, i t i s the cor re l a t ion coe f f i c ient between the var iable under consideration and the f ac to r s . Communality The proportion of common variance of a var iable accounted for by a 2 f a c t o r . I t can be regarded as the R between the var iable under consideration and a f a c t o r . Factor Score The score that an i n d i v i d u a l obtains for a p a r t i c u l a r f ac tor . I t i s ca lculated from the scores the i n d i v i d u a l gets i n a set of var iables contr ibut ing to that factor by regress ion. Usual ly i t i s standardized and orthogonalized. (See Appendix C) Model An experimental design based on a theory. Being a s i m p l i f i e d representation of r e a l i t y , i t i s frequently truncated theor ies , 23 s a c r i f i c i n g richness and completeness for operat ional purposes. 16 Trip Generation A term commonly used to describe the number of t r ips starting or ending in a particular area in relat ion to the land use and/or socio-economic characteristics of that area. Total Trips Generated in a.Zone It is the number of person or vehicle t r ip s , by a l l modes of transport, made by residents to and from a zone. It does not include walk t r ips and tr ips by taxi and trucks. Total Trips Attracted to a Zone Refers to the number of person or vehicle t r i p s , by a l l modes of trans-port, but excluding walk t r ips and tr ips by taxi and trucks, ending in a zone. Prediction Conditional statements about future developments - statements which are 24 conditioned by varying assumptions of pol icy and external conditions. 2S Measurement and Specification Errors Two general categories of error can be distinguished in any experi-mental design. The f i r s t i s measurement error . It includes data col lect ion errors, errors of scaling and sampling errors . For the roost part, the model-builder is unable to control these errors unless he is responsible for the design of the data col lect ion survey. Specification error arises from a misunderstanding or a purposeful s implif ication in the model of the phenomenon we are trying to 17 represent e.g. the representation of a non-linear r e l a t i o n by a l i n e a r expression, omission of s i g n i f i c a n t v a r i a b l e s , i n c l u s i o n of i n t e r -c o r r e l a t e d v a r i a b l e s as w e l l as the f a i l u r e to c o r r e c t l y evaluate a • 25 model. These can be more e a s i l y c o n t r o l l e d with a good research design. 18 Footnotes ^Christopher R. Fleet and Sydney R. Robertson, \"Tr ip Generation In The Transportation Planning Process\", Highway Researcb Record, No. 240 (1968), p .11. U.S . Department of Transportation/Federal Highway Adminis tra t ion, Bureau of Publ ic Roads, Guidelines for T r i p Generation Ana lys i s , (June 1967), p.109. 3 I b i d , p.25. ^Wil l i am Alonso, \"Predict ing Best With Imperfect Data\", Journal of The American Ins t i tu te of Planners, V o l . 34, No. 3, (1968), p.249. 5 B r i t t o n H a r r i s , \"New Tools for Planning\" , Journal of The American In s t i tu te of Planners, V o l . 31, No. 2 (1965), p.95. 6 I b i d , p.95. ^ N . d . Cherukupalle,\"Regression Analysis - Interpretat ion of Computer Outputs, Etc.\", Planning 508 Course Notes, October 1969, School of Community & Regional Planning, U . B . C , p . l . 8 J . Johnston, Econometric Methods, New York, McGraw H i l l I n c . , (1963), p.201. ^K. Rask Overgaard, \"Urban Transportation Planning: T r a f f i c Es t imat ion\" T r a f f i c Quarterly, ( A p r i l 1967), p.202. 1 0 J e f f r e y M. Zupan, \"Mode Choise: Implicat ions for Planning\" , Highway Research Record, No. 251 (1969), p.l4. 1 1 K . Rask Overgaard, op. c i t . , p.202. 1 2James H. B j e r r i n g , J . R. H . Dempster and Ronald H . H a l l , U . B . C . TRIP (Triangular Regression Package), (The U n i v e r s i t y of B r i t i s h Columbia Computing Centre, January 1968). l 3James H . B j e r r i n g , U .B .C . FACTO - Factor Analysis Program, (The U n i v e r s i t y of B r i t i s h Columbia Computing Centre, May 1969). 19 14 An in terva l - sca le deals with quantative measurements i n equa l i ty of u n i t s , which means the same numerical distance i s associated with the same empir ica l distance on some r e a l continuum such as length and weight. 15 The ten dependent variables for the N . D. Lea Burnaby Transportation Study are : home-based work a t t r a c t i o n , home-based other a t t r a c t i o n , non-home-based des t inat ions , t o t a l a t t r a c t i o n , home-based work production, home-based other production, non-home-based production, non-home-based o r i g i n s , t o t a l production and t o t a l t r i p generation. 16 See Appendix A . 17 Basic Variables are variables co l l ec ted i n the survey. Complex and transgenerated var iables are. those obtained by combining basic var iables i n various manner, e , g . a d d i t i o n , subtract ion , m u l t i p l i c a -t i o n and d i v i s i o n , logarithm, cosine, and s ine , e t c . , e .g . In density i s derived from In ( t o t a l populat ion/area) . 18 „ For d e t a i l s on t h i s method, see Michael F . Dacey, A Review on Measures of Contiguity for Two and k-colour Maps\", S p a t i a l Analysis (New York: Prentice H a l l I n c . , 1968), Ed . by Brian J . Berry and D. F. Marble, pp.479-490. 19 E . N . Thomas and D. L . Anderson, \"Addi t iona l Comments on Weighting Values i n Corre la t ion Analysis of Areal Data\", l o c . c i t . , pp.431-445. 20 Christopher R. Fleet and Sydney R. Robertson, op. c i t . , p . 13. 2 1 Adapted from: M. A . Taylor , Studies of Travel i n Gloucester, Northampton & Reading, Road Research Laboratory Report, L .R . 141 (Mini s t ry of Transport, Great B r i t a i n , 1968), pp.142-149. 22 N . d . Cherukupalle, op. c i t . , pp.4-5. 23 B r i t t o n H a r r i s , \"The Use of Theory In The Simulation of Urban Phenomena\"> Journal of the American I n s t i t u t e of Planners, V o l . 32, No. 5 (September 1966), p.265. . . - . B r i t t o n H a r r i s , \"New Tools for Planning\" , op. c i t . , p.9L 2 5 W i l l i a m Alonso, op. c i t . , p.248. 20 ) / I 21 CHAPTER I I TRIP GENERATION ANALYSIS - AN OVERVIEW This chapter provides an overview of current pract ices and developments i n t r i p generation a n a l y s i s . P a r t i c u l a r reference i s being made to consideration and l i m i t a t i o n s i n using the mult ip le regression technique. 2.1 T r i p Generation In The Transportation Planning Process Decisions on transportat ion f a c i l i t i e s i n urban areas are made everyday. Each decis ion has complex i m p l i c a t i o n s . f o r the ent i re urban community. To a i d i n making these decisions, , e f fec t ive and accurate forecasts of t r a v e l demands are necessary. These forecasts are general ly made w i t h i n the framework of an urban transportat ion study which i s a systematic process serving as a basis on which to p l a n , design and evaluate transportat ion systems. The transportat ion planning process i s general ly considered to consist of the f o l l o w i n g : population and economic s tudies , land use s tudies , t r i p generation, t r i p d i s t r i b u t i o n , modal s p l i t , t r a f f i c assignment and system < evaluation.\"*\" 22 Trip generation is the term commonly used to denote the study of amounts of person and vehicular t rave l . This phase i s intended to prepare forecasts of travel demand, usually by small areas cal led t ra f f i c zones. The result i s , in essence, a spat ia l distr ibution on frequency of trip-making, defined at one end of the t r i p and s t ra t i f i ed \" 2 by the types of tr ips being made. The tradit ional linkage between land use and travel i s introduced in this phase when the number of t r ips that begin or end in a given zone can be related to the ac t iv i t i e s and socio-economic characteristics of that zone. The generated t r i p ends form the measure of ' t r i p production' and ' t r i p at tract ion' used in t r i p distr ibution and modal sp l i t models. The resulting travel patterns are then assigned to the highway or transit network in the t ra f f i c assignment stage. Many alternative plans of both land use and transportation systems can then be evaluated in the system analysis phase. It can be seen that\\ • . ' . 2.3 Approaches to Trip Generation Analysis Throughout the history of transportation planning, various techniques, each with Increasing sophistication, have been employed to 27 quantify and analyze travel patterns of urban dwellers. A l l the techniques developed are essential ly based on the assumption that people are pred ic tab le , . i . e . there i s a logical and orderly pattern such that mathematical formulae can be developed to express travel behaviour. Another important concept inherent in these procedures is that travel occurs only as the consequence of persons being unable to f u l f i l l a l l desires at a common location, I .e. when a l l functions cannot be incorporated into a single location. Different functions, 12 or land uses, which are spat ia l ly separated in i t i a te person t r i p s . A th i rd assumption is that the relationship between tr ips and land use and socio-economic variables is stable over time. Below i s a br ie f resume of the techniques used in this f i e l d : 1) Growth Factor Method It was much used prior to 1950 to obtain an estimate of the future t r i p generation of a zone. The present number of t r ips i s multiplied byVa growth factor, representing the product of the ratios between the future and the present population, car 13 density and car u t i l i z a t i o n . In essence i t i s an extra-polation technique. 2) Land Area Trip Rate Analysis Since early 1950, analyt ical techniques have been used in an attempt to quantify urban t r i p volumes in terms of the land uses associated with t r i p ends. Exist ing land uses are categorized by type of ac t iv i ty , location and intensity of use, such as res ident ia l , manufacturing, commercial, i 28 t ransportat ion, publ ic bu i ld ing and publ ic open space, e t c . T r i p rates are ca lculated r e l a t i n g observed number of t r i p s per acre of land to the land use categories . In other words, land use c l a s s i f i c a t i o n s are. used as an'end'or c l a s s i f a c t o r y v a r i a b l e . Another set of generation f igures may be obtained by r e l a t i n g the number of t r i p s to the f l o o r area . Many European studies have estimated future t r i p generation from . the number of residents and employees in the zones. This may be regarded as a spec ia l case of the land use method with only two land use categories being considered, namely r e s i d e n t i a l and employment a c t i v i t i e s . Project ions for the future are obtained by applying these t r i p generation rates per uni t of area i n a given period of time to the future land use p a t t e r n . 1 ^ 15 3) Cross C l a s s i f i c a t i o n Analysis Much of the ea r ly work on t h i s was undertaken by the Puget Sound Regional Transportation Study. I t i s a non-parametric or d i s t r i b u t i o n - f r e e technique. E s s e n t i a l l y , ' n ' number of var iables are s t r a t i f i e d in to two or more appropriate groups, creat ing an ' n ' dimensional matr ix . Observations on the dependent var iable are then a l loca ted to the various c e l l s of the matr ix , based on the values of the several independent va r i ab le s , and then averaged to obtain the t r i p rate per dwel l ing uni t with cer ta in socio-economic c h a r a c t e r i s t i c s . The fo l lowing table i s produced by t h i s technique. TABLE I TRIPS PER DWELLING UNIT CROSS-CLASSIFIED WITH HOUSEHOLD SIZE AND AUTO OWNERSHIP No. of Persons Per d . u . Average Tota l Person Trips Per d . u . No. of autos owned per d . u . 0 3 & Over Weighted Average 1 2 3 4 5 6 - 7 8 & Over 1.03 2.68 4.37 — 1.72 1.52 5.13 7.04 2.00 4.38 3.08 7.16 9.26 10.47 7.46 3.16 7.98 11.56 12.75 9.10 3.46 8.54 12.36 17.73 10.16 7.11 \\9.82 12.62 16.77 11.00 7.00 9.66 17.29 22.00 12.24 Weighted Average 1.60 6.62 10.53 13.68 6.58 Source: 1962 O.D. data by the Madison Area Transportation Study, Madison, Wisconsin. / 1 30 S i m i l a r l y , t r i p s per dwell ing uni t may be c r o s s - c l a s s i f i e d with other var iables considered by the analyst to be possible indica tors of t r a v e l demand, e . g . family income, stage i n family l i f e - c y c l e , e t c . Once the important indicators of household t r a v e l are i s o l a t e d , forecasts of dwell ing uni t s by car ownership and family s ize charac te r i s t i c s are appl ied to the base year t r i p rate matrix above. A straightforward approach would involve estimating percentages of the t o t a l future number of dwel l ing u n i t s , by zone, that are expected to f a l l in to each c e l l in the matr ix . To ta l t r i p production for a zone would then be determined by applying the appropriate t r i p rate to the number of dwel l ing uni t s and summing i n d i v i d u a l t r i p estimates. Por example, i f a zone i s expected to contain 500 dwell ing unit s i n the design year wi th 50$ having a family of three and owning one automobile, t h e i r share of the t o t a l person t r i p production estimate would be: 7.16 t r i p s / d . u . X 250 d . u . = 1,790 t r i p s The remaining 50$ of households would be apportioned among the appropriate t r i p rate c e l l s of the matrix i n a s i m i l a r way. The grand t o t a l would give the design year estimate of zonal t r i p productions. The same technique could be used for t r i p production estimates by purpose.. This method has the advantage of being able to detect c u r v i l i n e a r r e l a t i o n s h i p . Since i t need not assume normality 31 in the data, nominal and ordinal data can be handled as w e l l . The approach is somewhat tedious and more detailed than the r e l i a b i l i t y of the data or the s t a t i s t i c a l v a l i d i t y of the relationship would warrant. Moreover, the finer the s t ra t i f i ca t ion , the larger the sample required. Further, there is no simple way of measuring the amount of variation in the dependent variable explained by the independent variable under consideration. 4) Multiple Regression Analysis Multiple regression is by far the most popular technique currently employed in t r i p generation analysis . With the aid of computers, the development of t r i p generation models becomes a re la t ive ly fast 'pre-packaged' process. By this process future t r i p generation is determined from a regression equation using such explanatory variables as car density, distance from C .B .D . , res ident ia l density, income, e tc . With a proper combination of variables, i t i s often possible to develop from the survey data an expression for t r i p generation which is correlated s igni f icant ly , in a s t a t i s t i c a l sense, with the observed 16 number of t r i p s . In most applications of regression analysis, the assumptions of l inear i ty , normality and homogeneity of variance of a given set of data are accepted without s t a t i s t i c a l 17 ver i f i ca t ion . The different procedures used to develop an estimating equation are enumerated below: 32 a) Ear l ier model-builders attempted to search for independent variables that were individually correlated with the dependent variable. Multiple regression equations were then established consisting of various combinations and permeations' of these variables. Those f i n a l l y selected were more often than not those having the highest correlation coeff icient . Another method is the manual \"tear-down.\"'method where a l l variables and combinations of variables are included i n i t i a l l y and then eliminated by inspection of their simple correlation coeff icients . One of the variables in a highly correlated pair is eliminated and the regression calculations are then repeated; the F-ratios with and without the eliminated variable are compared as a check on the variable 's s ignificance. b) The former methods are now replaced by step regression. Two types of step regression programs are available. The f i r s t i s the 'build-up' method, i . e . a battery of independent variables, whether basic, complex or trans-generated, are fed into the computer which selects the variable best correlated with.the c r i t e r ion , one at a time, and adds i t to the equation, with the object of obtaining the highest R. The stepwise addition of variables / continues u n t i l the specified F-ratio of remaining variables i s no longer significant for inclus ion. 33 The second method which is less widely used is cal led the 'tear-down' method, i t successively deletes variables from an equation that at f i r s t contains a l l possible variables. The specified F rat io is the cr i ter ion used at each step for dropping out a variable. 2.4 Some Considerations in Using Multiple Regression Analysis Due to the fact that multiple regression analysis is invariably performed with the computer using prepacked programs, there is an inherent danger for the analyst to become more and more dissociated from the data he is analyzing. Consequently i t i s emphasized that the f i r s t task in analysis must be to establish a theoretical framework through conceptualization of the relationships to be investigated. Careful formulation of the problem and hypothesis enables the analyst to completely control the process, instead of leaving the job of finding relationships ent ire ly in the hands of the computer. Identifying and defining relationshipsfbetween travel demand and the urban environment not only assists in the selection of independent variables consistent with the hypothesis put foward, but also helps eliminate those associated with the dependent variable simply by chance. The use of intercorrelated independent variables should be reviewed c r i t i c a l l y prior to computation. The implication of this w i l l be dealt with at length in Chapters III and IV. / 34 Another point worthy of note is that the analyst should have an idea before-hand of the degree to which the equation produced can be expected to f i t the data. In other words, the amount of accuracy achievable by improving the multiple R and the standard error of estimate (S ) i s governed by the standard error of the mean (S- = — ) of the c r i t e r i o n . This s t a t i s t i c which indicates the sampling accuracy of the data being ' f i t t e d ' sets an upper l imit to which the analyst should attempt to improve the S of the regression equation. Por y.x S to be pushed to greater accuracy than S- i s spurious. Therefore, y.x x when S is approaching or equal to the value of S-, the regression y.x x analysis can be terminated as further 'fine tuning' only results in '18 false precis ion. When computation is completed, the models developed should be evaluated both s t a t i s t i c a l l y and ana ly t ica l ly . The former involves examining s t a t i s t i c a l measures of r e l i a b i l i t y and v a l i d i t y of the equation such as coefficient of multiple correlation and determination, standard error of estimate; , standard error of the regression coefficients and the distr ibution of residuals . Section 1.8 in Chapter I gives a detailed non-mathematical account of the meaning of these terms. Note that a l l four should be used simultaneously as each provides a measure of different aspects of the estimating equation. The t radi t ional over-emphasis on the coefficient of multiple correlation should be avoided. The satisfaction of a l l these s t a t i s t i c a l tests does not eliminate the need to evaluate the equation for reasonableness. As mentioned before, equations are l i k e l y to be v a l i d i f formulated on a reasoned 19 hypothesis . Those e x h i b i t i n g no causal or an i l l o g i c a l r e l a t i o n s h i p should be discarded i n favour of the ones with good explanatory and a n a l y t i c a l powers. The supporting arguments for t h i s are : 1) Mul t ip l e regression models are e s s e n t i a l l y predic t ive i n funct ion . Therefore, they must be capable of r e f l e c t i n g both r e a l world phenomena and to specify a causal sequence among v a r i a b l e s . The very form of the equation (e .g . one un i t of change i n X w i l l cause say, two uni t s of change i n Y) d ic ta tes causa l i ty as a necessary condit ion for i t to have any v a l i d i t y . 2) Regression models assume s t a b i l i t y of r e l a t i o n s h i p over t ime. The model i s a v a l i d forecast ing t o o l only i f the r e l a t i o n -ship on which i t i s based can be shown to be s t ab le . Whether or not these parameters can be expected to exh ib i t secular s t a b i l i t y depends l a rge ly on the extent to which the model includes s t r u c t u r a l r e l a t i o n s h i p s . 2 ^ Put in another way, the re la t ionsh ips are more l i k e l y to be stable i f the var iables cover those basic motivating factors of urban t r a v e l that are not l i k e l y to change with time or from one c i t y to another. In the process of p red ic t ing the value of the dependent var iable i n some design year, the forecast ing of independent var i ab le s , u sua l ly from other sources, i s a p r e - r e q u i s i t e . The model should be evaluated i n terms of whether the var iables used are easy t » p ro jec t . Those / whose future estimates are not ava i lab le or cannot be forecasted should be omitted. 36 A common dilemma facing the analyst is the question of whether the improvement to the equation by adding another variable is enough to offset the additional effort in forecasting i t . This is largely a trade-off s i tuat ion. On the one hand, over-simplified models, though • operationally feasible, may be theoret ical ly so crude that they have l i t t l e v a l i d i t y . On the other hand, over-complicated models based on obscure variables can be equally hazardous. What strategy to adopt w i l l have to be resolved on an individual basis, although i t i s often advisable to choose somewhere between the two extremes. 37 Footnotes . ^Christopher R. Fleet and Sydney R. Robertson, 'T r ip Generation i n The Transportation Planning Process\", Highway Research Record, No. 240 (1968), p.12. 2 I b i d . 3 U . S. Department of Transportation/Federal Highway Adminis tra t ion, Bureau of Publ ic Roads: Guideline for T r i p Generation Ana lys i s , (June 1967), P.4. ^Loc. c i t . , p .8. 5 S . T . V/ong, \"A Mul t ivar i a te Analysis of Urban Travel Behaviour i n Chicago\", Transportation Research, Volume 3 (1969), p.36. M. A . Taylor , Studies of Travel i n Gloucester, Northampton and Reading, Road Research Laboratory Report, LR l 4 l , (Mini s t ry of Transport, Great B r i t a i n , 1968), pp.153-155. K. Rask Overgaard, \"Urban Transportation Planning: T r a f f i c Es t imat ion\" T r a f f i c Quarterly ( A p r i l 1967), p.203. Q M. A . Taylor , op. c i t . , pp.153-155-^ U . S. Department of Transportation/Federal Highway Adminis tra t ion, Bureau of Publ ic Roads, op. c i t . , p.17. 1 0 W . L . Mertz, \"A Study of T r a f f i c Charac ter i s t i c s i n Suburban Res ident i a l Areas\" , Publ ic Roads, Volume 29 (August 1957), p.210. ^''\"Herbert S. Levlnson and F. Houston Wynn, \"Some Aspects of Future Transportation i n Urban Areas\" , Highway Research Board B u l l e t i n , No. 326 (1962), p.16. 12 Louis E . Keefer, P i t t sburg Transportation Research Letter , Volumes 2-4 (May I960), pp.12-13. 13 K. Rask Overgaard, op. c i t . , p.201. / • . , 38 14 U. S. Department of Transportation/Federal Highway Adminis tra t ion, Bureau of Publ ic Roads: op. c i t . , p . l . 1 5 I b i d , p.19. Data of Table I i s based on 1962 O.D. survey data supplied by the Madison Area Transportation Study, Madison, Wisconsin. 16 K. Rask Overgaard, op. c i t . , p.202. ^ W . R. J e f fe r ie s and E . C. Carter , \"S impl i f i ed Techniques for Developing Transportation Plans - T r i p Generation in Small Urban Areas\" , Highway Research Record, No. 240 (1968), p .73. 18 Christopher R. Fleet and Sydney R. Robertson, op. c i t . , p .19. ^ M . A . Taylor , op. c i t . , p . 165. 20 J . H . Niedercorn and J . F. Ka i n , \"Suburbanization of Employment and Population 1948-1975\", Highway Research Record, No. 38 (1963), p .37. 21 T. B. Deen, V/. L . Mertz and N . A. I r w i n , \"Appl icat ion of a Modal S p l i t Model to Travel Time Estimates for the Washington Area\" , Highway Research Record, No. 38 (1963), p.98. 39 CHAPTER I I I THEORETICAL EXPOSITION OP MULTICOLLINEARITY AS AN EXPLANATORY AND ANALYTICAL PROBLEM This chapter puts reward the idea that a regression model Should have three necessary a t t r i b u t e s . Within the framework of these a t t r ibutes the t h e o r e t i c a l impl icat ions of m u l t i c o l l i n e a r i t y to model-bu i ld ing i s examined. Due to the mathematical nature of the expos i t ion , a b r i e f summary i s provided i n Section 3.2 for the non-mathematical reader. Those interested i n pursuing the s t a t i s t i c a l proofs and theories .can turn to Section 3.3 for d e t a i l s . Empir ica l examples w i l l be represented i n Chapter IV . 3.1 Model At t r ibutes Before proceeding onto the v e r i f i c a t i o n of the general hypothesis, i t i s necessary to discuss the meaning of a n a l y t i c a l , explanatory and pred ic t ive power of the model. C h r i s t 1 enumerated several desirable properties which a model should possess. They are : relevance, s i m p l i c i t y , accuracy of c o e f f i c i e n t s , 40 theoretical p l au s ib i l i ty , explanatory a b i l i t y and forecasting a b i l i t y . In fact relevance and accuracy are implied in i t s explanatory and forecasting a b i l i t i e s . In sum, a model should possess three attributes explanatory, analyt ical and predictive powers. Explanatory a b i l i t y means that a model should be able to explain the behaviour of variables under examination. Consistency and relevancy are the main ingredients in this because they aim at eliminating redundant variables that do not contribute to the explana-tion of a given phenomenon, but are included only because of high correlation to the c r i t e r ion . An equation i s considered better, other 2 things being equal, the wider the range of data i t can explain. Therefore, a model i s a better explanatory model i f i t i s able to extract the pertinent underlying dimensionalities of the available data. Analytical power means that a model should be able to establish causal relationships, where possible, and enable the testing of specif i hypothesis through deductive reasoning. A model after a l l i s no more than a formal statement of the outcome of analysis by which theories can be conceptualized and formulated. v ; : , : Planning Is future-oriented, therefore, the analyst wants models that can forecast the future. The predictive a b i l i t y of a regression model i s a function of: , 41 1) I t s a b i l i t y to f i t the data (as shown by R and S ), y .x 2) I t s t h e o r e t i c a l p l a u s i b i l i t y , 3) Ease i n obtaining r e l i a b l e forecast of independent v a r i a b l e s . The p r i n c i p l e of t h e o r e t i c a l p l a u s i b i l i t y may urge the analyst to b u i l d a model based on a comprehensive theory, thus more often than not r e s u l t i n g i n a complex model. On the other hand, the las t p r i n c i p l e c a l l s for simple models. S i m p l i c i t y may re fer e i ther to the funct iona l form or the number of explanatory var iables included i n the r e l a t i o n -s h i p . Although s i m p l i c i t y i t s e l f i s a desirable feature, the model 3 must a lso be a p laus ib le one. Bearing i n mind that a complex model minimizes s p e c i f i c a t i o n error due to omission of var i ab le s , but Increases measurement e r r o r , and that a simple model does the exact 4 opposite, an optimal combination must e x i s t . I t i s poss ib le , up to a p o i n t , to gain advantage of spec i f i c a t ion without subs t an t i a l ly increasing the measurement e r r o r . Therefore, i n determining the pro ject ion impl ica t ion of the model, the analyst must scrupulously examine not merely the s t a t i s t i c a l measures appl ied to c a l i b r a t i o n , but a l so the model structure i t s e l f to discover possible inconsistencies and contrad ic t ions . I t i s possible, tha t , by reformulating a model, 2 i t s R may be lowered for the period of c a l i b r a t i o n , but that t h i s , for t h e o r e t i c a l reasons, w i l l increase the confidence i n i t s pred ic t ive 5 accuracy. 42 3.2 A Non-Mathematical Summary of the Theoret ica l Implications of M u l t i c o l l i n e a r i t y . M u l t i c o l l i n e a r i t y has the fo l lowing undesirable ef fects on the regression model: 1) C o l l i n e a r i t y causes de ter iora t ion i n the least-square estimating procedure i n the regression system. When two independent var iables are in te rcor re l a ted , one of them i s superfluous. (See Sections 4.3 and 4.4). Such redundancy i s contrary . to the properties of consistency and relevancy i n the model . construct . 2) C o l l i n e a r i t y i s a source for compounding errors of the data set , both during the sampling and forecast ing per iods . Large standard errors of the beta coe f f i c ient s u sua l ly r e s u l t . Since the values of the beta coe f f i c i ent s become extremely unstable and h igh ly susceptible to sampling e r r o r , c o n f l i c t i n g con-clusions regarding the behaviour of a var iable from d i f fe rent samples of the same population can be drawn. This i s hazardous to hypothesis t e s t i n g . This i s demonstrated e m p i r i c a l l y i n Section 4.3. 2 3) C o l l i n e a r i t y tends to make the value of R and R very unre l iab le and indeterminate. Hence, a degree of f i t obtained under t h i s • • / • ' 43 condition often amounts to f a l s e p r e c i s i o n and s e l f - d e l u s i o n . (See Section 4.4) 3.3 Problem of M u l t i c o l l i n e a r i t y - A S t a t i s t i c a l Exposition Using the three a t t r i b u t e s as c r i t e r i a f o r assessing the u t i l i t y of models, a discussion on the t h e o r e t i c a l implications underlying the problem of m u l t i c o l l i n e a r i t y i s i n order here. The following w i l l show how and why m u l t i c o l l i n e a r i t y v i o l a t e s the properties of a good model construct. 1) F i t t i n g A Line Instead of A Plane In the case of simple regression, s t a t i s t i c a l f i t t i n g of data points amounts to drawing a least-square l i n e through the s c a t t e r . For multiple regression models of 'n' v a r i a b l e s , t h i s amounts to f i t t i n g a n-dimensional regression surface to a l l the data p o i n t s . Geometrically, i n the three variable case, Y = f (X.^X^) and when X^ and X^ are not co r r e l a t e d , the-data points w i l l be widely scattered on the X^Xg plane. A 99$ e q u i p r o b a b i l i t y e l l i p s e w i l l then become a c i r c l e . The res u l t a n t regression surface w i l l be a three dimensional plane through the s c a t t e r . (See Figure 2 ) . However, when X and X 1 2 are c o r r e l a t e d , then the regression plane becomes an e l l i p s e , f l a t t e n e d i n one of i t s dimensions.; (See Figure 3). When X^ 46 and X^ are near perfectly correlated, i . e . a linear function exists between them. Therefore, Y = a + b ^ + b 2 x 2 Xj_= c + dX2 The geometric interpretation of least square f i t t i n g in this case is interesting and revealing. It means that the scatter of points in the X^X plane must l i e exclusively on the straight line X-j_ = c + dXg; the.Y value then gives r ise merely to a ver t i ca l scatter of points ( i . e . in the Y direction) above and below a single straight line in a three dimensional space. An attempt to f i t an equation to the data involves inserting a plane in a three dimensional scatter of points, but in this case, the scatter i s rea l ly only two dimensional, for the complete lack of scatter in the X-jXg plane means that a l l the sample points l i e in .a plane para l l e l to the Y-axis and which contains the l ine X^ = c + dX^. The regression plane then becomes a l i n e . (See Figure 4) Frisch termed this phenomenon as \"p-fold flattened\" regression when such clustering occurs in a n-dimensional regression surface (n ) 2). In the case quoted above, n = 3, p =.1. Therefore, the regression is \"one-fold f lattened\". It i s not a true three variable multiple regression problem but should be a two variable or simple regression problem. The variable X^ has nothing to 48 do in the l inear regression system. From the standpoint of l inear regression i t i s a superfluous var iable drawn into observation and the whole system of regression coe f f i c ient s can in fact be considered a r t i f i c i a l . The s igni f icance of t h i s l i e s in that inc lu s ion of c o l l i n e a r sets i s contrary to the properties of consistency and relevancy that are desirable i n the model construct . This i s obvious as the r e s u l t i n g model Includes redundant var iables that do not. ' e x p l a i n ' v a r i a t i o n i n the c r i t e r i o n . Moreover, t h e i r presence may preclude the inc lus ion of relevant var iables that have been overlooked. 2) Indeterminacy of Beta Coef f ic ients Usual ly Accompanied by a Large Standard Error When the corre la t ion between the independent var iables i s h igh , • the sampling error of the p a r t i a l slopes and p a r t i a l corre la t ions w i l l be quite l a rge . As a re su l t there w i l l be a number of d i f ferent combinations of regression c o e f f i c i e n t s , and hence p a r t i a l co r re l a t ions , which gives almost equal ly good f i t s to the empir ica l data . The fo l lowing example w i l l serve to 7 indicate the problem involved . Let Y = a + b_X + b^Z + e • 1 2 1 49 Suppose X and Z are per fec t ly re l a ted according to the equation X = c + dZ Putt ing in numerical values for the c o e f f i c i e n t s , for a = 6, = 5, = 3, c = 1 and d = 2, we have Y = 6 + 5X + 3Z + e (1 ) X = 1 + 2Z . . (2) (2) X 3 3X = 3 + 6z (3) (1 ) - (3) Y = 3 + 8 x - 3Z + ex ( 1 ' ) Eqn. ( 1 ' ) i s therefore mathematically the same as eqn. ( l ) . But there are obviously an i n f i n i t e l y large number of such equations that gives equal ly good f i t t i n g to the data. There-fore there i s no way of determining the coef f i c ient s uniquely . However, i f an error term e^ were to be added to eqn. (2) , a unique so lu t ion with least squares can then be obtained as eqn. (4) now i s mathematically d i s t i n c t from eqn. ( l ) : Y = 6 + 5X + 3 Z + e i * ( 1) X = 1 + 2Z + e . (2 1 ) (2') X 3 1 3X = 3 + 6Z + 3e 2 . (3') (1 ) - (3') Y = 3 + 8X - 3Z + ex - 3e . . . . . (4) But such a so lut ion w i l l not render the regression model desirable proper t ie s . This i s i n t u i t i v e l y obvious as the 50 entire estimate of parameters hinges on the error term e^ which means that with s l ight modifications of the magnitude that could easi ly be due to sampling or measurement error, one might obtain estimates which dif fer considerably from the 8 orig inal set. This may lead to erroneous conclusions about the hypotheses to be tested. Examination of the formula for standard (error of beta coefficients shows that the higher the correlation between independent variables, the greater the standard error of the coeff ic ient . 12.23 1 - R 2 1.234 m ,m 2.34 ,m ) (N - m) where m = number of variables in the equation N = number of observations R = multiple coefficient of determination:;. In the three variable case: 12.23 1.23 / 51 When variable 2 and 3 are h igh ly correlated the denominator of the equation becomes very small and hence the standard error w i l l increase considerably. When one considers the corre la t ion matrix of var iab le s , one can i n fact think of them as variances and covariances matrix for the same set o f .var i ab le s when they are standardized. The i n t e r c o r r e l a t i o n of independent var iables i s none other than t h e i r covariance. The covariance indicates the degree to which two var iables are l i k e l y to err i n the same or d i f ferent d i rec t ions because of sampling f l u c t u a t i o n s . I f covariance of two var iables i s p o s i t i v e , t h i s means that an overestimate of one w i l l lead to an overestimate of the other, and the same for underestimates. I f t h e i r covariance i s negative, the overestimate of one w i l l be accompanied by an underestimate of another, and v ice versa . I f t h e i r covariance i s near zero, then there i s no1 cor re l a t ion between the var i ab le s , the-over-estimate or. underestimate of one bears no r e f l e c t i o n on the other . The importance of t h i s concept i s that i f X^ and Xg are two corre lated var iables that have been included i n the model, 'the change i n X^ i n the sampling period i s always accompanied by the change i n X^. This being so, one could never discover the coe f f i c ient of ei ther. X^ or X^, and a l l we could t e l l i s when X^ (and hence X^) changes by one u n i t , Y u sua l ly changes, say, by 0.8 u n i t i n the same d i r e c t i o n . We could not ru le out 52 the pos s ib i l i ty that b^ (the b coefficient for X^) i s 0 and bg (the b coefficient for X^) i s 0.8, or that their beta values are respectively 0.8 and 0; or 0.4 and 0.4. This problem cannot be overcome even by taking large samples. The only recourse is Q to choose the correct model to begin with.- 7 One could argue that i f the aim is not primarily to estimate parameters in the regression equation, but instead to forecast the value of the dependent variable, then the i n a b i l i t y to determine the true separate value for beta coefficients w i l l not be problematic. The answer is both yes and no. One must realize that the whole basis for prediction is the assumption that the relationship observed between independent and dependent variables w i l l remain constant. If the joint distr ibution of the independent variables between themselves and also with the dependent variable stays the same in the forecasting period, then there i s no disadvantage in mult ico l l inear i ty . This i s , however, subject to the following qual i f icat ions; 1) That the standard error of the beta coefficient w i l l be great. This means that there is less faith in the predict ion. 2) That the high correlation may yie ld a higher multiple R than warranted. This w i l l render the estimate unrea l i s t i c . If the sampling relationship of the independent variables with the cr i ter ion is much altered during the forecasting period, 53 v a r i a t i o n of one necessitates the v a r i a t i o n of the other . Hence the predicted value w i l l have a greater margin of e r r o r . However, i f the independent var iables are not s i g n i f i c a n t l y corre la ted , the change i n the re l a t ionsh ip of one with the c r i t e r i o n need not a f fect the others . In t h i s way, the margin of error i s minimized and a more r e l i a b l e pred ic t ion can be obtained. 3) Ef fect on Mul t ip le Coeff ic ient of Determination There are two c o n f l i c t i n g ef fects that m u l t i c o l l i n e a r i t y has 2 on the mult iple R , namely: 2 a) Mul t ip le R increases as the s ize of i n t e r c o r r e l a t i o n of independent var iables decreases. 2 b) Mul t ip le R increases when the i n t e r c o r r e l a t i o n of independent var iables i s h i g h . This can be better understood by looking at the formula for mult ip le coe f f i c ient of determination i n . a three var iable case. H \\ . 2 3 .. 4 + -?3 - , . . . ( 5 ) 1 \" ' 23 „2 2 0 o r R 1.23 = r 12 •+• r l 3 , i f the i n t e r c o r r e l a t i o n of two independent var iables i s zero . . . . . (6) I f the c o r r e l a t i o n r i s zero , the t h i r d term i n the numerator o f eqn. (5) i s z e r o , which has a tendency to make R ^ 23 l a r g e r . On the other hand, there i s a d i s t i n c t gain i n having r ^ very l a rge , because of i t s r o l e In the denominator. I f r approaches 1.0, the denominator approaches z e r o . Even though 2 the numerator may become s m a l l , under these condi t ions R can 2 be qui te l a r g e . A large R i s thus obtained by having r' e i t h e r very smal l or very l a r g e . Th i s i s because i t s r o l e i n 2 the numerator on ly decreases R i n a l i n e a r manner, but i t s 2 10 r o l e i n the denominator increases R e x p o n e n t i a l l y . In order to v i s u a l i z e the e f f ec t o f i n t e r c o r r e l a t i o n of the 2 p r e d i c t o r s on mul t ip le R , Figure 5 i s p l o t t e d based on the fo l lowing t a b l e . 55 TABLE I I EXAMPLES OFfMULTIPLE CORRELATIONS IN A THREE VARIABLE PROBLEM WHEN. INTERCORRELATIONS VARY Example r i 2 r 13 r 23 R 2 1.23 R 1.23 1 0.4 0.4 0.0 0.3200 0.57 2 0.4 0.4 0.4 0.2286 0.48 3 0.4 0.4 0.9 0.1684 0.41 4 0.4 v, 0.2 0.0 0.2000 0.45 5 0.4 0.2 0.4 0.1619 0.40 6 0.4 0.2 0.9 0.2947 0.54 7 • . ' 0.4 . 0.0 0.0 0.1600 0.40 8 0.4 0.0 0.4 0.1905 .0.44 9 0.4 0.0 0.9 0.8421 0.92 Source: J . R. G u i l f o r d , \"Fundamental S t a t i s t i c s in Psychology and Education, (New York: \"McGraw H i l l I n c . , 1965), p.404.. 56 FIG. 5 GRAPH SHOWING MULTIPLE R AS A FUNCTION OF r 1.23 • 23 R 1.23 l.Or 0.8 0.6h 0.4 0.2 / / / / / / / / / (3) 0.2 0.4 0.6 0.8 1.0 k23 (1) as a function of r when r & r are the same (0.4). / 2 (2) R as a function of r when r (0.4) and r (0.2) are unequal. J- • £J 1 <£ ..•13 2 ^ 1 23 a S a fr\"10\"*'*011 °* w n e n one variable is not correlated with the dependent variable, r = 0.4, r = 0.0 1 2 . . . 1 3 . . 57 From the graph i t . can be seen that 1) When r and r are the same, increase in r w i l l 12 13 • 23 decrease multiple R . 2) When r and r „ are unequal, increase in r w i l l 12 13 2 23 decrease multiple R , up to a point, but once r 1.23 23 2 is above 0.6, then multiple R ^ ^3 increases steadily. 3) When r and r are very unequal, especially i f one 12 13 of them has no correlation with the criterion, then increase in r up to 0.24 w i l l decrease multiple 9 2 R , once above that, R increases very rapidly 1.23 1.23 towards unity. Therefore, there i s a distinct disadvantage in having correlated independent variables because i t tends to make the p value of R highly unreliable and indeterminate. By the same 2 token,a large R .obtained by having r ^ very small i s a more reliable estimate, than having r very large because of the foregoing explanation. 3.4 Conclusion The preceding attempts to show that prediction i s not independent of other model attributes. Explanatory/and analytical a b i l i t y can only be attained by a consistent and l o g i c a l model construct. Harris un-compromisingly favors the a n a l y t i c approach of t h e o r i z i n g i n model . construction, enlightened by an adequate inductive understanding 1 1 and Blalock asserts that \"understanding\" of the phenomenon under examina-12 t i o n i s the key to accurate p r e d i c t i o n . Both p o s i t i o n s are w e l l founded. v 59 Footnotes 1 C. F. Christ , Econometric Models and Methods, (New York: John Wiley & Sons Inc. , 1966), p.4. 2 Ibid, p .5. ^Walter Y. Oi and Paul W. Shouldiner, \"An Analysis of Urban Travel Demands\", (Transportation Centre, Northwestern University, 1962), p.73. \\ i l l i a m Alonso, \"Predicting Best With Imperfect Data\", Journal of the American Institute of Planners, Volume 34, No. 3. (1968), pp.248-251. ^Britton Harris , \"Quantitative Models of Urban Development: Their Role in Metropolitan Policy-Making\", Issues in Urban Economics, Edited by Harvey S. Perloff & Lowdon Wingo J r . , (Johns Hopkins Press, 1968), p.383. ^R. Fr isch, ^Correlation and Scatter in S t a t i s t i c a l Variables, (University of Oslo, 1934), p.57. 3. M. Blalock J r . , \"Correlated Inc Mul t ico l l inear i ty\" , Social Forces, Volume 42 (December 1963), pp.233-234. 8 I b i d . 9 ' C. F. Chris t , op. c i t . , p.389. ^ J . P. Guilford, Fundamental Stat i s t ics in Psychology and Education, (New York: McGraw H i l l Inc . , 1965), p.404. 11 7 H. M. Blalock J r . , \"Correlated Independent Variables: The Problem of Britton Harris , op. c i t . , p.38l. 'H. M. Blalock I960), p.274. 12 H. M. Blalock J r . , Social S ta t i s t i c s , (New York: McGraw H i l l Inc . , / 6o CHAPTER IV EMPIRICAL VERIFICATION OF HYPOTHESES 4.1 Summary of Empirical Findings This chapter verif ies the general hypothesis through the testing of three operational hypotheses. By f i r s t examining a t r ip generation model with coll inear variables (Model 1), i t i s shown that: a) Within the coll inear set, one variable is a linear trans-formation of the other and is redundant. b) The large standard error of the constant confirms that co l l inear i ty i s a; source of compounding error. . c) Simple and par t i a l correlation coefficients exhibit remark-able discrepancies in the equation. Conflicting conclusions can be reached for the relationships among variables. d) The high R of this model implies greater accuracy than jus t i f i ed by the input data. Secondly, the data is subjected to factor analysis with a view to obtaining a set of orthogonal factors. When the reinforcing effect of the coll inear variables in Model 1 i s eliminated, the R i s s igni f icant ly lowered,as in Model 2 which incorporates basically the 61 same fac tor s . C o l l i n e a r i t y makes R very unre l iab le and i t loses., much of i t s value as a s t a t i s t i c a l measure of the strength of the model. I t i s also noted that the orthogonal factors are more e f f i c i e n t in detecting the t r a f f i c - l a n d use re la t ionships i n the d i s t r i c t s than are the o r i g i n a l var iab le s , which are subject to the subtle influence of many in terac t ing f ac tor s . T h i r d l y , i t i s discovered that the omission of land use dimensions have resu l ted i n large res iduals i n Model 2 . An alternate model i s developed. I t incorporates land use factors that not only give the model a better t h e o r e t i c a l construct , but which are a lso capable of producing a good f i t of data. This f inding appears to indicate that there i s no a r t i f i c i a l d i s t i n c t i o n between a model's a n a l y t i c a l , explanatory and pred ic t ive funct ions . A l l three, i n f ac t , must go hand-in-hand i n order to produce an operational model. 4.2 Formulation of Three Operational Hypotheses This sect ion attempts to t e s t , e m p i r i c a l l y , the General .Hypothesis: \"when c o l l i n e a r i t y ex i s t s i n a regression model, explanatory and a n a l y t i c a l power are decreased, despite the. apparently good predic t ive power shown by a high mult iple cor re l a t ion c o e f f i c i e n t . \" / 62 Three operational hypotheses are formulated for this purpose, namely: H^: When co l l inear i ty exists, the true contribution of some independ-ent variables may be exaggerated, obscured or suppressed. H^: When highly correlated independent variables exist in a model, 2 the multiple R is an unreliable estimate of the true relation-: ship between the predictors and the c r i t e r ion . H^: When highly correlated independent variables are included in a model, other significant explanatory variables may be omitted due to the predominance of coll inear sets. 4.3 Validation of Hypothesis 1 To verify hypothesis 1, multiple regression analysis is applied to the t r i p generation model derived by step regression for Greater Vancouver. This w i l l henceforth be referred as Model 1. (Details of this computer output appear in Appendix E) The equation takes the form: Total Trips Generated = 338.7013 - O.65I x (Labour Force) (594.0954) (0.1574) + 2.5415 X(Dwelling Units with Car) (0.2666) - 79.4897 X(Area) (26.5996) R 2 = 0.9647, R = 0.9822, / S 1842 y.x .(The figures in parentheses denote standard errors of regression coeff icients . ) . ; 6 3 The regression analysis reveals that 9 6 $ of the variance i n \"Total T r i p s Generated\" i s explained by \"Labour Force\", \"Dwelling Units with Car\" and \"Area\". The i n t e r c o r r e l a t i o n between \"Labour Force\" and \"Dwelling Units with Car\" i s 0 . 9 7 5 , but there i s no s i g n i f i c a n t c o r r e l a t i o n between Area and the other two independent v a r i a b l e s . In view of the presence of a c o l l i n e a r set i n the model, a simple regression i s performed which indicates that the second variable i s merely a l i n e a r transformation of the f i r s t , as follows, Labour Force = 1 . 6 5 7 1 (D.U.W.C.) - 6 6 8 . 6 0 7 4 r = 0 . 9 7 5 ' The explanation i s obvious as both variables describe aggregated c h a r a c t e r i s t i c s of the household, and both are stable proportions of the s i z e of zonal inhabitants. This a n t i c i p a t e s the r e s u l t of the f a c t o r a n a l y s i s . A point.worthy of note i s that large standard error (594.095^0 of the constant ( 3 3 8 . 7 0 1 3 ) . The confidence i n t e r v a l f o r the value of the intercept at 9 5 $ l e v e l i s 3 3 8 . 7 0 1 3 ± 664.24. Therefore, the value of the constant can be anywhere between - 3 2 5 . 5 3 8 7 and 1 , 0 0 2 . 9 4 1 3 . 2 The e r r o r i s considered unusually large f o r an equation with a R of 0 . 9 6 4 7 . In f a c t i t would be of i n t e r e s t to compare the difference in r e s u l t s i f the regression l i n e i s forced through zero, i . e . with the constant eliminated. / 64 Another p o i n t o f i n t e r e s t i s that the standard e r r o r of estimate f o r 'Total T r i p s Generated\" i n t h i s model i s 1842, which i s even l e s s than the standard e r r o r of the mean of the sample. (The sample s i z e . c i s 32, and the standard d e v i a t i o n i s 9314. Therefore, S- = = x y / X 9314 = 1892). As p r e v i o u s l y p o i n t e d out i n . S e c t i o n 2.4 (p.34), */32 when the e s t i m a t i n g equation i s pushed t o greater accuracy than j u s t i f i e d by the input data, t h i s r e s u l t s i n f a l s e p r e c i s i o n . Hence 2 the v e r y high R obtained can be considered spurious because the degree of \" f i t \" i s c l o s e r t o the to l e r a n c e l i m i t s than those a s s o c i a t e d w i t h the input data. Although the difference' i n magnitude i s not b i g , i t demonstrates that t h i s phenomenon can occur by the i n c l u s i o n of • c o l l i n e a r v a r i a b l e s . A comparison of the simple and p a r t i c a l c o r r e l a t i o n c o e f f i c i e n t s of the dependent and independent v a r i a b l e s i s r e v e a l i n g . (See Table I I I ) TABLE I I I ' SIMPLE AND PARTIAL CORRELATIONS.OF MODEL 1. V a r i a b l e s Simple C o r r e l a t i o n P a r t i a l C o r r e l a t i o n Remarks r r 2 v. . r 2 Labour Force 0.9209. 0.848-1 -O.6158 0.3792 P a r t i a l r changes • s i g n * DUWC 0.9700 0.9409' 0.8744 0.7645 P a r t i a l r lower* . Area •0.0242 .0.00059 - -0.4917 0.2419 P a r t i a l r h igher* * T h e i r d i f f e r e n c e s are s i g n i f i c a n t at 0.01 l e v e l . 65 The simple correlation coefficients represent the effects of one independent variable on the dependent variable, with the effects of other variables allowed to vary at the same time. Part ia l correlation coefficients represent the effects of one independent variable on the dependent variable, holding constant the effects of other variables. The conclusion to be drawn from the simple correlation coefficients are: 1) \"Labour Force\" i s very highly correlated with \"Total Trips Generated\" in a positive direct ion. It explains about 85$ of the la t ter ' s variance. 2) \"Dwelling unit with Car\" is also very highly correlated with \"Total Trips Generated\" in a positive direct ion. It explains 9k% of the latter*s variance. (Column 3 of Table i l l ) 3) \"Area\" i s s l i ght ly correlated with \"Total Trips Generated\" in a positive d irect ion. It explains pract ica l ly nothing of the la t ter ' s variance, 'i However, when the influence of other variables is being part ia l led out, the conclusion to be drawn from the par t ia l correlation coefficients are: 1) \"Labour Force\" is moderately correlated with 'Total Trips Generated\" in a negative d irect ion. In other words, the larger the Labour Force, the fewer the tr ips generated. The explanation seems to l i e in the fact that in this set of data, \"Labour Force\" i s negatively correlated with: \"Cars per Dwelling Uni t \" , \"Population per Dwelling Uni t \" , \"Percentage of Dwelling Units with Car\", \"Time to C . B . D . \" , \"Area\" and \"Income per Dwelling U n i t \" . 66 This suggests that d i s t r i c t s with a large labour force tend to have lower car ownership, lower income per dwell ing u n i t , and fewer persons per household. These d i s t r i c t s are also close to the C.B.D. and have small areas. These charac te r i s t i c s point to d i s t r i c t s with higher density dwel l ings , lower socio-economic s tatus , s ingle person households and areas of mixed land uses. Area of mixed land uses and high density u sua l ly generates fewer vehic le t r i p s because of a v a i l a b i l i t y of employment, shopping ,1 and entertainment f a c i l i t i e s nearby. Thus, the negative, r e l a t ionsh ip between 'Tota l Trips Generated\" and \"Labour Force\" appears p l a u s i b l e . In add i t ion , \"Labour Force\" r e a l l y does not explain very much of the variance of the c r i t e r i o n - only 37.92$ as opposed to the somewhat exaggerated estimate shown by the simple cor re l a t ion c o e f f i c i e n t . The reason for the discrepancy between the simple and the p a r t i a l co r re l a t ion coe f f i c ient s i s that the strong pos i t ive r e l a t i onsh ip between \"Labour Force\" and \"Dwelling Unit wi th Cars\" , which i s p o s i t i v e l y corre lated with \"Total Trips Generated\", obscures the true negative re l a t ionsh ip c i t e d . Hence h i g h l y misleading conclusions can be drawn by examining simple cor re l a t ion coe f f i c i ent s alone in a model with c o l l l n e a r se t s . 2) Corre la t ion of \"Dwelling Units with Car\" and \"Total T r i p s ' Generated\" i s lowered when the r e i n f o r c i n g ef fect of \"Labour Force\" i s removed. 3) \"Area\" is shown to explain a much larger portion of the variance of \"Total Trips Generated\" than warranted by the simple correla-tion coeff icients . This indicates that i t s true effect on the cr i ter ion has earl ier been suppressed due to the dominance of the coll inear set. At f i r s t glance the outcome appears un-reasonable because the absolute area of a d i s t r i c t has no bearing on the number of t r ips generated. Boundaries are but arbitrary lines on the map. However, close examination reveals that the t ra f f i c d i s t r i c t s are set up in such.a way that a l l large tracts happen to be rural areas outside the City of Vancouver. Therefore, \"Area \" becomes a proxy for distance from C.B.D. and to some extent represents the degree of urbanization p of the tract . In the light of th i s , the higher par t i a l r then appears plausible . Results of the multiple regression analysis indicates that Model 1 has a few. undesirable properties: 1) It does not explain the underlying relationships among variables in their true perspective, as evidenced by the discrepancies in the simple and par t i a l correlation coeff icients . This makes the testing of hypotheses a d i f f i c u l t task. 2) The high intercorrelation of \"Labour Force\" with \"Dwelling Units with Car\" produces a 'one-fold flattened' regression.system. One of the two variables appears superfluous. , 68 3) There i s a p o s s i b i l i t y that other important dimensions that could explain t r i p generation have not been entered into the model due to the predominance of the c o l l i n e a r se t . This ana lys i s , therefore, supports Hypothesis 1 which states tha t : \"When c o l l i n e a r i t y e x i s t s , the true contr ibut ion of some independent var iables may be exaggerated, obscured or suppressed.\" Under such circumstances, i t i s d i f f i c u l t to decide from the model which are the causal factors for t r i p generation. 4.4 V a l i d a t i o n of Hypothesis 2 A. Factor Analysis In view of the above f ind ings , the set of data was subjected to factor analys i s by the p r i n c i p a l component method. Varimax ro ta t ion was employed to obtain a simple s t ruc ture . Since t r i p generation i s a function of land use and socio-economic charac te r i s t i c s of the populat ion, i t might be in te re s t ing to determine the underlying dimensions that explains i t . P r i n c i p a l component analys i s i s Ideal for handling such a problem, i t el iminates a l l redundant factors w i t h i n a set of var iables and produces and underlying set of orthogonal 2 f ac tor s . Out of a t o t a l of twenty-nine var i ab le s , factor analys i s only produces seven major f ac tor s . The loadings of var iables on the factors are c l e a r , i . e . each loads very h igh ly on one major factor alone, with no var iable loading hal f-and-hal f on two f ac tor s . A 69 diagrammatic representation of the composition of these seven major factors is shown in Figure 6 . (Detailed results of the factor analysis are shown in Appendix F ) . Factor I (Size): This factor accounts for 43$ of the variance, i t is composed of variables descriptive of the size of population. As expected, \"Labour Force\" and \"Dwelling Units with Car\" are collapsed into this factor, meaning that they in fact explain the same dimension in the data. A l l variables load posi t ively on this factor. One point of interest i s that variables for single family dwellings are picked up here whereas those for multiple family dwellings are picked up in Factor III (Density). This shows that single family dwelling variables are good approximations of the tota l population since this is the predominant North American way of l i f e . The same may not apply to c i t i e s where apartment l i v ing is more prevalent, such as in Asiat ic c i t i e s . ^ Factor II (Employment): A l l employment variables are collapsed into this dimension accounting for 25$ of the variance. These variables load posi t ively on the factor with two exceptions: \"Cars per Dwelling Uni t \" and \"Percentage of Dwelling Unit with Car\". The explanation l ies in that commercial and industr ia l areas have lower car ownership as a result of lack of res identia l uni t s . F i g . 6 COMPOSITION OF SEVEN MAJOR FACTORS OUT OF 29 VARIABLES Factor I Size Variance explained 43 fo 1. total population 2. pop. single family <1. labour force total 5.labour force,sing.fam. 7.dwelling unit, total S.sinple family d.u. 10.d.u. with car 11 .s.f'.d.u. with car 13.cars total 19. gross income 20. bus mil os Factor II Employment 25 % F. I l l Density 12 ? F. IV Income 14.car Percentage of trace: per d.u.* 3.pop. 94.7 of„ multi. farm* 22. 1 6 . f d.u. with car* 6.lab. force, m.f.* 23. total employment 9.multi.fan. d.u.* 24. employ, public 12.m.f.d.u. witli car* 25. emp. industry 29.population density* 26. emp. service 27-emp. entertainment 28.emp. density income pe r d.u. F. V F. VI Student F. VII Household Are a 4 fo Size 5 ,o 2.7/o 18.time to 17.student 15.popul. C.H.D. 4 -6 pm. per d.u. Note: * denotes negative factor loadings o 71 Factor III ( D e n s i t y ) : This f a c t o r includes a l l v a r i a b l e s f o r m u l t i p l e f a m i l y d wellings and \"Population Density\", and accounts f o r 12% of the v a r i a n c e . A l l v a r i a b l e s load n e g a t i v e l y on t h i s f a c t o r , t h i s means th a t t r a c t s with p o s i t i v e loadings on i t w i l l be low d e n s i t y areas whereas those w i t h negative loadings w i l l have higher d e n s i t i e s . Factor IV (income): This f a c t o r • i n c l u d e s only one v a r i a b l e , \"Income per D w e l l i n g U n i t \" , and accounts f o r 5/o of the v a r i a n c e . S t r a n g e l y enough \"Gross Income\" i s not p i c k e d up i n t h i s f a c t o r but i n Factor I , showing that i t i s a b e t t e r measure of s i z e than a c t u a l economic s t a t u s of the t r a c t . Factor V (Area): This f a c t o r c o n s i s t s of \"Time t o C.B.D.\" and \"Area\". The former v a r i a b l e loads p o s i t i v e l y here because the l a r g e r the a r e a l u n i t s , the longer time i t takes t o reach C.B.D. This f a c t o r accounts f o r 4$ of the v a r i a n c e . Factor VI (Student): I t i s composed of only one v a r i a b l e , \"No. of Students'' i n the d i s t r i c t at 4-6 p.m. This f a c t o r accounts f o r 3$ of the v a r i a n c e . Factor V I I (Household S i z e ) : The only v a r i a b l e that loads i n t h i s f a c t o r i s \"Population per Dw e l l i n g U n i t \" . 2.7$ of the variance i s exp l a i n e d by t h i s dimension. Three graphs have been prepared to i l l u s t r a t e the behaviour of v a r i a b l e s i n one f ac tor i n j u s t a p o s i t i o n with another . In doing so, i t i s hoped that r e l a t i o n s h i p s not otherwise revea led by mul t ip le regres s ion ana ly s i s can be d i s covered . Figures 7, 3 and 9 show loadings of v a r i a b l e s on Factor I versus Factor I I , Factor I I versus Factor I I I and Factor I I I versus Factor I V . Each arrow represents a vector for a p a r t i c u l a r v a r i a b l e i n a two-dimensional space. The longer the arrow, the higher the l o a d i n g . V a r i a b l e s c o n t r i b u t i n g h e a v i l y to one f ac tor w i l l l i e close to the ax i s of that f a c t o r . The c l o s e r the vectors are to one another, the more c o l l i n e a r the v a r i a b l e s sets a r e . I f the angle between two vectors approaches 9 0 ° , the c o r r e l a t i o n between them approaches z e r o , i . e . they are independent and or thogona l . Figure 7 revea l s that va r i ab le s loading h i g h l y on Factor I load very l i t t l e on Factor I I , and v i c e v e r s a . Thi s means there i s not much employment opportuni ty i n r e s i d e n t i a l a reas . V a r i a b l e 28 (Employment Densi ty) fur ther substant iates t h i s fact because i t loads nega t ive ly on Factor I but p o s i t i v e l y on Factor I I . V a r i a b l e s 14 (Cars per Dwel l ing Uni t ) and 16 (% o f Dwel l ing Uni t wi th Car) loads nega t ive ly on Factor I I , but p o s i t i v e l y on Factor I meaning that employment areas have low car ownership but r e s i d e n t i a l areas have high car ownership. V a r i a b l e l8 (Time to C . B . D . ) loads n e g a t i v e l y on both of the two factors showing that the fur ther away from C . B . D . , the lower the populat ion and employment o p p o r t u n i t i e s . Thi s land use pat tern i s true fo r Vancouver but may not apply fo r c i t i e s such as Boston. 73 FIG. 7 LOCATION OF TIE FIHST & SECOND COMPONENT VECTORS FOR TI-D-J VARIABLES IN TtfO-DI MENS IONAL SPACE FACTOR II 14 16 74 Figure 8 shows the loading of variables on Factor II versus Factor III . Variables loading highly positive on Factor II load negatively on Factor III , meaning that in areas of high employment opportunities, there are more multiple family dwelling units . This factor manages to pick up areas of mixed land uses. Figure 9 shows the loadings of variables on Factor III versus Factor IV. Note that variables loading negatively on Factor III also load negatively on Factor IV. This implies high density areas generally have lower income. Variable 19 (Gross Income) and 29 (Population Density) load negatively on Factor III but pos i t ively on Factor IV showing that gross income diminishes with lower density although Income per Dwelling Unit may l ike ly be higher in the latter areas. If the three graphs are superimposed, there i s v i r t u a l l y no overlap in the position of component vectors in the factor space. This further confirms that the resultant factors are dist inct and uncorrelated dimensions of the data. 3. Regression on Two Factors: Size & Area Results of the factor analysis indicates that the inclusion of both \"Labour Force\" and \"Dwelling Units with Car\" in Model 1 i s s t a t i s t i c a l l y and theoret ical ly incorrect because they explain the same thing. A new regression model (Model 2) is formulated by regressing Factor I (Size) and Factor V (Area) on \"Total Trips Generated\". Now that these two factors are orthogonal, reinforcing 76 FIG. 9 LOCATION OF Till:: THIRD & FOURTH COMPONENT VECTORS FOR fill-: VARIABLES IN f.vO-DIiUiNSIOXAL SPACE FACTOR IV 25 -1.0 77 ef fec t of c o l l i n e a r sets i s e l iminated and the r e s u l t a n t estimate i s l i k e l y to be more r e a l i s t i c . Th i s can be seen i n the lack of s i g n i f i c a n t d i f ference between the simple and p a r t i a l c o r r e l a t i o n s shown i n Table IV below. The new model takes the form of : To ta l T r i p s Generated Per Day = 0.9157X(Size) - 0.0588X(Area) R 2 = 0.8275 , R = 0.9097 TABLE IV SIMPLE AND PARTIAL CORRELATIONS OF MODEL 2 Simple C o r r e l a t i o n P a r t i a l C o r r e l a t i o n Remarks r = 0.9078 12 r - -0.0431 13 r i 2 = ° ' 8 2 4 1 r 2 = 0.0016 13 r ^ - 0.9095 r = -0.1399 13.2 r 2 = 0.8272 12.3 r 2 = 0.0i95 13.2 No s i g n i -f i c a n t d i f ference between the simple and p a r t i a l ' r ' s at 0.05 l e v e l Model 1 which e s s e n t i a l l y has only the same two dimensions as 2 Model 2 y i e l d s a much higher R of 0.9647 compared wi th 0.8275 f o r the l a t t e r . The lowering of R i s s i g n i f i c a n t at 0.01 l e v e l . However, one may a.rgue that the lowering of R is not attributed to elimination of co l l inear i ty , but due to loss of information in the process of factor analysis. A table is therefore computed to find out i f this is true. TABLE V LOSS AND GAIN OF COKMUNALITIES IN MODEL 2 COMPARED WITH MODEL 1 Variables in Model 1 Factor I (Size) Factor V (Area) Comrnu -nal i t ies R Loss of Informa-tion 1 - R 4.Lahour Force 0.82 0.0025 0.8225 0.1775 10.D.U.W.C. 0.91 — 0.91 0.09 21.Area 0.015 0.866 0.881 ' 0.119 Other Variables Gain of Information* 1.Pop.Total 0.93 — 0.93 0.93 2 .Pop.S.F. 0.99 0.0006 0.9906 0.9906 5.Lab.Force S .F. 0.98 0.0008 0.9808 O.9808 7.Dwelling Unit Tota 1 0.82 — 0.82 0.82 8 .S .F .D.U. 0.99 0.001 0.991 0.991 l l . S . F . D . U . with Car 0.99 0.0016 0.9916 0.9916 13-Cars Total 0.91 0.0002 0.9102 0.9102 iS.Time to C.B.D. 0.05 0.343 0.393 0.393 19.Gross Income 0.596 0.0006 0.5966 0.5966 20.Bus Miles 0.523 0.178 0.701 0.701 * Only those with high contributions are presented. The above table shows that in fact the loss of information in Model 2 compared with Model 1 is more than compensated by the communalities contributed by other variables to the two factors in the 2 equation. Therefore, the R of 0.8275 i s a l ibera l estimate of the two dimensions that are present in Model 1. Hence Hypothesis 2 which states that \"When highly correlated 2 independent variables exist in a model, the multiple R is an unreliable estimate of the true relationship between the predictors and the 2 c r i t e r i o n \" , i s validated by comparing the R of Models 1 and 2 . The 2 significance of this finding is that the high R in Model 1 i s un-rel iable and implies a degree of f i t not warranted by the data. 4 . 5 Validation of Hypothesis 3 A. Search for Missing Factors To find out i f there are any missing dimensions in Models 1 and 2, their residuals are plotted (See Figures 10 and 11). Residuals of Model 1 gives s l ight ly better f i t of the data than Model 2 (See Appendices E and G for residual values). This Is attributable to the high R in the former. Both models give poor estimate of Di s t r i c t 3 (Point Grey) and 30 (North Surrey). In addition, while residuals for Dis t r ic t s 13 (North Vancouver City) and 29 (Newton) are re l a t ive ly large for Model 1, the same applies to Dis t r ic t s 2 (West End), 4 (Kitsilano, Fairview and Shaughnessy), 8 (South Vancouver) and l o (New Westminster) for Model 2 . 8 o P I G . 10 O B S E R V E D & C A L C U L A T E D V A L U E O F Y F O R MQDETJ 1 ( STANDARDIZED V A R I A B L E S ) A Y 8l PIG. 11 OBSERVED & CALCULATED VALU1J OF Y FOR MODEL 2 A Y T2.5 (STANDARDIZED VARIABIJ;S) o 8 o 3 • 82 The residuals for Model 2 are again plotted on a map (See Figure 12). Their distr ibution reveals an interesting pattern. The west side of Vancouver City (West of Cambie) and V/est Vancouver are consistently being over-estimated whereas the east and south portions of the metropolitan area are generally being underestimated, excepting New VJestminster. The large positive residuals are found at Di s t r i c t 1 (C.B.D.) , Di s t r i c t 2 (West End), D i s t r i c t 3 (Point Grey), Di s t r i c t 4 (Kitsi lano, Fairview and Shaughnessy), and Di s t r i c t 16 (New Westminster). A possible explanation is that these are areas of mixed land uses; the omission of Employment and Density Factors results in an over-estimate of vehicle tr ips generated based only on the Size and Area Factors. As previously pointed out, employment opportunities and higher density within the tracts decreases the number of t r ips generated because of the ava i l ab i l i ty of jobs, shops and entertainment nearby. The largest negative residual occurs in Di s t r i c t 30 (North Surrey). One suspects that an underestimate here can be explained by the omission of the Density and Household Size Factors. F i r s t , families further away from the c i t y tend to be larger in size and hence the higher frequency in trip-making. Also, in areas of lower density, more tr ips per dwelling unit are generated because of more extensive travel requirements to satisfy employment, shopping' and entertainment needs. / FIG. 12 MAP SHOWING DISTRIBUTION OF RESIDUALS FOR MODEL 2 84 Since i t i s suspected that the inclusion of land use factors such as employment and density w i l l provide a better understanding and estimate of t r i p generation, the scores of these two factors have been mapped. (See Figures 13 and 14). The purpose i s to see whether t h e i r factor score d i s t r i b u t i o n coincides with areas of poor estimate. A rule of thumb i n the search for additional explanatory factors Is to look for the ones with low or negative scores for areas with large positive residuals, and the opposite for areas with large negative r e s i d u a l s . By doing so i t was hoped that, the value,of the residuals of Model 2 could be minimized. 3 After detailed examination of the factor score d i s t r i b u t i o n , the following table was arrived at: TABLE VI A LIST OF POSSIBLE EXPLANATORY FACTORS OMITTED BY MODEL 2 Area of Poor Estimate Residuals Possible Explanatory Factors Factor Score D i s t r i c t 1. 0,6645 VII. VI -0.39595 0.13083 D i s t r i c t 2 O.8767., . I I I -4.20216 D i s t r i c t 3 1.0566'. I I -0.2656 2 D i s t r i c t . 4 0.8668' I I I IV -2.82124 -0.41607 D i s t r i c t 8 -O.6743.. I I I 1.00236 D i s t r i c t 16 0.6391'-- I I I -0.5523 D i s t r i c t 30 -0.5274'- VII 2.97536 FIG. 13 FACTOR SCORE DISTRIBUTION FOR. FACTOR II (EMPLOYMENT) FIG. U FACTOR SCORE DISTRIBUTION FOR FACTOR 111 (DENSITY) 87 B. Development of an Alternate Model Using the above r e s u l t s as a guide, a number of regression equations using both factors and v a r i a b l e s were t r i e d . The object was to develop an a l t e r n a t i v e model capable of incorporating causative factors of t r i p generation i n addition to meeting a l l the s t a t i s t i c a l measures of p r e d i c t i v e e f f i c i e n c y . I t was found that while models developed by using v a r i a b l e s only, In general, s a t i s f i e d the s t a t i s t i c a l t e s t s , they were incapable of explaining a wide range of data and to include the land u s e - t r a v e l r e l a t i o n s h i p s . Hence they were discarded i n favour of models developed from f a c t o r s . The following model, designated Model 3, i s considered the most s a t i s f a c t o r y one. I t shows that t r i p generation i s a p o s i t i v e function of population s i z e , i n t e n s i t y of land use a c t i v i t y (commercial, indus-t r i a l , i n s t i t u t i o n a l and school) and a negative function of density, i . e . T o t a l T r i p s Generated - 0.9904 x(Factor I - Size) V (0.0478)* + 0.2675 x(Factor I I - Employment) (0.0603) - 0.2718 X(Factor I I I - Density) (0.0462) + 0.1776 x(Factor VT - Student) (0.0447) S = 0.2489 R = 0.973 ' ' R 2 = 0.946 y.x ^Figures i n parentheses denote the . standard errors of regression c o e f f i c i e n t s . 3oth the R and S (See Figure 15 and Appendix H) are s i g n i f i c a n t y.x improvements over Model 2. Moreover, the relationship expressed i s l o g i c a l and causative. The method of using t h i s model for prediction i s i n Appendix C . Up to the present, many transportation studies have postulated that t r i p generation i s a function of land use. Despite t h i s , so far few regression models have been developed to incorporate t h i s r e l ationship i n a comprehensive manner, apart from the land-area t r i p rate method which employs-land use.as \"end\" variables. One explanation being that model-builders are content with securing a. high R using a minimum number of variables i n order to make the model operational, so that the th e o r e t i c a l structure i s s a c r i f i c e d . In using factor analysis to extract the \"hidden dimensions\" of the data, not only can a more i n t e l l i g e n t selection of factors be made, but the danger of including c o l l i n e a r variables i s also eliminated.^ Therefore, Model 3 can be considered as a step towards i n j e c t i n g a stronger s t r u c t u r a l relationship into the equation rather than being s a t i s f i e d merely with i t s a b i l i t y to f i t the data. In addition, the land use factors are not used as 'end' or exogenous variables but has become endogenous. The model i s , therefore, more dynamic and responsive to transportation-land use p o l i c y implications. FIGURE 15 OBSERVED & CALCULATED VALUE OF Y FOR MODEL 3 90 In order to predict the future t r i p generation, forecasting independent variables such as car ownership for t r a d i t i o n a l regression models has to be derived i n two steps. F i r s t l y land use a c t i v i t i e s have to be projected to the design year based upon which population estimates and hence the number of cars i n a zone can be estimated. 3y making land use factors endogenous i n Model 3, one step i n the forecasting process i s eliminated as land use projections becomes the d i r e c t input, thus minimizing some measurement errors. Despite the fact that Model 3 has more variables, i t .is believed that i t has gained s u f f i c i e n t advantage In s p e c i f i c a t i o n without introducing s i g n i f i c a n t additional measurement errors to the model. In addition, i t s better t h e o r e t i c a l base coupled with s t a t i s t i c a l e f f i c i e n c y enables us to have more confidence i n i t s predictive power. However, at t h i s stage i t i s unable to demonstrate qu a n t i t a t i v e l y the r e l a t i v e reduction or gain i n the two types of errors introduced by the added complexity of factor analysis. . I t i s f e l t that further research into t h i s issue may be of i n t e r e s t . A comparison of Mode Is 1 and 3 demonstrates that the former has indeed omitted some s i g n i f i c a n t land use explanatory variables (such as employment and density) in the estimating equation. Consequently ' Hypothesis 3 which states that 'When highly correlated variables are included i n a model, other.significant explanatory variables may be omitted due to the predominance of c o l l i n e a r set' i s validated. 91 4,6 Conclusion This chapter substantiates the theme of the preceding chapter, that mult icol l ineari ty is in fact an explanatory and analytical problem in model^construction. By rigorous s t a t i s t i c a l analysis of the empirical data collected in Vancouver, It is shown that the presence of coll inear set of variables has a number of undesirable effects on the performance of the model, such as exaggerating, obscuring and suppressing plausible relationships which make the testing of hypotheses d i f f i c u l t . In addition, one has less faith in such a model as a predictive tool because of the lack of log ica l theory in i t s construct. Through the validation of the three operational hypotheses, the general hypothesis: \"When co l l inear i ty exists in a regression model, explanatory and analyt ical powers are decreased, despite the apparently good predictive powers shown by a high multiple correlation coeff ic ient\" , can be accepted as generally applicable. Also, this \"finding bears, truth on the philosophy that even for models that are bui l t for prediction, they must also be concerned with explanation. The popularly-held view of the dichotomy between predictive and explanatory models appears fa l lacious . Another outcome of the data analysis is the development of an ' alternate model as a step towards giving t r i p generation models a more so l id theoretical framework. In this process, i t is found that the tota l tr ips generated per areal unit is a direct function of measures of population s ize , intensity and characteristics of land use in the tract , whereas socio-economic characteristics do not come Into play at the zonal l eve l . The low correlation between \"Total Trips 92 Generated\" and var iables such as \"Car Ownership per Dwelling U n i t \" (-0.0382), \"Persons per Dwelling U n i t \" (-0.1457), \"% Dwelling Unit with Car\" (-0.0393) and \"Income per Household\" (0.0697) supply ample proof of t h i s statement. Hopefully t h i s suggests Where research e f for t s should be directed in b u i l d i n g t r i p generation models at the zonal l e v e l . / 93 Footnotes 1 A. M. Voorhees, Transportation Planning and Urban Development\", Plan: Canada, Volume 4, No. 3. (1965), p.101. p Shue Tuck Wong, \"A Multivariate S t a t i s t i c a l Model for Predicting Mean Annual Flood i n New England\", Annals, Association of American Geographers, Volume 53 (1963), pp.298-311. • 3 Factor scores for seven factors are in Appendix F. 1 9h CHAPTER V TRANSPORTATION MODELS - A PERSPECTIVE VIEW 5.1 Summary of Research Findings The. foregoing investigation, -based both on s t a t i s t i c a l theory and empirical results , has shown that in formulating multiple regression models for transportation planning purposes, the use of intercorrelated predictors not only gives r ise to specification error, but also to spurious inferences and to spurious predictions. This renders the model less effective as a predictive and analytic t o o l . One of the possible ways to overcome this problem is by subjecting a l l input variables to a factor analysis to determine the underlying dimensions of the data set as well as to eliminate redundant or • confounding variables. By experimenting with t r i p generation data for Vancouver, the result i s suf f ic ient ly promising to warrant wider use in the transportation,'planning process. The more salient contributions of this approach can be summarized as: . 1) Mul t ico l l inear i ty i s eliminated.) 2) The sharp reduction of variables into smaller number of factors assist in organizing huge masses of data, into .manage-able size for further analysis . 95 3) The factors themselves form meaningful constructs that give further insight into the trip-generation-land use relat ionship. 4) The factor scores have more desirable s t a t i s t i c a l properties (e.g. greater r e l i a b i l i t y ) than those of single variables in i so la t ion . As the factors combine information from several variables, predictive accuracy tend to increase due to the gain in specif icat ion. In addition, the explanatory and analytic powers of the model are enhanced. In the land area t r ip rate analysis, i t i s shown that different land uses adequately isolate attributes which result in different t r i p generation rates. Oi and Shouldiner, however, fe l t that the absence of any s t a t i s t i c a l significance tests suggests caution in 1 accepting this assumption. This method is incapable of handling the effects of the interaction among different arrangements of land uses on the number of t r ips generated, and i t s treatment of land use as a non-quantifiable explanatory variable i s somewhat unsatisfactory. On the other hand, the regression technique thus far employed emphasizes on prediction, hence often use a simple explanatory variable, such as car ownership, in the equation. These simple regressions cannot be interpreted as neat causal relationships. The intercorrela-tions among alternative explanatory variables confound the parameter estimates. The neglect of a l l but a single explanatory variable tends to overstate i t s true effect because of \"its correlations with other 96 variables. However, even when other variables are included, the overall goodness of f i t w i l l not be appreciably improved. This gives r ise to the d i f f i cu l ty that even when the analyst wants to include more dimensions into the data, s t a t i s t i c a l test of significance wi l l .not just i fy their,*--'inclusion, although they may be va l id on 2 theoretical'grounds. As a corollary to eliminate multicollinearity> this investigation indicates that the combined factor analytic and regression solution seems capable of overcoming the p i t f a l l s of both approaches as evidenced in the result of Model 3. Unlike the t r i p rate method, land use variables are used as explanatory rather than class i f icatory variables. Interaction of different patterns of land use on t r i p generation is taken into account and tests of significance are attached to the resul t s . Secondly, the pertinent causal relationships are included and the confounding effect of correlated variables i s ironed out. A l l explanatory factors are found to be s igni f icant . This analysis shows that in an attempt to isolate causal re lat ion-ships which conform to some theoretical framework and yet satisfy s t a t i s t i c a l c r i t e r i a , the model gains additional strength as a predictive t o o l . It also demonstrates that explanation and prediction can and should be combined in the same analysis because i t yields more f r u i t f u l resul t s . The following sections w i l l place the significance of the findings into the larger framework of model-building in the transportation planning process. 9 7 5.2 U t i l i t y of Transportation Models In general, wide variation in the ava i lab i l i ty-of resources and data have led to an almost equally wide variation in the scope, . coverage and complexity of transportation studies. While a number of combinations of techniques have been t r i ed , the general cr i t ic i sm appears to be the i n a b i l i t y of transportation models to move away from 3 the turgid empiricism of data- f i t t ing . The Rand Report observed that even under the best of execution and circumstances, most transportation studies have been remarkably mechanic in.conception, especially in establishing the relationship between land use and t r i p generation. 4 W. L. Garrison also remarked that: \"I have serious reservations in my own mind with respect to the role of these models in (transportation) studies. This is because I am unable to express a theory or even provide a simple description of the choice behaviour that these models represent.\" Such shortcomings largely result from the strong emphasis on prediction of most transportation models. The transportation planner is often so engrossed with the number emerging from the model that his real objective - to find out the hows and whys of interaction between urban ac t iv i t i e s so that plans can be formulated and evaluated - tend to be lost sight of . ;. * At this juncture, a c l a r i f i ca t ion of the u t i l i t y of transportation models in the planning process is in order. Essential ly a transportation 9 8 model i s an experimental device to abstract t r a v e l demand and patterns so that the funct ion ing of the urban system can be observed by vary ing t ranspor ta t ion and land use i n p u t s . The knowledge gained w i l l form a systematic bas is whereby a l t e r n a t i v e p o l i c i e s and plans can be proposed and eva luated . To achieve t h i s g o a l , the model should be capable o f : a) P r e d i c t i n g what e f f ec t w i l l occur over time i f the e x i s t i n g s i t u a t i o n i s a l lowed to run on u n a l t e r e d . By showing what modifying e f f ec t s can be produced by a p a r t i c u l a r d e c i s i o n or p o l i c y or by a new arrangement of the elements a f f e c t i n g movement, i t enables us to judge between a l t e r n a t i v e s i n the l i g h t of t h e i r future consequences. In order to p r e d i c t , one of two kinds o f knowledge i s needed. We may understand the dynamics of an event , which are the theor ie s that descr ibe how i t changes. Together wi th the i n i t i a l c o n d i -t i o n s , a knowledge of the dynamics i s s u f f i c i e n t to determine the f u t u r e . T h i s approach c a l l s h e a v i l y on the p l a n n e r ' s a b i l i t y to understand urban development and to systematize h i s knowledge. A second avenue i s to p ro j ec t from past events . In t h i s case, due to the lack of a theory , the e n t i r e p r e d i c t i o n r e s t s on the q u a l i t y of our knowledge of the pas t , thus making a s c r u t i n y of t h i s q u a l i t y an important matter . The past must be representa t ive of the present and the future for the purpose of p r e d i c t i o n . No contingency can be covered unless i t has a l ready occurred and been recorded. This method is often questioned because the rapid change that technology and economy has brought about render many past events i rrelevant . Of the two ways, the f i r s t is favoured because f i r s t l y , i f prediction should succeed, we shal l want to say why. Part of the payoff of a good prediction is the insight i t provides into mechanism a n d ' r e l a t i o n s S e c o n d l y , i f we want to evaluate pol icy alternatives, i t i s essential that the'model can adequately \"explain\" movements as they actually occur, and that the process employed for prediction takes proper account of a l l the major factors involved in determining future movements, including land use with which planners are part icular ly 7 concerned. In addition to prediction, models are important educational and research devices. Their formulation reveals the importance Of structural interrelationships which otherwise may pass unnoticed or may not be given their due emphasis. In the construction.of a model, the analyst becomes aware of the sensitive linkages in the research scheme and he is therefore able to give attention to these areas as required. This sometimes results in re-formulation of the problem as new thoughts are generated about fundamental factors which might have gone unnoticed except 8 for their discovery in the model-building process. . / ' 100 .In t r anspor ta t ion s tud ie s , engineers and planners are concerned with the behaviour of households and business establishments i n making use of the t r anspor ta t ion system and i n making l o c a t i o n a l d e c i s i o n s . Such behaviour i s the source of t r a v e l demand. I f we understand thoroughly the whole c o n s t e l l a t i o n of dec i s ions made by i n d i v i d u a l s and f i rms , we could understand at the same time the extent to which var ious urban arrangements s a t i s f i e s t h e i r needs. Such an understanding i s v i t a l to producing plans and 9 p o l i c i e s best to serve the pub l i c i n t e r e s t . Sound a n a l y t i c models f a c i l i t a t e a n a l y s i s of the context of p o l i c y , by c l a r i f y i n g the areas w i t h i n which dec i s ions must be made, thus making pos s ib le more po inted c r i t i c i s m s of the postulates on which present p o l i c y i s based. A l s o , good explanatory and a n a l y t i c a l models are invaluable for bas ic re search , even i f they do not 10 f i n d p r a c t i c a l a p p l i c a t i o n . I t i s sometimes argued that while planners are concerned with d e c i s i o n s , design and p lanning , 'academic' researchers are concerned with explanat ion and t h e o r y - b u i l d i n g , and that these two sets of a c t i v i t i e s are ra ther d i f f e r e n t . From the above i t i s apparent that planners need a l l the knowledge suppl ied by . researchers i n order to p l a n . In fact i t i s the understanding of the planned systems which give planners techniques for p r e d i c t i o n . Indeed, i t can even be s a i d that \"understanding\" can be s u b s t i t u t e d for \" p r e d i c t i o n \" as being of more genera l • 11 a p p l i c a t i o n . 101 5.3 Implications for Model Building in the Transportation Planning Process In view of impending urban growth a d e c i s i o n to plan the arrange-ment and I n t e n s i t y of land use a c t i v i t i e s i s an important one. The t r a n s p o r t a t i o n element i s not only a prime v a r i a b l e i n the achievement of a de s i red p l a n , but i s a l so a major cost component of urban growth, a cost which depends s i g n i f i c a n t l y on the form of the land use plan i t s e l f . However, the s a t i s f a c t o r y i n t e g r a t i o n o f t r anspor ta t ion i n t o the land use plans w i l l requi re much more t e c h n i c a l expert i se and understanding than has h i t h e r t o been demonstrated. In p a r t i c u l a r , a change i n the a t t i tude towards the development and refinement of t r anspor ta t ion models i n r e l a t i o n s h i p to land use i s c a l l e d f o r . Forc ing the construct of t r anspor ta t ion models i n t o some larger view of t h e o r y - b u i l d i n g ra ther than us ing them p u r e l y for s t a t i s t i c a l p r e d i c t i o n w i l l , most l i k e l y turn out to be an advantage. 12 The l o g i c behind t h i s i s put forward most s u c c i n t l y by A l o n s o . He f e l t that i n an explanatory model, we are asking what are the r e l a t i o n s among the measured v a r i a b l e s , and whether they conform to what we would expect from var ious theor ie s and p r i o r e m p i r i c a l work. On the other hand, p r e d i c t i v e models are concerned only with the numerical product that emerges. As these numbers become v a r i a b l e s and feed in to other models, they tend to have a large s p e c i f i c a t i o n e r r o r when p r e d i c t e d for a future state of the system. From these cons idera t ions , i t would seem that a model which seeks to increase our 102 understanding by asking how c e r t a i n v a r i a b l e s r e l a t e to each other i s i n a sense less subject to some of the sources of e r r o r than i d e n t i c a l models designed to p r e d i c t the fu ture . There fore , a model with a sound theory w i l l often r e s u l t i n bet ter p r e d i c t i o n , not through i t s d i r e c t use, but by shedding l i g h t on some facets of the s t ructure we are cons ider ing ; p r e d i c t i o n i t s e l f proceeds i n a fashion which he c a l l e d \" m u l l i n g o v e r \" . By the same token, for a given q u a l i t y of data , the explanatory model i s more t o l e r a n t of complexity of formulat ion than a p r e d i c t i v e model . I t i s not s u r p r i s i n g therefore to f i n d that a s i g n i f i c a n t t rend i s t ak ing p l a c e . A decade ago, models were viewed p r i m a r i l y as p r e d i c t o r s of the f u t u r e . Somewhat l a t e r , s t re s s was p laced on t h e i r use as c o n d i t i o n a l p r e d i c t o r s of the consequences o f a l t e r n a t i v e p o l i c i e s , and e f f o r t s were made to incorporate i n t o them p o l i c y v a r i a b l e s which permit such exper imentat ion. More r e c e n t l y , as experience has been gained, the p r a c t i t i o n e r s of t h i s c r a f t have tended to p l a y down the a b i l i t y of models to p r e d i c t , and to s t res s t h e i r value as educat iona l instruments which serve to b r i n g to the con-sciousness of those who make dec i s ions the complex i n t e r r e l a t i o n s among the v a r i a b l e s , i n c l u d i n g those which can be manipulated for normative 13 purposes . Thus the downgrading of the importance of the p r e d i c t i v e funct ion and the emphasis of the explanatory and a n a l y t i c a l values of 14 the model i s i n accord with the viewpoint being advanced here . Stegman, i n h i s examination of urban r e s i d e n t i a l models a s ser ted that fo r models that su f fer from inadequate t h e o r e t i c a l s t r u c t u r e s , be t ter data would not n e c e s s a r i l y improve performance. There fore , manipulat ing and , 1 0 3 a d j u s t i n g the parameters of equations i n order t o improve the ' f i t ' of the models t o the data w i l l not make the models b e t t e r p r e d i c t o r s . He put forward the view that p r e d i c t i v e models may be more u s e f u l i n p r o v i d i n g policy-makers w i t h a general understanding of the magnitudes, d i r e c t i o n and i n t e r a c t i o n of the f o r c e s a t p l a y i n the urban system, than i n p r o v i d i n g a c t u a l p r e d i c t i o n s . As t r a n s p o r t a t i o n models have a l r e a d y reached a high l e v e l of s o p h i s t i c a t i o n i n the d a t a - f i t t i n g aspect, the planner's f u t u r e c o n t r i b u t i o n l i e s i n the improvement of the q u a l i t y and range of data and the t h e o r e t i c a l b a s i s of the model, p a r t i c u l a r l y i n the treatment of f a c t o r s a f f e c t i n g t r a v e l demands which stem;- from l a n d use c h a r a c t e r i s t i c s . In other words, a t h e o r e t i c a l l y sound and s c i e n t i f i c approach t o system s i m u l a t i o n of t r a n s p o r t a t i o n and l a n d use i s advocated here. In a d d i t i o n , a f u r t h e r and p o t e n t i a l l y more important t r e n d suggested by W. D. Peters\"*\"-* - th a t of merging environmental s t u d i e s w i t h t r a n s p o r t a t i o n s t u d i e s - me r i t s s p e c i a l c o n s i d e r a t i o n . Combined s t u d i e s o f t h i s k i n d can have important e f f e c t i n \"humanizing\" the t r a n s p o r t study process, a p o i n t which has been s t r e s s e d r e c e n t l y from the t r a f f i c engineering side by A. M. 16 Voorhees. 5.4 Conclusion Mathematical models f o r both res e a r c h and p r e d i c t i o n have become e s t a b l i s h e d during the l a s t few years i n the plan n i n g p r o f e s s i o n , i n 104 p a r t i c u l a r i n the transportation f i e l d , as indispensable a n a l y t i c t o o l s . The value and q u a l i t y of these models are not r e a l l y given adequate a t t e n t i o n . I t has been the object: of t h i s t h e s i s to discuss some of the problems involved by using t r i p generation models as an example. I t i s demonstrated that i n using l i n e a r p r e d i c t i v e modelling techniques, such as multiple regression, the mathematical framework places severe demand on the model-builder because: i t i s associated with a h i g h l y r e s t r i c t i v e set of assumptions. I t i s , therefore, imperative that, where multiple regression models are used i n planning, t h e i r l i m i t a t i o n s and the Implications of s t a t i s t i c a l procedures are c l e a r l y understood. This study has shown that m u l t i c o l l i n e a r i t y i s an explanatory problem to model construction and hypothesis t e s t i n g . I t s s t a t i s t i c a l s i g n i f i c a n c e has also been demonstrated. I t would be meaningful to investigate i t s p r a c t i c a l s i g n i f i c a n c e i n shaping a c t u a l transportation-land use p o l i c i e s . A further objection to past uses of these models i n transporta-t i o n studies i s ' t h e i r t h e o r e t i c a l content, without which they are but extrapolation of s i g n i f i c a n t s t a t i s t i c a l r e g u l a r i t i e s . These extra-p o l a t i o n do not contribute very much to the theories of urban structure and development since they ignore the behaviour of the urban system. Moreover, the myopic concern with p r e d i c t i o n has l e d to the formulation of some questionable models. In view of the large amounts of money, time and e f f o r t i n data c o l l e c t i o n and a n a l y s i s , the b u i l d i n g of models f o r p r e d i c t i o n only i s unrewarding. In f a c t , i t i s argued that 105 the d i s t i n c t i o n between explanatory and p r e d i c t i v e a b i l i t i e s of the model i s on ly a r t i f i c i a l , not r e a l . A suggestion i s therefore made towards greater emphasis on t h e o r i z i n g i n model-construct ion to l ay f i rmer foundations upon which s t a t i s t i c a l a n a l y s i s can be based; thus moving away from the realm of t u r g i d empiricism of c u r v e - f i t t i n g prevalent i n most t r anspor ta t ion s t u d i e s . The s t a t i s t i c a l techniques used in t h i s study are l a r g e l y designed to t e s t hypotheses based on a des i re to gain a be t ter under-standing of urban t r a v e l behaviour . I t i s found that by us ing the combined f a c t o r - a n a l y t i c and regres s ion method, i t i s capable of i d e n t i f y i n g and incorpora t ing the causa l r e l a t i o n s h i p between land use and t r i p generation i n t o a s i n g l e model. I t w i l l be i n t e r e s t i n g to extend the work to modal s p l i t models which up to now has not yet e s t a b l i s h e d a w e l l - d e f i n e d set of causa l f a c t o r s . Research e f f o r t may a l so be d i r e c t e d to the e f f ec t s introduced by the f ac tor a n a l y t i c model fo r pred ic t ion\"purposes i n terms of gain and reduct ion i n measurement and s p e c i f i c a t i o n e r r o r s . Fur ther , the idea of combining t r anspor t a t ion and environmental s tudies to \"humanize\" the t r anspor ta -t i o n ' p lanning process meri t s fur ther e x p l o r a t i o n . These may w e l l be new areas fo r fur ther r e s e a r c h . 106 Footnotes 1 Walter Y. Oi and Paul W. Shouldiner, An Analysis of Urban T r a v e l Demands,(Published for the Transportation Center at Northwestern U n i v e r s i t y by Northwestern U n i v e r s i t y Press, 1962), p.47. 2 I b i d . , p.51. . '3 The Rand Corporation, Transportation for Future Communities: A Study Prospectus, (Rm-2824-7F, The Rand Corporation, Santa Monica, C a l i f o r n i a , August 10, 196l), p.11. 4 W. L. Garrison, \"Urban Transportation Planning Models i n 1975\", Journal of the American I n s t i t u t e of Planners, Volume 31, No. 2 (May 1965), p. 12. 5 \"Aaron F l e i s h e r , \"On Prediction, and Urban T r a f f l e \", ,.Papers and Proceedings of the Regional Science A s s o c i a t i o n , Volume 7 (l96l) P.45. 6 I b i d . 7 Paul Brenikov, \"Land Use/Transportation Studies — Methods and L i m i t a t i o n s \" , Report of Proceedings, Town and Country Planning Summer School, (U n i v e r s i t y of Nottingham 10-21 September 1969, published under the auspices of the Town Planning I n s t i t u t e , B r i t a i n ) , p.25. 8 Louis A. Loewenstein, \"On the Nature of A n a l y t i c Models\", Urban Studies, Volume 3, No. 2 (1966), p.113. 9 B r i t t o n H a r r i s , \"The Use of Theory i n the Simulation of Urban Phenomena' . Journal of the American I n s t i t u t e of Planners., Volume 32, No. 5 (September 1966), pp.269-270. 1 0 B r i a n L. J . Berry, \"The R e t a i l Component of the Urban Model\", Journal of the American I n s t i t u t e of Planners, Volume 31, No. 2 (May 1965), p.150. ^ A . G. Wilson, \"Models in Urban Planning, A Synoptic Review of Recent L i t e r a t u r e \" , Urban. Studies, Volume 5, No. 3 (November 1968) p.250. 1? W. Alonso, \"Predicting B t with Imperfect Data\", Journal of the American I n s t i t u t e of Planners, Volume 3.4, No. 3 (1968), p.254. 107 13 I b i d . Ik Michael A l l e n Stegman, An Ana ly s i s and Eva lua t ion of Urban R e s i d e n t i a l Models and T h e i r P o t e n t i a l Role i n C i t y P lanning , unpublished P h . D . t h e s i s , ( U n i v e r s i t y of Pennsylvania , 1966). ^ w . D. Pe ter s , \"Planning Aspects of Land Use Transporta t ion S t u d i e s \" , Journa l of the Town Planning I n s t i t u t e , Volume 55, No. 2 (February 1969), pp.59-61. 16 Paul Brenikov , op . c i t . , p . 2 7 . 10'8 BIBLIOGRAPHY Books Berry, Brian J . L. and Marble, D. 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Department of Transportation/Federal Highway Administration, Bureau of Public Roads,. Guideline for Trip Generation Analysis, (June 1967). 1 1 8 APPENDIX A A LIST OF THE VARIABLES USED IN THIS STUDY The 29 independent variables are: 1 . Population, Total 2 . Population, Single Family 3 . Population, Multiple Family 4. Labour Force, Total 5 . Labour Force, Single Family 6 . Labour Force, Multiple Family 7 . Dwelling Units, Total 8 . Single Family Dwelling Units 9 . Multiple Family Dwelling Units 1 0 . Dwelling Units with Car 1 1 . Single Family Dwelling Units With Car 1 2 . Multiple Family Dwelling Units With Car 1 3 . Cars, Total 14. Cars Per Dwelling Unit 1 5 . Population Per Dwelling Unit 16 . % of Dwelling Units With Car 1 7 . Students (4 - 6 p.m.) 1 8 . Time to C.B.D. in Minutes 1 9 . Gross Income X 1 0 ~ 5 2 0 . Bus Miles 2 1 . Area (in Acres) 2 2 . Income Per -Dwelling Unit 2 3 . Employment, Total 24. Employment: Public U t i l i t i e s , Government and Inst i tutional Services 2 5 . Employment: Industrial , Wholesale and Unclassified 2 6 . Employment: Service Industries 2 7 . Employment: Entertainment 2 8 . Employment Density Per Acre 2 9 . Population Density Per Acre The dependent variables i s : Total Trips G-nerated per day (vehicle t r ips only) . 119 APPENDIX 5 . STATISTICAL TEST OF AUTOCORRELATION OF MODEL 2 BY USING THE \"CONTIGUITY MEASURE POR k-COLOR MAPS\" TECHNIQUE NOTATION B B Jo ins : Joins with pos i t ive res iduals i n contiguous zones. W W Jo ins : Joins with negative res iduals i n contiguous zones. B W Jo ins : Joins with po s i t i ve res idual s i n cont inguity with negative r e s i d u a l s . L^ '••. Number of contiguous zones of a t y p i c a l zone k , k = 1 to N . Two zones are considered contiguous i f they had an edge and/or vertex i n common. K = t o t a l number of zones that are not common to a t y p i c a l zone k, k = 1 to N . Sum of B B Joins.= z Sum of B W Joins = y Sum of W W Joins = x , x + y + z = L Appendix B (cont'd). Page 2. ZONES 1 4 2 4 3 3 4 7 5 7 6 5 7 • .'• 6 8 7 9 4 10 3 11 7 12 2 13 3 14 5 15 6 16 5 17 8 18 2 19 5 20 .' 6 21 6 22 5 23 5 24 . . 7 25 6, 26 • 4 27 6 28 • • 5 29 6 30 4 31 2 32 4 N z \\ - 159 V 1 \\ 'V1* 3 12 3 12 2 6 6 42 0 42 4, 20 5 • . 30-6 42 3 12 2 r O 6 42 1 2 2 6 4 ' • 20 5 30 4 20 7 56 1 2 4 20 5 30 5 30 4 20 4 20 r O 42 5 30 3\" 12 5 30 4 20 5 30 3 12 1 : 2 3 :.12 1 N k=l . Appendix B ( cont 'd) . Page 3 . B 3 JOINS B W JOINS : W W JOINS 12-13 13-14 14-19 12- 2 6-14 14-25 13- 2 6-19 14-26 2-1 6-20 19-25 2- 4 6-5 19-20 1-4 1-5 19-24 3- 4 4-5 20-5 3- 7 7-8 20-24 4- 7 7-11 25-24 1-6 7-9 28-24 17-16 3_9 25-27 29-16 21-20 25-26 17-29 21-5 26-27 21-8 27-24 21-22 27-28 29-15 24-23 21-23 23-22 21-24 23-15 16-28 22-15 16-23 ' , 22-11 16-15 22-8 16- 29 8-5 17- 18 - 8-11 17-14 9-10 17-26 9-11 17-27. 10-11 17-28 11-32 17-30 . . 11-15 29-30 15-32 29-31 30-31 -'•• 29-32 .. 30-18 z = 13 y = 31 x - 31 L = z + y + x = 13 +31 + 31 =75 Let p = p r o b a b i l i t y for z q - p r o b a b i l i t y for x p + q = 100$ / p = 1 3 / ( X + Z ) = l £ = 29.5$ q - 70.5$ 122 •Appendix B (cont'd). Page 4. | i ( z ) = p 2 ( L ) *' 0.2952 x 75 •'••.=. 0.087 x 75 = 6.55 j i ( x ) - q 2 ( L ) = 0.7052 x 75 = 0.497 x 75 = 37,3 n(y) ~ 2pq (L) = 2 x 0.705 x 0.295 x 75 z 1.51 x 0.295 x 75 = 0.445 x 75 = 33.4 52{z) = p 2 L + p 3K - p 4 ( L + K ) , = 6.55 + 0.2953 (712) - 0.295 (75+ 712) = 6.55 + 0.02567 x 712 - 0.007573 x 787 = 6.55 + 18.3 - 5.96 - 18.89 52(x) = q 2 L + q 3K - g 4 (L + K) 4 r 37.3 + 0.705^ (712) - (0.705) (75 + 712) r 37.3 + 0.35 x 712 - 0.247 x 787 = ••37.3 + 249 - 194 = 92.3 52(y) = 2pqL + pqK - 4 p 2 q 2 (L +K) = 33.4 +0.445 (712) - (4 x O.087 x 0.497)(75 +712) = 33.4 + 0.445 x 712 - 4 x O.087 x 0.497 x 787 = 33.4 + 317 - 136 = 214.4 To compute theZ scores f o r the three s e t s : Zx =• 31-37.3 - -6.3 - -O.656 A/92.3 9.607 z y =31-33.4 _ _2.4 = -0.164 A/214.4 14.64 z z = 13-6.55 = 6.45 = 1.483 A/18.89 4.346 Conclusion: Since a l l of the three t e s t s t a t i s t i c s are less than I.96 at 5$ l e v e l of s i g n i f i c a n c e , i t i s concluded that the r e s i d u a l d i s t r i b u t i o n i s random, i . e . there i s no s i g n i f i -cant autocorrelation i n t h i s set of data. 123 APPENDIX'C METHOD OF USING MODEL 3 FOR PREDICTION Model 3 takes the form of Total t r ips generated = 0.9904x(Factor I) +0.2675x(Factor II) - 0.2772X(Factor III) + 0.1776x(Factor IV) . Since the independent variables in this model are in the form of factor scores;, the following steps are necessary in order to project them to some future year: 1) Project the variables that, constitute the factors in question for each t ra f f i c d i s t r i c t . Transform the variables into standard scores by using Z = x i - x , x (the mean) ando\"(standard deviation) 6 have been calculated for the previous set of data, e .g. Factor VI consists of one variable, variable \"Students\". Its present mean is 1003, and standard deviation, is 3490. Di s t r i c t 1 now has 1,600 students. An estimate of the future number of students in Di s t r i c t 1, say five years ahead, i s , for the sake of i l l u s t r a t i o n , 2,000. Transform this number into standard scores according to the formula Z = 2,000 - 1,003 =•997 3,490 37^90 ' 2) Convert the standard scores for the variables in the factors according to the formula: F l i - (a,,z + a z + . 1 1 . l i 21 2 i . . . a z ) ml mi ( i A i ) a l l i s the factor loading of variable 1 on factor 1. z l i i s the standard score of individual i on variable 1. a21 is the factor loading of variable 2 on factor 1. Z 2 i i s the standard score of individual i on variable 2. 3 ml i s the factor loading of variable m on factor 1. zmi i s the standard score of individua1 i on variable m. A i i s the eigenvalue of the factor under consideration. 124 Appendix C (cont'd). Page 2 Again, u s i n g Factor VI and D i s t r i c t .1 as an example, F*-. \" (a-,~ /-z ) ( 1 A i ) 6 l 17.6 17. V 1 • F means the f a c t o r score of Factor VI f o r D i s t r i c t 1. 61 a17 . 6 m e a n s the f a c t o r l o a d i n g of v a r i a b l e 17 (students) on .* Factor V I . z means the standard score of v a r i a b l e 15 f o r D i s t r i c t 1. .'. F = (0.64 x 997 ) ( 1 A.53) 6 1 3490 = 0.119 3) A f t e r o b t a i n i n g the scores of a l l the four f a c t o r s f o r D i s t r i c t 1 i n the model, d i r e c t s u b s t i t u t i o n of these values i n t o the equation would y i e l d the t o t a l number of t r i p s generated there f i v e years from now. / / RFS NO. 019807 UNIVERSITY OF B C COMPUTING CENTRt MTS I AN0!>9 ) JUB blARI: I b: 11:61 03-2b- /U APPENDIX E (CONTINUED) MULTIPLE REGRESSION OUTPUTS OF MODEL I (STANDARDIZED VARIABLES) > : — ^ — { $SsIGNON PLAK TIME=5M PAGES=;50 C0PlES=36 PRIO=V **LAST SIGNON WAS: 21:27:25 02-24-70 USER \"PLAK\" SIGNED ONI AT 15:11:35 ON 03-25-70 $RUN *WATFOR 5=*,S0URCE* 6=*SINK* 4=-A EXECUTION BEGINS ^COMPILE C PROGRAM TO FIND RESIDUALS' C 1 DIMENSION X( 32 t 4) , F ( 32 , 2 )j, B ARX ( 4) ,STDX(4), STDSC0(32,4) , ~~ 1 Y ( 3 2 ) , R E S Y ( 3 2 ) , Y Y ( 3 2 ) » R E SYY ( 32 ) 2 READ'S,!) ( (XI I , J) t J = l »4)» 1 = 1, 32) 3 1 FORMAT (F10.'5/3F10.3) 4 WRITE (6*4)' 5 WRITE(6,3) ( (X( I ,'J ) ,J=1,4) , 1=1,32) 6_ 4 FORMAT (' TRIPGN LABFiOR DUWC AREA 1 ) T % 6 FORMAT (2F10.7) 8 £ READ(5,3) (13 AR X ( J ) , J= 1, 4) 9 H - READ(5,3) ( S T D X ( J ) , J = l , 4 ) 10 =j|;3 FORMAT (4F10.3) 11 WRITE (6,-7) 12 7 FORMAT ('MEANS AND STANDARD DEVIATIONS') T 3 WRITE(6,8) (BARX(J),J=2,4) 14 W R I T E ( 6 „ 8 ) (STDX(J)» J=2 ,4) 15 |jf=58 FORMAT (3F10.3) 16 f : DO 20 J = 2,4 17 £ DO 2 5 1=1,32 18 ^ \" 2 5 STDSCO( U J ) = ( X ( 1 , J ) - B A R X ( J ) )/STDX( J) 1 9 ~ 2 0 CONTINUE 20 WRITE(6,9) 21 9 FORMAT ('STANDARD SCORES OF THE VARIABLES') 22 00 30 1=1,32 23 WRITE (6, 10) X( I , 1) , ( STDSCO ( I , J ) , J=2,4 ) 24 3D WRITE(4,.I0) X( I,1),(STDSCO(I , J) , J = 2,4 ) 25 10 FORMAT (4F10.3) 26 STOP 27 END 0 0 0 1 1 1 2 2 2 2 3 * 3 • 3 • 4 • 4 • 5 • 5 • 6 • 6 • 7 • 7 • 8 1 6 9 2 5 8 1 4 6 8 0 1 5 0 5 0 5 0 ' 5 0 5 0 • • » • • • • • • • * CONTROL CARDS J. . ...IN MS DC 2. STPREG 3. STPREG 4 . PARCOR 4 3 3 1 5 6 2333 333 5. END MOTE: OUTDATED *INVR* OR * H U L R E G * ROUTINES HAVE BEEN REPLACED BY THE EQUIVALENT *STPREG* CONTROL CARD NO. * INMSDC * FORMAT CARDS ( F 1 0 . 5 / 3 F 1 0 . 3 ) INPUT DATA TRIPGN LABFOR DUWC AREA 288 .0 2 8 8 0 . 864 .0 1. 229 0.1532D 0.3486D 0 .2216 0 i 0.2739D 0.1392D 0 . 1602D 05 0 . 2251D 05 05 0 . 2753D 05 .0.5 J0_OiL8JLD_CL5_ 05 0 . 3 7 4 5 0 05 05 0.1753D 05 05 Q.1471D 05 0 .11880 05 0.1995D 05 0.172 7D 05 0.2118D 05 9743 . 0 .11 U P 0 5 0 .6820 4 .895 4 .818 7.420 4 . 0 5 0 5 .480 0 .29660 8190 . .__7_7_1_7_._ 1553. 0 .15450 0 .21930 05 05 05 0 . 38210 0.5 8190 . _83_95_. 3364 . 0 .1274D 05 0.1597D 05 0.2245D 05 4809. _J>X$XL 1551. 9464. 0 .1164D 05 9 .810 15. 40 11.97 18.75 16. 01 9 .788 0.1022D 2 8 6 2 . C.J. 51.00 0 .1889D 4388 . 0.1066D 05 0 . 1272D 05 5 4 0 6 . .03 .0_U.2.8.6.D_Q5_ 05 0.1682D 05 5081 . 05 0 .1 HOD 05 0 8674. 2225 . _2_Q5J_. .11620 05 300 1 . 6910 . 21 .64 2 .073 4 .312 27.68 27 .68 4 .031 1997 . 7074. _6.1.U... 6955 . 2038. 5449 . 2 2 3 8 . 7638 . 3j55_3_._ 7 8 1 6 . 1634. 3778 . 1425. 4 9 6 5 . _3677. 2 .451 2.203 5.892 5119 . 1139 . 2530 . ' 3 .654 3 .728 3 .15 8 23 .00 1095. 29.76. 0.2145D 3807 . 6728 . 6 9 . 0 0 960 . 0 _32.5JL._ 4 6 . 0 0 706 .0 ' _2.178_._ 3 .296 2 .855 3 .397 05 0.1844D 05 6772. 7 5 0 5 . 0 .13020 05 5925. ' 6469 . 35 .83 26 . 97 51 . 09 2862 . 2864 . 32 OBSERVATIONS 31 _D_E.GRJE_E_S__D,F FRJEJLDOM 3 4 3 6 . 51 .02 NAME MEAN S . D . TRIPGN 0 .1079D 05 9 3 1 4 . CORRELATION MATRIX VARIABLE TRIPGN LABFOR 0.1178D 05 0 .10510 05 DUWC 7512 . 6185 . AREA 12.29 U.._7_Z_ LABFOR DUWC AREA TRIPGN LABFOR DUWC . -AREA 1.0000 0 .9211 0 .9700. - 0 . 0 3 6 4 1.0000 0 ._97_5_2_ • 0 . 0835 JL.OQPJL 0 .0117 1.0000 ARRAY WR ITT FN TN AR FA CONTROL CARD NO. * ST PREG * DEPENDENT VARIABLE IS TRIPGN RSQ 0.9647 F PRO B. STD ERR 0.0000 = 1841.7498 VAR CONST . LA8F0R COEFF 338.7013 -0.6510 STD ERR 594.0954 0 .1 5 74 F-RAT 10 17 .1011 FPROB. 0.0003 DUWC AREA 2.5415 -79.4897 0.2666 26.5996 90.8980 8.9304 0.0000 0.0057 NO. OBSERVED CALCULATED RESLOUAL NO. OBSERVED CALCULATED RES I DUAL 1. 2 . 3 . - 1 . 1 2 7 0 0 .48700 2 .5840 - 1 . 0 9 8 3 0 .49451 2 .4627 - 0 . 2 8 7 4 2 E - 0 1 -0 .75117E-02 0 .12125 4. 5. 6 . 7 . 8 . 9 . 1 .2210 1.7820 0 .33600 0 .56200 2 . 0 2 6 0 - 0 . 2 7 9 0 0 1.3269 2 .0342 0.296C4 0 .40358 2 .3681 - 0 . 3 50<83 - 0 . 1 0 5 9 3 -0 .2522 4 0 .39964E-01 0 .15842 - 0 . 3 4 2 0 6 0 . 71834E-01 ... - - - -.... ._ -10. 11 . 12. 13 . 14. 15. - 0 . 3 2 900 - 0 . 9 9 1 0 0 .. . 0 . 50100 1.1960 - 0 . 6 0 0 0 0 E - 0 1 - 0 . 8 5 1 0 0 - 0 . 1 9 2 3 1 - 0 . 8 8 7 7 1 0 .2 5862 0 .65623 0 .10716 - 0 . 8 2 8 6 7 - 0 . 1 3 6 6 9 - 0 ; 1 0 3 2 9 0 .24238 0 . 53977 - 0 ; 1 6 7 1 6 - 0 . 2 2 3 3 2 E - 0 1 - - - • - - — - - - • - - - .. - -16. 17 . 18,. 19 . 20 . 2 1 . 0 .46300 0 .87000 - 0 . 6 8 7 0 0 - 0 . 1 3 0 0 0 E - 0 1 -;0 .944 00 - 0 . 3 9 8 0 0 - 0 . 9 4 1 7 6 E - 0 1 0 .59127 - 0 . 5 6 2 9 8 - 0 . 8 1 3 2 1 E - 0 1 - 0 . 9 5 5 2 8 - 0 . 3 7 3 4 0 0 .55718 0 .27873 - 0 . 1 2 4 0 2 0 .68321E-01 0 .11279E-01 - 0 . 2 4 6 0 4 E - 0 1 _- . • -— - - -- - - — - ' 22. 2 3. 24 . 2 5 . 26 . 27 . - 0 . 5 0 2 0 0 ^ 0 . 4 1 1 0 0 - 0 . 9 3 9 0 0 - 0 . 5 7 3 0 0 - 1 . 1560 -1 .0400 - 0 . 5 8 4 3 1 - 0 . 4 5 3 6 1 -1 .0132 -0 .72477 - 1 . 1 7 6 2 - 0 . 8 0 5 5 4 0.82 3 06E-01 0 .42615E-01 0 .74238E-01 0 . 15177 0 .20213E-01 - 0 . 2 3 4 4 6 • - • - -i .. ... . - - . -• 28. 29. 3 0 . 3 1 . 32. - 0 . 8 3 8 0 0 1. 1450 - 0 . 7 4 9 0 0 - 0 . 4 3 6 0 0 - 0 . 8.5100 -0 .79665 0.93311 - 0 . 1 8 4 3 7 - 0 . 6 7188E-01 - 0 . 7 0268 -0. :41347E-01 0 .21189 - 0 . 5 6 4 6 3 - 0 . 3 6 8 81 - 0 . 1 4 83 2 — -- - - - - - - -END OF, CONTROL SET * STOP 0 •XECUTI.ON TERMINATED iSlGNOFF NO. 1 . 2. 3 . OBSERVED 288 .00 15318. 34857. CALCULATED 562.13 15816. 32729. RES I DUAL -274.13 -497.81 2127.5 NO. OBSERVED -\\ CALCULATED RESIDUAL / 4 . 5. 6 . 22162. 27387. 13916. 21149 . 29210. 13367. 1013.1 -1823 .1 548.51 \\ 7. 8. 9 . 16019. 29656. 8190.0 18573 . 31731. 6005.7 -2554.3 -2075.4 2184.3 10. 11. 12. 7717. 0 1553.0 15448. 10069 . 600.11 148 23. -2351 .7 952.89 624. 52 13. 14. 15. 21928. 10222. 2862.0 18745 . 12381. 2309.7 3183.0 -2158. 7 552.27 i 16. 17 . 1.8.. 15102. 18891. 4388.0 14640. 16731. 2458.2 462.12 2159.5 1929.8 19. 20 . 21. 10660. 1997.0 7074.0 10356. 2 30 8.7 7810.2 303.52 - 3 1 1 . 69 -736.20 22. 23. ..... . . 24. . 6111.0 6955.0 2038.0 5535.6 '7 970.4 1873.5 575.36 -1015.4 164.52 25. 26 . 27. 5449.0 23 .000 1095.0 4058.4 148.70 1281.1 1390.6 -125.70 -186.15 28 . 29. 30_.__ 2976.0 21454. 3807. 0 3485.9 18573 . 8844.7 -509 . 88 2880.7 -5037.7 31. 32. 6728.0 2862.0 7833.5 3151.1 -1105.5 -289 .11 CONTROL CARD NO. 3 * STPREG * ARRAY RESTORED FROM AREA 5 ARRAY WRITTEN IN AREA 6 CONTROL CARD NO. 4 * PARCOR * ARRAY RESTORED FROM AREA 6 F V 1 >ART IAL CORRELATIONS VARIABLE TRIPGN \"RIPGN 1.000 LABFOR DUWC AREA t [ I .ABFOR-0.6158 )UWC 0.8744 ^REA -0 .4917 -1 .000 0.9797 -1 .000 ' -0 .4289 0.4223 -1.000 t END OF CONTROL SET * ( E s STOP 0 iXECUTION TERMINATED RFS NO. 019808 UNIVERSITY OF B C COMPUTING CENTRE MTS(AN059) JOB START: 16:10:22 03-25-70 APPENDIX E MULTIPLE REGRESSION OUTPUTS OF MODEL I (UNSTANDARDI ZED VARIABLES) $SIGNON PLAK TIME=5M PAGES=50 C0PIES=36 PRIO=V - =**.LA.ST SIGNON WAS : 16:04:29 03-25-70 USER \"PLAK\" SIGNED ON AT 16:10:27 ON 03-25-70 :»RUN *TRIP 4=*S0URCE* EXECUTION BEGINS TR I P / 3 6 0 IMPLEMENTATION 3/18/70 21 22 23 24 25 26 0 .7280 0 .0242 0 .0697 0 . 1639 0 .189 3 0 .2396 0 .7016 0 .0562 -0 .0354 0 .2218 0 . 1925 0.3655 0 .7 000 0 .1450 0 .0 146 0 .1342 0 . 0 8 74 0.^2900 0 .2312 -0.2643 -0.1814 0.3692 0 .4244 0 .3783 0 .6846 •0 .0489 -0.1229 0 .2773 0.2608 0 .4116 0 .7302 0 .0829 •0 .0418 0 . 1585 0 . 1116 0 .3131 0 .1868 -0.2781 -0.2089 0 .345 3 0.3984 0.3598 0 .6816 0 . 0 0 9 4 -0 .0449 0 .2473 0 .2394 0 .3493 0 .7217 0 .1468 0 .0096 0 .1406 0 .1027 0 . 2783 0.2092 •0 .2632 -0 .1248 0 .3118 0 .3671 0.2852 0 .7 046 0 .0590 0 .0168 0 .1991 0 .1977 0 .3059 27 28 29 30 C O R R E L A T I O N M A T R I X 0 .0753 0 .0769 -0. 1420 0 .2309 0 .1177 0 .1111 L0I_-J.J)_62_ 0 .2318 0 .0420 0 .0 356 -0_-\\lZ6_ 0 . 0 2 9 5 0.2906 0 .2875 0 .2008 0 .1664 0 .1611 -0 .0511 0.0647 0 .0573 -0 .1590 0 .2670 0.2686 0 .1909 0 .1522 0 .1555 -0.0558 0 .7552 0 .3556 0 .0323 0.7750 0 .3928 0 .0539 0 .0459 -0._172_0 0 .0436 0 .2556 0 .2792 JD.2026 0 .845 2 0 .1041 0 .0996 -0.1187 0 .2752 VARI ABL E :i2 JL3__ :.4 1.5 :.6 12 1 .0000 0 .2489 0 .9579 0 .0319 0 .0191 13 J.JL_QOOO__ 0 . 4 7 9 4 -0.4124 -0 .5530 14 1.0000 -0 .6 118 -0. 1300 15 16 17 18 19 20 21 22 1.0000 0.5949 1 .0000 317 8 .19 2.0 i l l 22 0 .0 525 0 .2838 :0..19_7 5-0 .7880 0 .7094 0 .1729 -0 .3942 0 .2170 -0 .5575. •0 .0337 0 .3063 •0 /2979 0.8222 -0.0785 0.5 110 0 .6271 -0.1111 0 .3438 1.0000 -0.0909 0 .4903 1.0000 -0.2082 1.0000 0 .6140 0 .2714 -0.2840 0 . 8 9 4 2 0 .7 004 0 .0918 -0.0655 -0. 1871 0 .2618 -0.2742 -0 .2037 0.1005 -0.1074 -0 .2169 0 .2350 0 .3939 0 .3579 -0.0560 -0.3616 -0 .5949 0 .6541 1 .0000 0 .6075 0 .1029 1.0000 •0 .3087 1.0000 23 2 4 25 2'6 2 7 28 0 .0730 0 .1293 0 .108 5 0 .2548 0 .0424 0 .0332 -0 . 1451 0 .2691 iL^32_12_ 0 .2619 0 .2089 0 .2199 0 .0798 0.1 82 3 0 .1968 0 .3841 -0.6377 •0 .5620 0 . 1042 -0.3907 •0 .4302 0 .3557 -0 .7367 -0.6757 0. 03 34 0 .1075 0 .2180 0 .1695 -0 . 5900 -0.5675 0 .3378 0 .1252 0 .1973 0 .0202 0 .4197 0 .3714 0 .4107 - 0 . 2 4 3 4 - 0 . 2 0 6 4 0.2 800 0 .0905 0 .0718 -0.5539 -0.6471 •0 .6886 -0 .2207 -0.4228 -0.4483 -0.6264 -0.7494 •0 .7813 -0.0278 0 .1027 0.13'05 -0 .5813 -0 .5272 -0.5778 0. 1107 0 .0724 0 .0894 0 .4279 0 .3846 0 .3735 - 0 . 2 6 8 4 - 0 . 2 1 5 8 - 0 . 2 4 1 1 ^9 30 •0 .1844 0 .0183 C O R R E L A T I O N MATRIX V A R I A B L E 23 23 1 .0000 0 .1298 0 .8057 24 -0.1448 0 .1970 -0.69 36 -0.4750 -0.4389 -0.4776 -0 .7998 -0.4457 0 .0281 -0.0009 -0 .4796 -0 . 5094 -0.0967 0 .4335 0 .1840 0 .0439 - 0 . 2 3 7 9 - 0 . 3 0 2 5 25 26 27 28 29 30 24 25 26^ 27 2 3 29 - 0 . 2650 - 0 . 1 3 3 6 H3_.462.1. - 0 . 1806 -0 .1957 - 0 . 1 9 8 9 1.0000 0 .9517 J)..900_4_ 0 .9726 0 .9501 0 .8975 1.0000 0 . 7 89 3 1.0000 0 .9183 0 .8940 0 .8336 0.7970 0 .7732 0 .7001 1 .0000 0 .9690 0 .9459 1.0000 0 .9590 1.0000 30 - 0 . 0 8 6 8 0 .1041 0 .0982 0 .1050 0 .0735 0 .1818 ' * END OF CONTROL S E T * 0 .1650 1.0000 STOP 0 E X E C U T I O N T E R M I N A T E D $ S I G 32 .00 2976. 2178 . 6 0 . 0 0 2.8 5 5 9102 . 2127 . 3 .397 5710 . 8902. 51 .00\" 5182 .\" 1362. 2 0 0 . 0 3 0 2 1 . 828 .0 161 .0 3254 . 1.208 255.0 898 .0 3152. 3 .640 243.0 2 3 4 . 0 102.0 0 .8690 283 .0 19 .00 2502 . 0 .0 4 7 . 0 0 477 .0 2425 . 2 3 . 6 0 244 .0 1140. 77 . 00 9 7 . 58 2 6 8 2 . 0 .2145D 05 0.1302D 05 .._1...0.0JO_ 0.5174D 05 0 . 1275D 05 _J3_5_._83 0 .50650 05 271 .0' 6.30X.I 1084. 0 .2034D 05 6208. 0 .18440 05 1.440 1341. 0.1790D 05 3.670 2942 . 542 .0 0 .9220 1635 . 0 .1410D 05 0. 0 290 .0 0 .1356D 05 3 8 .30 173 .0 5 4 2 . 0 695 .3 1442. 3807. 5925 . 0 .2793D 05 5502. 0 .2581D 05 423 . 0 2115 . 7616 . 6772 . 1. 286 6349. 4 .710 423. 0 1.000 5925. 0 . 0 5502 . 3 1 . 00 423 .0 3 2 2 . 9 1.000 672.8.._ 6469 . 1. 000 26 .97 _0_._2_7J_6.Q_Q.5_ 6 4 6 9 . 51 . 09 7467 . 0 . 0 6 6 4 9 . 3 5 3 2 . JL73_JL 9 3 1 5 . 2842 . 595. 0 75 0 5 . 1. 091 551.0 1076. 6987 . 1620. 518 .0 3 . 180 621.0 0 .7590 1369. 241 .0 8538 . 0 .0 301 .0 131.0 8021 . 42 .00 56. 00 1035 . 5 1 7 . 0 4 6 5 . 3 531 . 0 2862 . 3436. ._1...0.0.0_ 9 7 8 9 . 3436. 3X._Q.2_ 9 7 8 9 . 0 . 0 __3563. 0 . 0 4 2 9 4 . 1796. 2864. 1.152 828. 0 2864. 2 .630 203 .0 0 . 0 0 .9220 620 .0 3 7 2 2 . 0 . 0 77 .00 3722 . 3 1 . 00 3 5 . 0 0 0 . 0 255 .0 192 .0 32 OBSERVATIONS 31 DEGREES OF FREEDOM NAME MEAN S . D . NAME MEAN S .0 . NAME MEAN S . D . 1 2 3 0.1079D 05 0. 2939D 05 0.2565D 05 9314 . 0 .24490 05 0. 2226D 05 11 12 13 7 512. 6 3 0 3 . 1209. 6185. 5381 . 1990. 21 22 23 133.8 12 .60 5885 . 129 .9 13.71 1806. 4 5 6 7 8 9 3 8 3 4 . 0.1178D 05 ^94_41_.. 2 33 8 . 8877. 709 2 . 6599 . 0 .105 ID 05 87 2 5 . 4438 . 7599 . 6 2 4 7 . 14 15 16 0.1047D 1.220 3.40 8 05 8460. 0 .2574 0 . 5529 24 25 26 9695 . 2485 . 3378 . 0 .1402D 05 3533. 4 3 1 3 . 17 18 19 0 .8661 1003 . 21 .34 0 .1253 3490 . 9 .686 27 28 29 3067 . 7 4 9 . 3 3 452 . 5611 . 1369. 0 .1070D 05 10 1783. 3210 . 20 414 .1 357.2 30 5 4 5 3 . 0 .10370 05 XORREL.AT ION MA.TR IN-VARIABLE 1 1 1.0000 _2J 0 .9478 10 1 1 1.0000 3 I 4 ! 6 7 8 0 .9147 0 .4442 .0_._9_2r>.9_ 0 .9081 0 .3960 0 .9439 0.9642 0 .4672 ..0_.J9J_Q5_ 0 .9575 0 .4162 0 .9741 1.0000 0 .2170 _o_.JL&__L 0.~9 856 0 .1621 0 . 8 89 1 1. 0000 0 .6191 1.0000 0 .2396 0.9930 0 .6216 0 .9095 0 .5800 0 .9858 1.0000 0 .1889 0 .8932 1 .0000 0 .5783 1.0000 9 10 J..1-12 13 0 .9285 0 .4278 .0...9.7JDLCL 0 .9356 0 .4 844 0 .9705 0 .9687 0 .4211 _P_._9_8jb7_ 0 .9592 0 .4725 0 .9704 0 .9935 0 .1717 _0 .9.362 0.2528 0.9800 0 .5133 0 .9044 0 .5741 0 .9751 0 .9901 0 .2319 0 .9324 0.2316 0.9688 0.4655 0 .8910 0 .6211 0 .9529 0 .9885 0 . 1911 0.9.379 0 .9838 0 .2548 0 .9353 0 .1994 0.9813 0.4654 0 .9108 0 .5952 0 .9860 0 .1770 0 .9677 0 .4183 0 .8966 0 .6400 0 .9593 1.0000 0 .2103 0 .9517 0 .9931 0 .2722 0 .9474 1 .0000 .0 .482 5 0 .1900 0 .9857 0 .4276 1.0 000. 0 . 9 502 0 .5384 0 .9877 15 16 17 18 19 _2J) -0 .0382 -0. 1457 ^.A39JL 0.4101 •0 .3300 0 .8915 -0 .1239 -0.0702 -0.0984 0 .2702 -0.3546 0 .8300 -0.0027 0 . 0 735 0 .0292 -0.4447 -0.5023 -0.4532 -0.1882 -0 .2005 -0.1770 •0 .0010 0 .0259 0.0199 -0.4424 -0 .5241 -0 .4570 -0.2120 -0.2406 -0 . 1947 -0.0235 -0.0034 0 .0005 -0 .4561 •0 .5628 •0 .4619 0 .2354 -0 .2120 0 .7431 0 .2043 -0.5895 0.5782 0 .2510 -0 .4453 0 .8264 0 .2273 -0 .2511 0 .7227 0. 1479 -0.5598 0.53 5 5 0 .3191 -0.4237 0 .8829 0 .2843 -0.2220 0 .7678 0 .2024 -0.5712 0 .5963 -0 .1049 -0.1613 l O . O S l 1 0 .3168 -0.3512 0 . 8 832 348. 0 16.01 0 . 1 0 7 5 0 05 5121 . 1302. 624 .0 2763. 432 . 0 320 .0 2 02 5 . 0 . 2 1 9 3 0 0 .11640 2 9 4 .0 0 5 05 0 . 4 9 7 9 0 0 . 1110D 9 .788 05 05 0 .4817'D 542.0' 7743 v 05 1623. 0 .1786D 9806 . 05 0.1597D 1.347 1996. 05 0.1488D 3 .760 3229 . 05 1082 . 0.8780 3770 . 0 .1326D 0 . 0 8 1 1 . 0 05 0.1218D 17.00 1003. 0 5 1083. 815 .6 5090. ) 0.1022D 8674 . 168 .0 05 0.3239D 7903. 21 .64 05 . 0 .30460 7 7 1 . 0 6 3 0 7 . \" 05 1 9 3 0 . 0 . 1214D 4 7 9 4 . 05 0 . 1272D 1.370 1424. 05 0 .11760 3.560 2398. 05 964. 0 0 . 9780 782 .0 8867. 0 . 0 190.0 8096 . 18 .00 221 .0 771 .0 437 . 1 1492 . <\\ 2862 . 2225 . 9540 . 1272. 7314. ' 9 5 3 . 0 2226 . 349 7 . 5406. 1. 002 2862 . 3 .000 2544 . 0 .7010 3178 . 0 . 0 2225 . 28 .50 9 5 3 . 0 4 9 . 2 6 6 2 . 0 0 2 .0 73 1891 . 4187 . 806 .0 3512 . 380 .0 91 .00 2022 . 4 6 1 0 . 0 . 15100 05 0.2602D 05 0.1 95 3D 05 6484 . 0.1286D 05 7625. 5240 . 9 5 3 2 . 57 20 . 3 8 1 3 . 9057. 219 .0 5720. 4 .312 3337 . 48 23.'\" 0 . 11910 0.1609D 05 05 1.250 4526. 2 .730 4 7 4 1 . 0 .9500 5120 . 0 . 0 1103 . 27 . 00 3735 . 371 .7 6030 . 0.1889D 0 .1162D 3 7 . 0 0 05 05 0 .44200 0.1071D 27 .68 05 05 0 . 4 4 1 5 D 9 0 8 . 0 57 77.\" 05 3045 . 0.1610D 8757 . 05 0.1682D 1.323 3682. 05 0 . 1592D 3 .640 3505. 05 895.0 0 .9560 1283. 0 . 12 1 70 0 . 0 2 8 7 . 0 05 0.1108D 28 .60 3 1 6 . 0 05 1090 . 530 .5 1595 . 4388 . 3001 . 0 .12240 3001 . 05 0.1224D 0 . 0 05 0 . 0 5 5 4 1 . 5081 . 1. 599 5081 . 3 .540 0 .0 0 .8670 3 4 6 3 . 0 . 0 3 4 6 3 . 38 .50 0 . 0 161 .9 1. GOO 27 . 68 6003 . 2361 . 1160 . 465 .0 586 .0 150. 0 85 . 00 4 4 1 . 0 0 .1066D 05 0 .2854D 05 0 .2582D 05 2724 . 0.1110D 05 9743. 1354. 8152 . 7 1 1 3 . 1040 . 6910. 22 6 . 0 6067. 4 .0 31 8 4 3 . 0 5 8 8 8 T 9662 . 2940 . 1 .183 725. 0 3 .500 739 .0 0 .8480 1309. 0 . 0 172 .0 17. 00 729 .0 343 .2 7070. 1997. 1425 . 6 6 . 0 0 5146. 1248 . 2 .451 4 7 4 2 . 177 .0 5018 . 4 0 4 . 0 2013 . 7 4 8 0 . 2238 . 1.310 2206 . 1951 . 3 .350 1862. 287.0 0 .9280 1990. 1536. 0 .0 1421 .__ 1359. 16 .00 3 0 5 0 . 177 .0 65 . 89 2097 . 7 0 7 4 . 4 9 6 5 . 0.1784D 3103 . 05 1 x 0 . 12 2 5D 1862 . 05 5588 . 6 7 3 2 . 7638. 1.153 4 8 1 5 . 3 .060 2823 . 0 .8510 5840 . 3500 . 3 4 1 4 . 19 .70 2427 . 227 .8 9 7 . 0 0 2 .203 5156. 4371 . 340 .0 1958 . 1836. 2 3 6 . 0 1986. 8110. 6111 . 0.J.445D_ 05 0 .140 I'D 05 4 3 9 . 0 5653. 5454. 199. 0 4119 , 3 9 0 0 . 219 .0 3677 . 114 .0 3506. 5 .892 171. 0\" 4 7 54.\" 5616 . 2 1 1 1 . 1.364 202 .0 3.510 1536. 0 .8920 310.0 0 . 0 63 .00 2 5 . 60 358 .0 146. 2 2455 . 6955 . 5 1 1 9 . 115 .0 0.1885D 4270 . 3 .654 05 0.1668D 849 . 0 5005 .\" 05 2 1 6 7 . 7019 . 6997 . 7816 . 1. 153 1644. 6657 . 3 . 100 3301 . 1159. 0 .8420 1816. 6087 . 0 . 0 2 3 6 . 0 5093 . 22 .90 1919. 9 4 4 . 0 2 3 7 . 4 5 1 6 0 . 2038 . 1139 . 460 7 . 1120. 4465 . 19 .00 142 .0 1678 . 1634. 1.300 1615. 3.160 19.00 0 .8840 1289 . 0 . 0 1256 . 17 .40 3 3 . 0 0 5 1 . 6 9 40 .00 3 .728 5502.\" 3351 . 2293 . 659 .0 252 .0 147.0 8 9 8 . 0 1236. 5449. 0.10750 05 0 .1028D 05 475 .0 3778 . 3586. 192. 0 2664. 2530 . 134 .0 2530 . 58 .00 2396. 3 .158 134. 0\" 62 95 . 3678 . 7 0 0 . 0 1.370 59 .00 4 .040 3 51 .0 0 .9500 261 .0 0 . 0 29 .00 22 . 20 222 .0 124 .5 3 4 0 5 . 23 .00 46 .00 15 .00 161 .0 f 4 6 . 0 0 3 .296 161 .0 0 . 0 5050.\" 0 . 0 ' 4 6 . 0 0 1554 . 69 .00 1. 000 0 .0 69.00 ' 3 . 500 242 .0 0 .0 1.000 1300. 46 .00 0 . 0 12 . 00 4 6 . 00 26 .40 4 7 2 . 0 0. 0 1.794 4 9 . 0 0 1095 . 706. 0 3254 . 706. 0 32 5 4 . ' 0 . 0 0 . 0 1133 . 960 .0 1.504 960 .0 4 .320 0 . 0 0.9480 7 5 3 . 0 5000. 753 .0 2 5 . 2 0 0 . 0 3 5 . 2 0 J CONTROL CARD NO. 1 * INMSDC * CRM AT CARDS 1 F 1 0 . 5 / 8 F 9 . 3 / 8 F 9 . 3 / 8 F 9 . 3 / 5 F 9 . 3 ) INPUT DATA I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 1.6 17 18 19 20 21 22 2 1 24 25 26 27 28 29 30_ 2.8.8..J0 547-2.. 1.13-2 4 3 2 0 . 2880 . 576 .0 2304. 2304. 2 8 8 . 0 2 0 1 6 . 8 6 4 . 0 245 .0 288 .0 1.229 576. 0 4555.\"' 8 6 4 . 0 0 .7469D 05 0 . 3 750 0.17610 05 2 .370 0.1812D 05 0 .3750 0.3132D 05 1600. 7634 . 2. 600 0 .6075D 05 58. 18 4 5 5 0 . 0 . 153 2D 0 .1188D 45...0LC 05 05 0.4031D 3126 . _ 0_. 6.82Q 05 0 .14370 8750 . 5900. ' 05 0 .2594D 0 . 1 2 50D 7044 . 05 05 0.2261D 0 .6560 1742 . 05 4 6 9 0 . 2 . 120 1361. 0 .17820 0 .6220 247 1 . 05 0.1906D 0 . 0 1470. 05 4376. 3 .600 0.1032D 05 0.1469D 1039. 0.5910D 0 5 05 0 .3486D 0.1995D 05 05 0.7248D 0.1692D 05 05 0 .6 415D 303 0 . 0 5 8337 . 0 .2677D 05 0.27530 1.12 8 05 0.2348D 3.060 05 4041 . 0 .8410 0 .2374D 0.1900D 05 05 0 .1944D 1 3 . 1 0 05 4 2 9 3 . 1288 . 414 .0 14.89 6735 . 0.1208D 05 5287. 1058. 3828 . 1313 . 810 .0 4860 . _0...2.2i.6D_ -0.5 0..64 85D _Q5__ 0.3682D 05 0 .2803D 05 0 .34870 05 0.1629D 05 0.1858D 05 0.2281D 05 0.1140D 05 0.1140D J35 0 .17270 190 .0 05 0 . 10 430 4 .818 05 6843 . 4536.\" 0.2574D 0.3438D 05 05 1. 128 0.10820 05 2 .840 0.11680 05 0 .7570 0.1011D 05 3000 . 1768 . 6 . 300 7 1 3 0 . 9 8 8 . 9 0 . 1345D 0 5 0 .2739D 0 .21180 4_Q_8_. 0 05 05 0.9194D 0.1779D 7 .420 05 05 0 .8 216D 3390 . 2910. ' 05 9779. 0 .2599D 0.2307D 05 05 0.3745D 0 .9700 3274 . 05 0.3186D 3. 430 0 .10590 05 05 5588 . 0 .7890 7877 . 0.2683D 0. 0 1330. 05 0.2316D 10 .40 3110 . 05 3672 . 6 2 6 . 5 2400. 0 .1392D 9743 . 05 0.4954D 8908. 05 0 .43970 835. 0 05 5562 . 0 .1197D 05 0.1753D 0.9750 05 0.1419D 4 .050 05 3338. 0 .7950 0.1225D 0 . 0 05 0 .1058D 8 .500 05 1670. 362 . 5 189 .0 4 .050 3 7 5 1 . 0.2252D 05 4085. 0.1388D 05 3248 . 1306 . 5 5 5 5 . 0 . 1222D 05 _.0.. .1.6.0.2 D. _0_5_ . 0 , 3.9880 03 0.3465D 05 5232 . 0 .1471D 05 0.1177D 05 2943. 0.1209D 05 9480. 2 6 1 3 . . 0 . 1111D 210. 0 05 9 1 5 3 . 5 .480 1961. 9294 .\" 0 .17330 0 .1134D 05 05 1.433 4257 . 3 . 300 3269. 0 .9100 3397. 0 .0 618 .0 12 .80 2 0 7 0 . 9 0 8 . 3 7275 . 0 .2966D 0.2245D 416 .0 05 05 0 .8871D 0.2164D 9 .810 05 05 0.8684D 802 .0 4738. 05 1869. 0 .3099D 0. 1291D 05 05 0.3821D 1. 170 1628. 05 0.3714D 3. 350 6458 . 05 1069. 0 .8750 3 4 2 2 . 0 .2565D 0 . 0 1404. 05 0 .24580 15 .20 1318. 05 1069. 965 .8 9040. 8190. 4 8 0 9 . 0 .2084D 4809 . 05 0 .20 840 0 . 0 05 0 .0 6590 . 8190 . 1.273 8190. 4 .030 0 .0 0 .9300 5165. 0 . 0 5165 . 2 2 . 9 0 0 . 0 302.7 106.0 15.40 848 2 v 7742 . 4148. 1164. 1885. 545 .0 503 .0 1354. 7717 . 0..24.05D. 05 0.2 360D 05 4 5 4 . 0 8395 . 8168 . 227 .0 6 807 . 6580 . 2 2 7 . 0 6 3 5 3 . 76 .00 6 1 2 6 . 11 .97 227.6 7224 8849 . 2 3 4 6 . 1. 298 495 .0 3. 520 1276. 0 .9340 476 .0 0 . 0 99 . 00 28 . 10 196 .0 3 4 9 . 9 2 001 . 1553. 1551. . 2 8- .-0.0 646 8 . 1551 . 18 .75 6468 . 0 . 0 4374 . ' 0 . 0 2 587 . 4938 . • 3364. 1.668 76 .00 3364. 4 . 170 4138 . 0 .0 1.000 3 8 9 . 0 1551 . 0 . 0 135.0 1551 . 24 . 10 2 6 3 . 0 0 . 0 48 .24 3 4 5 . 0 0.1545D 05 0.3244D 05 0 .3 070D 05 1737 . 0 .1274D 05 0.1216D 05 579.0 0 .10040 05 8884. 1159 . 9 4 6 4 . 8498 . 966 .0 0 . 1564D 05 1. 55.6 3 .230 0 .9410 0^0 19 .50 8 7 6 . 3 ) • • • • 0 • • 0 • • • 0 • • • • 1 • • • 1 • • 1 • • • 2 1 6 9 2 5 8 1 • • • • • * • • • • * • • • • • • • • * • :ONTROL :AR.DS 2 2 2 4 6 8 3 3 0 1 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 1. JNJi.SJ3_C__3_P_ 2 . END r R F S /NO. 019809 UNIVERSITY OF B C COMPUTING CENTRE APPENDIX D MTS( AN059) JOB START: 16:03:13 03-25-70 INPUT DATA AND THE CORRELATION MATRIX SSIGNCN PL08 TIME=5M PAGES=50 C0PIES=36 PRIO=V THE. ISK SPACE ALLOTTED THIS USER ID HAS BEEN EXCEEDED. **LAST SIGNON WAS: 14:53:52 03-25-70 USER \" P L 0 8 \" SIGNED ON AT 16:03:22 ON 03-25-70 $RUN *TRIP 4=*S0URCE* \"_ EXECUTION BEGINS TRIP/360 IMPLEMENTATION 3/18/70 VARIAR1.F NAMFS 1. T o t a l T r i p G e n e r a t e d _2-.-_Popu-1-a-t-i-on/---T-o-ta-l 3. P o p u l a t i o n , S i n g l e F a m i l y 4. P o p u l a t i o n , M u l t i p l e F a m i l y JL. L a b o u r F o r c e , T o t a 1 6. 7. - 8 — 9. 10. 11. L a b o u r F o r c e , S i n g l e F a m i l y L a b o u r F o r c e , M u l t i p l e F a m i l y -D-we-l-l-i-n-g—U-n-i-t-s-/—-Total S i n g l e F a m i l y D w e l l i n g U n i t s M u l t i p l e F a m i l y D w e l l i n g U n i t s D w e l l i n g U n i t s P e r C a r 12. S i n g l e D w e l 1 i n g 13. M u l t i p i e F a m i 1 y -1-4-.—Car-s-,—Total 15. C a r s , P e r D w e l l i n g 16. P o p u l a t i o n P e r U n i t s W i t h C a r D w e l 1 i n g Uni t s W i t h Car Uni t Dwe1 1i ng U n i t 17. % o f D w e l l i n g U n i t s W i t h C a r 18. S t u d e n t s (4 - 6 p.m.) 19. Time t o CBD Xn M i n u t e s -2-0^—G ross—l-neome—(-1-GvO—E—-5-)-21. Bus M i l e s 22. A r e a i n A c r e -2-3-.—Income P e r D w e l l i n g U n i t 24 25. -2-6-.-27. 28. -13-Emp&oyment, Employment: -Employment-: Employment: Employment T o t a l P u b l i c U t i l i t i e s , Government and I n s t i t u t i o n a l -l-ndus-t-r-i-a-1-,—V>/ho-l-esa-l-e-and—Unc-l-ass-i-f-i-ed — S e r v i c e I n d u s t r i e s E n t e r t a i nment S e r v i c e s Employment D e n s i t y ; P e r A c r e 30. P o p u l a t i o n D e n s i t y ^ P e r A c r e $DATA TRIPGN - 1 . 1 2 7 0 .487 2 .584 1.221 LABFOR 2880 .000 225G8.COO 27526 .000 34870 .000 OUWC 864 .000 11876.000 19948.CCO 17270.000 AREA 1.229 0 .682 4 .895 4 .818 1.782 0 . 336 0 .562 2 .026 - 0 . 2 7 9 - 0 . 329 37446 .000 17530.000 14711.000 38212.000 8190 .000 8395.COO 21183.OQO 9743 .000 11114.OCO 22446 .000 4809 .000 6353.OCO 7 .420 4 .050 5 .480 9 .810 15 .396 11 .970 - 0 . 9 9 1 0 .501 1.196 - 0 . 0 6 0 - 0 . 8 5 1 0 . 4 6 3 3364.COO 12744.000 15967 .000 12724. 000 5406 .000 12865.000 1551.000 9464 .000 11638.000 8674.OCO 2225.000 9057 .000 18 .753 16 .006 9 .788 21 .642 2 .073 4 ,312 0 .870 - 0 . 6 8 7 - 0 . 0 1 3 - 0 . 9 4 4 - 0 . 398 - 0 . 5 0 2 16817 .000 5.081. 000 11097.000 2238 .000 7638 .000 5653.COO 11623.000 3001 .000 6910.OCO 1425.000 4965 .000 3677.OQO 27 .678 27 .678 4 .031 2 .451 2 . 2 0 3 5 .892 - 0 . 4 1 1 - 0 . 9 3 9 - 0 . 5 7 3 - 1 . 1 5 6 - 1 . 0 4 0 - 0 . 8 3 8 7816 .000 1634 .000 3778 .000 69.COO 960.COO 32 54 .000 5119.000 1139.000 2530 .000 4 6 . 0 0 0 706.OCO 2178.OCO 3. 654 3 .728 3.158 3 .296 2 .855 3 .397 1. 145 - 0 . 7 4 9 - 0 . 4 3 6 - 0 . 8 5 1 MEANS AND 11779.780 18439.000 6772.COO 7505 .000 2864 .000 STANDARD 7511 .938 13018.000 5925.000 6469.OCO 3436 .000 DEVIATIONS 12 .289 3 5 . 8 2 7 26 .974 51 .086 51 .024 10509.600 6184 .680 SCORES OF - 0 . 847 1.021 1.498 2 . 197 STANDARD 1. 127 0 .487 2 .584 1.221 13.767 THE VARIABLES - 1 . 0 7 5 - 0 . 8 0 3 0 .706 - 0 . 8 4 3 2 .011 - 0 . 5 3 7 1.578 - 0 . 5 4 3 I 1.782 0 .336 0 .562 2 .026 - 0 . 2 7 9 - 0 . 3 2 9 2 .442 0 .547 0 .279 2 .515 -0.342 -0.322 2 .210 0 ,361 0 .582 2 .415 -0,437 -0,187 -0.354 -0.598 -0.495 -0.180 0 .226 -0,023 - 0 . 9 9 1 0 . 501 1.196 , - 0 . 0 6 0 - 0 . 8 5 1 ! 0 . 4 6 3 -0. 801 0 .092 0 .398 0 .090 -0.606 0 . 1 0 3 -0.964 0 .316 0 .667 0 .188 -0.855 0 .250 0 .470 0 .270 -0.182 0 . 6 7 9 -0.742 -0.579 0 .870 - 0 . 6 8 7 - 0 . 0 1 3 - 0 . 9 4 4 - 0 . 3 9 8 - 0 . 5 0 2 0 .479 -0.637 •0 .065 -0.908 -0.394 -0 .583 0 .665 -0.729 -0.097 -0.984 -0.412 -0.620 1.118 1.118 -0.600 -0.715 -0. 733 -0.465 - 0 . 4 1 1 - 0 . 3 7 7 - 0 . 3 87 - 0 . 6 2 7 - 0 . 9 3 9 - 0 . 9 6 5 - 1 . 0 3 0 - 0 . 6 2 2 - 0 . 5 7 3 - 0 . 7 6 1 - 0 . 8 0 6 - 0 . 663 - 1 . 1 5 6 - 1 . 114 - 1 . 2 0 7 - 0 . 6 5 3 - 1 . 0 4 0 - 1 . 0 3 0 - 1 . 1 0 0 - 0 . 6 8 5 - 0 . 8 3 8 - 0 . 8 1 1 - 0 . 8 6 2 - 0 . 6 4 6 1.145 0 .634 0 .890 1.710 - 0 . 7 4 9 - 0 . 4 7 6 - 0 . 2 5 7 1.067 ' - 0 . 4 3 6 -0. :407 - 0 . 1 6 9 2 .818 - 0 . 8 5 1 - 0 . 8 4 8 - 0 . 6 5 9 2 .814 C O M P I L E T I ME= 0.21 S E C E X E C U T ION T IME= 0.50 SEC,OBJECT COOE = 1824 BYTES,ARRAY AREA • 1824 BYTES,UNUSED : 98752 BYTES m O T I m • $STOP EXECUTION TERMINATED $RUN -LQAD#+;*TRI P 4--A 5-.*SOURCE* 6=*SINK* EXECUT I.ON BEGINS T R I P / 3 6 0 IMPLEMENTATION 3/L8/70 0 0 0 1 1 1 2 2 2 2 3 3 3 4 4 5 5 6 6 7 7 8 1 6 9 2 5 8 1 4 6 8 C 1 5 0 5 0 5 0 5 0 5 0 • * • • • • • * * • • • -• * • • * • • • * • » • • • * • • * • • • • * • >• CONTROL CARDS \" L. INMSDC 4 1 1 1 1 2. STPREG 3 1 1 2333 3. END NOTE: OUTDATED *INVIR* OR *MULREG* ROUTINES HAVE BEEN REPLACED BY THE EQU1V ALENI *S«PRbG* CONTROL CARD NO, INMSDC FORMAT CARDS ( 4 F 1 0 . 3 ) INPUT DATA TRIPGN L A B F O R DUWC AREA - 1 . 127 - 0 . 8470 - 1 . 0 7 5 - 0 . 8 0 3 0 0 .4870 2 .584 1.221 1.782 0 .3360 0 .5620 1.021 1.498 2 . 197 2.4 42 0 .5470 0 .2790 . 7060 2 .011 1.578 2 .210 .3610 .58 20 -0.8430 -0.5370 -0.5430 -0.3540 -0.5980 -0.4950 2 .026 •0 .2790 • 0 . 32-90 •0 .9910 0 .5010 1.196 2 .515 2 .415 -0.3420 - 0 . 4 3 7 0 -0.3220 - 0 . 1 8 7 0 -0.8010 - C . 9 6 4 0 0 .9200D-01 0 .3160 0 .3980 0 .6670 -0.1800 0.2260 •0 .23C0D-01 0.4700 0.2700 -0.1820 •0.6:0000-01 0 .9000D-01 0 .1880 0 .6790 •0 .8510 - 0 . 6 0 6 0 - 0 . 8 5 5 0 - 0 . 7 4 2 0 0 .4630 0 .1030 0 .2500 - 0 . 5 7 9 0 0 .8700 0 ,4790 0 .6650 I .118 •0 .6870 - 0 . 6 3 7 0 - 0 . 7 2 9 0 1.118 •0 .1300D-01 - 0 . 6 5 0 0 0 - 0 1 - 0 . 9 7 C 0 D - 0 1 - 0 . 6 C 0 0 •0 .9440 ^0. 3980 '0 .5020 •0 .4110 •0 .9390 -0.5730 -0.9080 -0.3940 -0.5830 • 0 . 3770 -0.9650 -0.7610 - 0 - 0 - 0 - 0 - 0 .9840 .4120 . 6 2 0 0 . 3870 1.030 .8060 -0.7150 -0.7330 -0,4650 -0.6270 -0.6220 -0.6630 - 1 . 1 5 6 - 1 . 0 4 0 -0 .8380 1. 145 -0 .7490 -0 .4360 - 1 . 1 1 4 - 1 . 0 3 0 -0 .8110 0 .6340 -0 .4760 -0 .4070 -:0 0 - 0 -:0 1.207 1.100 . 8 6 2 0 . 89C0 .2570 . 1690 •0 ,6530 -0.6850 -0,6460 1.710 1. 067 2 .818 - 0 . 8 5 1 0 - 0 . 8 4 8 0 - 0 . 6 5 9 0 32 OBSERVATIONS 31 DEGREES OF FREEDOM NAME MEAN S . D . TRIPGN-0 .3125D-04 0 .9999 2 .814 LABFOR 0 .31250-04 0 .9999 DUWC 0 .6250D-04 1.000 AREA 0 .6250D-04 1,000 CORRELATION MATRIX VARIABLE TRIPGN LABFOR DUWC AREA TRIPGN LABFOR DUWC AREA 1,0000 0 ,9211 0 .9700 - 0 . 0 3 6 6 1.0000 0 .9752 -0.0836 1.0000 0 .0115 l.COOO CONTROL CARD NO. 2 * S T P R E G * DEPENDENT VARIABLE IS TRIPGN RSQ = 0*9648 FPROB.; = 0.0000 STD ERR Y = 0.1974 VAR COEFF STD ERR F-RATIO FPROB. CONST. -0 .1064D-03 0.0349, LABFOR -0 .7354 0.1773 17.1945 0.0003 DUWC 1.68 83 0. 1767 91.2683 0.0000 AREA -0 .1175 0.0392 8.9625 0.0056 r~ \\ NO. 08SERVED CALCULATED RESIDUAL NO. OBSERVED CALCULATED RESIDUAL 1. - 1 . 1 2 7 0 - 1 . 0 9 7 9 - 0 . 2 9 1 4 4 E - 0 1 i 2 . 0 .48700 0 .54008 - 0 ; 5 3 0 8 2 E - 0 1 V 3 . 2 .5840 2 .3566 0 .22737 ) 4 . 1.2210 1.1123 0 . 10874 5 . 1. 7820 1 .'9769 - 0 . 1 9 4 9 1 6 . 0 .33600 0 .2 7739 0 .58610E-01 7 . 0 .56200 0 .8 3549 - 0 . 2 7 3 4 9 8 . 2 .0260 2 .2489 - 0 . 2 2 2 8 9 -9 . - 0 . 2 7 9 0 0 - 0 . 5 1 2 9 6 0 .23396 10 . - 0 . 3 2 9 0 0 - 0 . 7 6 3 3 1 E - 0 1 - 0 . 2 5267 1 1 . -0.9910,0 - 1 . 0 9 3 8 0 .10284 12. 0 .50100 0 .43403 0 .66970E-01 13 . 1.1960 0 .85472 0 .34128 14 . - 0 . 6 0 0 0 0 € - 0 1 0 .17134 - 0 . 2 3134 15. - 0 . 8 5 1 0 0 - 0 . 9 1 0 8 2 0 .59815E-D1 16. 0 .46300 0 .41426 0 .48740E-01 17 . 0 .87000 0 ,63 904 0 .23096 18. - 0 . 6 8 7 0 0 - 0 . 8 9 3 8 2 0 .20682 19. - 0 . 1 3 0 0 0 E - 0 1 - 0 . 4 5 5 8 1 E - 0 1 0 .32581E-01 20. - 0 . 9 4 4 0 0 - 0 . 9 C 9 7 0 - 0 . 3 4 3 0 1 E - 0 1 2 1 . - 0 . 3 9 8 0 0 - 0 . 3 1 9 8 4 -0 .78159E-O1 2 2 . - 0 . 5 0 2 0 0 - 0 . 5 6 3 5 2 0 .615156-01 2 3. - 0 . 4 1 1 0 0 - 0 . 3 0 2 5 9 - 0 . 1 0 8 4 1 2 4. - :0 .93900 - 0 . 9 5 6 3 7 0 .17372E-01 > 2 5 . - 0 . 5 7 3 0 0 - 0 . 7 2 3 3 9 0 .15039 ' 26. - 1 . 1 5 6 0 - 1 . 1 4 2 0 - 0 . 1 4 0 0 6 E - 0 1 27. -1 .0400 - 1 . 0 1 9 4 - 0 . 2 0 6 4 6 E - 0 1 i 28 . - 0 . 8 3 8 0 0 - 0 . 7 8316 - 0 . 5 4 8 4 0 E - 0 1 1 29 . 1.1450 0 .83537 0 .30963 30 . - 0 . 7 4 9 0 0 - 0 . 2 0933 - 0 . 5 3 9 6 7 3 1 . - 0 . 4 3 6 0 0 - 0 . 3 1 7 2 2 -0 .11878 3 2 . - 0 . 8 5 1 0 0 - 0 . 8 1 9 7 4 - 0 . 3 1 2 6 3 E - 0 1 I * END OF CONTROL SET * STOP 0 EXECUTION TERMINATED $ SIGNOFF RFS NO. 019810 UNIVERSITY OF B C COMPUTING CENTRE MTS» 10411 0.38458 ROW 27 0.11114 _ 0_.„033_19L -0.24105 0 .03557 0_t2198_9_ -0. 19 573 0.28751 0.07184 0.95007 0.16112 -0 .68859 0.05732 •0.44825 0.26859 0.78134 0.15553 0.13052 0.89397 0.77321 0.96904 1.00000 0.04586 -0.57782 0 .9 5903 0 .27919 0.08936 0.18176 0 .09963 0.37354 ROW 28 ROW 29 0.23183 - 0 . 10617 -0.18443 -0.23787 -0. 17758 0.12978 -0_«.1_9_8_8_8_ 0.20075 -0.14484 JL.8974'8 -0 .05111 -0.69365 0 .83357 -0.15895 -0.43887 0.70013 0.19093 -0.79977 0.94589 -0.0 55 84 0.02806 0.95903 -0.17201 -0 .47958 1.00000 0.02955 0.75517 0.35555 0.03227 0.77497 0.39276 0.04360 0.20265 -0.09667 0.16498 0 .84516 -0.11871 0.18402 0.27518 0.01832 •0.30253 EIGENVALUES 12.38673 0.80566 -0.08684 0.19696 0.10408 -0 .47498 0.09824 -0.47758 0.10495 -0.44571 0.07346 •0.00087 0.18176 -0. 50942 0.16498 0.43346 1.00000 0.04389 7.31579 3.63327 1.52941 1.23195 0.88700 0 .77393 0.45769 0.20327 0.15438 0 .13926 0.00156 0.10893 0.00086 0.06794 0.00031 0.03440 0 .00011 0.03048 0 .00008 0.01884 0.00000 0.01307 0.00000 0.00457 0.00350 0.00203 CUMULATIVE PROPORTION OF EIGENVALUES 0.42714 0.67942 0.80470 0.85744 0.89993 0.93051 0.95720 0.97298 0.97999 0.98532 0.99012 0.99388 0.99622 0.99741 0.99846 0.99911 0.99956 0.99971 0.99983 0.99990 0 .99996 0.99999 1.00000 1.00000 1.00000 1.00000 1.00000 EIGENVECTORS 0.24842 0 .21422 - 0 . 0 4 8 8 4 VECTOR 2 - 0 . 1 6 7 4 1 0 .21196 0 .20454 -0 .03894 -0 .21361 0 .20757 0 .24249 0 . 15754 0 .09524 0 .26292 •0 .12817 0 .15377 - 0 . 1 2 4 3 2 0 .21695 -0. 11785 0 . 16811 •0 .20314 0 .19594 -0.13284 0 . 13256 0 .10450 0 .26418 0.09391 0 .13454 -0.12996 0 .21924 -0.18417 0 .08027 - 0 . 2 0 8 6 7 0 . 19885 0 .23050 0 .13472 0 .09840 0 .25220 0 .20831 -0 . 16761 - 0 . 2 1 8 4 4 - 0 . 1 4 7 8 9 0 .06978 -0.12219 -0. 18263 0 .25185 -0.24919 0 .24101 -0.17669 0 .18858 -0.27251 0 .26738 -0 .03198 0.27403 - 0 . 15641 0 .31497 VECTOR 3 0 .05551 0 .14271 0 .15144 -0.33599 -0 .30194 0 .03773 •0 .01338 0 .00480 0 .14891 0 .14629 •0.32285 0 .02893 -0.03086 0 .01420 0 .136 50 0 .03283 -0 .14039 0 .10091 -0 .33874 -0.09247 - 0 . 0 5 3 0 1 0 .01606 0 .18845 0 .08019 - 0 . 0 1 2 6 7 0 .22941 0 .18155 0 .22180 0 .23565 0 .21353 0 .18983 - 0 . 3 7 5 2 0 -v-ECXOR--0.04501 0 .01192 0 .56068 -0 .04987 0 .01033 0 .57454 0 .00597 0 .04890 0 .04319 -0.08045 0 .00365 0 .15173 -0.09265 -0.26187 •0 .18703 -0.00877 -0.07425 0 .12219 0 .00246 0 .14369 0.113 31 -0.02450 0 .23254 0 .12691 0 .05374 0 .25619 -0 .00667 0 .01369 •0 .10614 VECTOR 5 _j a...0.8.5.2.8_ ! 0 . 0 4591 i 0 .42497 J0_.JX8J3.3_ •0.00652 •0 . 35275 J0_._Q3_653_ 0 .01485 0 .02307 0 .09158 • 0 . 18192 -0.07939 0 .07549 0 .06820 -0.06248 0.18825 -0.16107 -0 .01741 0 .06285 -0.50514 -0 .03750 0 .07203 0 .36864 0 .00133 0 .00855 -0 .15104 0 .04336 0 .03785 - 0 . 3 5 2 5 1 VECTOR 6 - 0 . 0 1 2 7 5 JX._0.20_9_5_ 0 .07163 VFf*. TOR 7 0 .00743 :_0.._Q.2.65_5_. -0 .42767 -0.07567 -0.. 03.565 -0.11188 -0.02543 -0. 28562 0 .01180 -0.29147 -0.08320 -0 .22141 0.03506 0 .675 00 0 .06910 0 .20297 •0 .05171 •0 .06869 0 .00969 0 .00316 - 0 . 1 0 0 8 9 - 0 . 17099 - 0 . 0 8 2 6 2 -0 .04060 - 0 . 0 4 3 9 4 - 0 . 0 8 7 4 8 0 .00478 - 0 . 0 4 2 2 3 0 .15361 VECTOR 8 0.09751 -0.06623 0.11805 iO__lJit8.L 0 .25487 0 .03874 0 .16163 0 .03894 0 .32171 0 .28303 -0.06944 0 .39220 0 .20510 0.23002 0 .21446 0 .06577 -0 .00643 0.3 7 342 -0 .02577 -0 .07274 0 . 14833 -0 .05580 0 .12669 -0.05566 -0 .27937 0 .00124 -0.27621 0 .11979 -0 .04017 - 0 . 0 4 6 3 0 - 0 . 0 1 0 2 1 - 0 . 0 9 1 5 1 0 .03057 0 .03528 0 .00423 - 0 . 0 2 1 3 2 0 .01449 0 .10578 • 0 . 10544 0 .12852 •0 . 10838 -0.04874 -0. 32049 • 0 . 14588 0 .66177 -0.00886 -0 . 16813 -0.04431 0 .209 13 0.10413 -0.12624 0 .13569 VECTOR 9 -0 .041 18 0 .01382 -0.01155 -0.01169 • 0 . 11955 0 .12538 0 .00190 0 .59574 0 .032 87 0 . 0 6773 -0 .06142 - 0 . 3 7 8 6 1 0 .00036 -0.00322 -0 .01945 0 .38689 0 .06380 0 .405 38 0 .03875 0 .18281 - 0 . 2 4 1 8 3 0 .00826 -0.01495 - 0 . 2 4 2 9 7 - 0 . 1 5 9 5 3 -0 .01312 - 0 . 0 7 7 5 6 -0 .13295 0 .08426 0 .17183 0 .22902 0 .27817 \\ ECTOR 10. - 0 . 0 2 9 6 5 - 0 . 0 3 8 9 5 0 .43811 -0.03009 -0 .14153 -0 .11713 -0.0 25 58 -0 .07646 -0.01737 -0.01979 0 .41240 •0 .10402 -0.00920 -0.15853 0 .36436 - 0 . 0 2 9 13 -0 .22659 - 0 . 2 3 7 5 7 -0.02568 0 .10684 -0.03777 -0 .00583 -0 .50146 -0.07471 •0 .04931 0 .01689 0 .17308 -0.07943 0 .08186 VECTOR 11 0 .05143 - 0 . 0 9 3 5 5 - 0 . 0 5 9 8 6 -.0_._0.0_9.03_. -0.04098 0 .20093 0 .16491 - 0 . 0 2 9 2 1 - 0 . 1 2 3 3 3 0.17536 -0.00617 0 .00429 0 .00037 -0.02 5 8 7 •0 .08484 0 .00273 0 .22311 0 .09538 - 0 . 6 4 8 1 0 -0 .02457 •0.06961 -0 .32775 0 .13334 -0.22216 10 .JL2356. 0 .06211 -0 .32464 IO.J3.9459 0 .28852 VECTOR 12 - 0 . 0 1 4 7 9 -0_.1.1_7_9_9__ 0 .31871 VFf. TDR 13 -0 .04926 _J3_._27_623_ - 0 . 0 8 0 3 5 0 .04198 -0.16046 -0 .00190 0 .03563 -0.02680 0.18718 0 .04708 0 .16183 0.04476 -0.00004 0 .00559 - 0 . 4 3 3 6 5 - 0 . 0 4 9 8 7 0 .26037 0.13845 -0.01117 0 .13065 0 .11517 0 .12903 -0 .20500 0 .00996 -0 .0 1379 0 .58065 - 0 . 0 2 8 6 4 0 .02488 - 0 . 1 2 1 5 9 VECTOR 14 0 .05895 0 .00422 0 .02186 0 .07504 - 0 . 0 0 0 9 3 -0 .13455 0 .05431 0 . 11649 0 .15610 •0 .17749 -0 . 14569 -0.06095 -0 .07147 •0 . 19238 -0 .0 70 48 0 .62821 -0 .07576 -0.04181 0 .23173 -0 .15404 -0.01919 -0.07283 0 .11184 -0.10949 0.033 21 -0.07642 0 .39626 -0.08257 0 .04560 -0 .02515 0.2 4937 0 .27386 - 0 . 0 1 1 2 0 0 .02866 0 .18062 0 .00802 - 0 . 3 5 1 3 2 0 . 0 30 57 -0. 12109 0 .02692 - 0 . 1 4 7 9 4 VECTOR 15 0 .05515 - 0 . 0 3 2 6 3 -0.04792 0 .10991 0 .0610 1 0 .18293 0 .14812 0 . 0 0 155 0 .03550 -0.64046 -0. 13838 0 .20736 0.01067 0 .32384 0 .07894 -0.14255 -0 . 13512 0 .24812 -0 .00097 -0.22423 0 .17107 0 .13504 0 .25262 -0 .13288 -0. 09206 •0 .10419 0.08623 0 .16786 0 .11843 0 .14677 0 . 1 1 4 5 4 -0.27767 -0.02825 -0.63028 - 0 .14510 0 .40484 0 .05009 0 .01180 0 .19148 -0 .02302 -0 .1 5060 0 .03208 0 .16355 J/ECX0.RJ.6_ - 0 . 2 0 3 1 4 0 .02095 - 0 . 0 2 0 8 2 -0. 31819 -0.53179 0 .09674 0 .15334 0 . 1086'4 -0.02711 0 .40970 -0.09445 -0 . 15125 0 .32551 -0.00305 0 .05565 0 .33177 0 .07880 •0 .03859 -0.07930 0 .07341 0. 16884 -0.08624 0 .12861 -0. 01910 -0 .01943 -0.02290 0 .07886 -0. 15289 0 .08280 VECTOR 17 -0 .14785 0 .06089 0 .11995 - 0 . 1 0 7 7 2 0 .02817 0 .10142 0 .19074 -0. 13496 -0 .159 94 0 .03582 -0.10325 0 .15925 -0 .02444 -0.05742 0 .17308 0 .07145 -0.05461 0 .04139 0 .07592 0 .00276 -0 .67667 -0.18 568_ -0. 05075 0 . 4 8 9 0 3 -0 .01944_ 0 .03519 0 .12245 0 .06452 0 .12477 VECTOR 18 - 0 . 2 5 0 0 5 - 0 . 2 7 9 8 7 -0.17699 0 .32368 -0.28862 •0 .29415 0 .25035 -0.05756 0 .37932 0 .05964 -0 . 15712 -0.03206 0 .13307 -0 .02274 0 .11715 -0 .01775 -0.01530 -0 .01276 - 0 . 0 1 5 7 9 -0 .01833 0 .13441 0 .00732 -0 .00004 - 0 . 0 6 8 4 3 0 .08365 0 .42268 -0.192 25 -0.13895 0 .12679 VECTOR 19 -0 .06490 0 .11649 0 .00255 -0.07539 0 .38483 0 .07617 0 .14635 0 .19214 -0 .19389 0 .04671 -0 .06480 -0.09097 0.08972 0 .06241 0 .10331 -0.06127 • 0 . 11258 -0.45959 -0.2 86 75 -0.01617 0 .34425 -0.22341 -0. 00450 0 .22201 -0 .23618 -0.04264 -0 .23070 0 .22516 -0.00298 VECTOR 20 - 0 . 1 2 2 2 0 - 0 . 1 3 6 1 4 - 0 . 5 4 9 8 9 0 .02316 -0 .25791 0 .55864 0 .17287 0 .21446 0 .00086 0 .16649 0 .18327 - 0 . 0 0 9 5 1 VECTOR 21 0 .01116 - 0 . 0 5 8 5 2 0 .02490 0 .04002 -0 .05577 -0 .06141 0 .00643 -0.00656 0 .04545 0 .00801 -0.00684 -0.15182 -0.00082 -0.06975 -0 .06000 0 .29018 -0 .02141 0 .25059 -0 .38823 0 .41743 0 .10852 -0 .03979 0.05461 0 .03196 0. 15866 •0 .08840 -0.2 73 61 0 .06298 -0.21523 -0. 11222 -0 .09395 -0.10598 -0 .22314 -0.10040 - 0 . 0 2 4 1 8 0 .02923 -0.09592 0 .06822 0 .01481 0 .08089 - 0 . 0 6 1 8 8 -0 .02327 0 .37789 - 0 . 0 2 0 6 8 - 0 . 4 0 8 5 9 0 . 15553 VECLOR„22„ - 0 . 4 0 0 0 7 0 .32929 0.01096 -0.51954 0 .04104 -0.01390 0 .17195 0 .08720 0 .11322 -0 .16710 -0.02168 -0.00780 -0 .06468 0 .09946 -0.00068 -0.26141 -0.08371 0 . 10846 0 .20810 -0 .04299 0 .00175 0 .25566 -0 .03751 -0.24411 -0.04710 •0 .08587 0 .09241 0 .29996 •0 .01749 VECTOR 23 „ - 0 . 1 A 5 9 i t 0 .29184 -0 .00914 0 .19123 - 0 . 2 1 4 2 7 0 .00911 0 .07377 •0. 13489 -0 .07768 - 0 . 4 1 7 2 6 0 .66972 0 .20914 -0.14052 0 .04004 -0 .06526 0 .06602 -0 .01855 -0.08622 0 .01375 0 .03914 •0 .10029 -0.01923 •0.00065 0 .02297 •0 .03085 • 0 . 12262 -0.09136 -0 .16261 - 0 . 0 1 7 9 4 VECTOR 24 I 0 .25035 - 0 . 2 8 8 3 1 -0.30252 •0 .01380 -0.17321 0 .55697 -0 .08715 -0.05942 0 .00268 0 .04085 -0.21327 0 .00558 0 .21757 -0.00895 0 .09230 -0.01798 0 .35289 -0 .18793 -0.25584 0 .02307 0 .01937 0 .03349 0 .07201 0 .00708 0 .01089 - 0 . 2 4 5 0 6 0.03718 0 .09131 - 0 . 0 7 2 08 I VFCTOR 25 r\"0.6 8 4 6 7 0 . 1 9 9 3 0 -0 . 0 1 2 4 3 VECTOR 2 6 - 0 . 0 0 3 2 4 - 0 . 5 2 4 9 8 - 0 . 0 1 9 5 7 - 0 . 0 2 2 5 0 0 . 0 0 6 8 3 -0 . 0 9 2 1 4 - 0 . 3 2 4 5 5 0.0792*8 - 0 . 0 0 0 5 4 0 . 0 3 5 0 4 0 . 0 2 5 3 2 - 0 . 0 1 7 1 5 0 . 5 0 5 4 4 0 . 0 5 4 2 5 -0 .0 2 3 4 6 - 0 . 0 3 2 9 8 - 0 . 4 1 6 4 7 - 0 . 0 3 2 1 0 - 0 . 0 1 4 8 2 0 . 0 2 9 7 0 - 0 . 2 0 7 9 7 - 0 . 1 2 3 7 4 - 0 . 0 0 7 2 5 -0 . 0 3 6 4 8 0 . 2 4 6 0 0 - 0 . 1 8 3 0 2 0 . 0 1 3 7 1 -0.0 3 0 6 7 - 0 . 2 0 7 8 5 -0 . 0 0 1 4 0 0 . 1 0 4 0 8 - 0 . 0 1 3 8 9 - 0 . 1 1 1 0 4 0 . 1 5 2 7 9 - 0 . 0 1 2 3 3 0 . 4 6 7 8 5 - 0 . 4 1 0 0 5 0 . 0 0 0 15 - 0 . 1 4 8 2 9 0 . 0 0 0 1 6 0 . 0 0 1 3 3 0 . 0 4 4 5 9 - 0 . 0 0 0 2 1 -0 . 0 1 2 4 4 - 0 . 0 0 0 0 9 - 0 . 0 1 3 8 7 -0. 0 0 0 7 7 - 0 . 0 1 8 1 4 0 . 0 0 0 2 5 • 0 . 0 0 3 8 9 - 0 . 0 0 0 7 1 0 . 0 0 0 5 5 0 . 0 0 1 5 9 - 0 . 0 0 1 3 3 -0 . 0 0 0 7 7 VECTOR 2 7 0 . 0 1 3 5 4 '. - 0 . 1 9 6 3 7 - 0 . 0 2 1 6 0 • 0 . 0 7 5 5 9 0 . 0 0 4 2 9 - 0 . 0 0 7 2 8 0 . 1 2 1 2 7 0 . 0 0 0 8 0 - 0 . 1 0 3 5 1 - 0 . 0 0 0 0 8 • 0 . 0 5 7 2 8 0 . 0 0 0 4 7 -0.6 82 7 3 • 0 . 0 0 0 5 3 0 . 5 6 7 3 9 0 . 0 0 1 0 3 0 . 2 8 3 2 5 0 . 0 0 1 8 2 0 . 2 3 8 0 2 0 . 0 0 0 2 2 - 0 . 0 0 0 4 7 - 0 . 0 0 1 2 5 - 0 . 0 2 9 2 4 0 . 0 0 9 4 6 0 . 0 0 8 9 9 0 . 0 1 6 6 7 0 . 0 0 0 7 5 - 0 . 0 0 3 5 8 0 . 0 0 3 7 5 .6 RR.OR—B.O.U N D-S-F-0 R_E XGEflVALUES^ 0 . 0 0 0 1 4 3 5 0.0000361 0 . 0 0 0 1 3 2 6 0 . 0 0 0 0 3 1 4 0 . 0 0 0 0 9 7\"8 0 . 0 0 0 0 3 8 1 0 . 0 0 0 0 9 3 8 0 . 0 0 0 0 2 1 8 0 . 0 0 0 1 0 8 5 0 . 0 0 0 0 6 1 5 0.0000592 0 . 0 0 0 0 1 2 4 0.00005 29 0 . 0 0 0 0 1 1 1 0 . 0 0 0 0 1 8 2 0 . 0 0 0 0 1 7 2 0 . 0 0 0 0 2 3 7 0 . 0 0 0 0 1 5 7 0 . 0 0 0 0 4 0 9 0 . 0 0 0 0 1 2 1 0 . 0 0 0 0 1 7 0 0.0000151 0 .0000583 0 . 0 0 0 0 2 9 4 0 . 0 0 0 0 0 6 0 0 . 0 0 0 0 1 8 1 0 . 0 0 0 0 1 3 6 0 . 0 0 0 0 1 0 8 0 . 0 0 0 0 2 3 5 E.RR-0.R^B0UNOS_E0R^EJ_G.E,NV.E.CXQR,S.. 0 . 0 0 0 0 5 6 6 0 . 0 0 4 7 7 1 8 0 . 0 0 0 0 7 2 0 0 . 0 0 2 0 7 1 3 0.0 00093\"0 0 . 0 0 2 2 7 4 6 0 . 0 0 0 6 3 0 4 0.0111186 0 . 0 0 0 7 2 9 4 0.03136 56 0 . 0 0 1 0 4 7 7 0 . 0 0 4 2 8 8 8 0 . 0 0 0 9 3 5 8 0.003 8 5 1 5 0 . 0 0 0 1 4 2 9 0.0322166 0 . 0 0 0 9 6 9 7 0 .0293792 0 . 0 0 5 4 0 4 4 0 . 0 5 1 2 8 7 7 0 . 0 7 2 1 2 6 9 0 . 0 5 4 4 0 6 8 0 . 5 8 5 8 5 1 4 2 . 1 0 8 3 4 4 1 0 . 4 2 7 4 1 3 2 2 6 . 2 1 6 6 7 4 8 1 9 . 6 7 8 3 9 0 5 9 . 3 5 2 7 5 9 4 20 .3988953 FACTOR MATRIX ( 2 7 FACTORS) VARTAB1 F L VARIABLE 2 0 . 7 4 5 9 8 0 . 8 7 4 3 1 0 . 0 1 9 1 9 _0_..OJO.O_4_t_ - 0 . 4 5 2 8 0 - 0 . 0 0 4 8 8 •JL.JLU.2A. 0 . 1 0 5 8 0 -0 .00 7 4 6 - 0 . 0 0 3 2 6 • 0 . 0 5 5 6 6 0 . 0 1 0 9 3 0 . 0 0 2 6 1 0 . 0 9 4 6 6 0 . 0 0 9 6 3 0 . 0 0 6 1 5 - 0 . 0 1 2 0 1 - 0 . 0 2 7 8 8 - 0 . 0 0 0 0 1 0 . 0 0 4 2 0 - 0 . 0 1 6 9 0 0 . 0 0 0 0 1 0 . 0 6 5 9 7 - 0 . 0 1 6 9 0 - 0 . 0 1 8 5 7 -0 . 0 0 3 8 4 - 0 . 0 1 1 6 5 -0 . 0 0 5 5 1 • 0 . 5 7 7 7 7 0 . 2 8 8 6 6 - 0 . 0 6 1 6 7 0 . 0 9 6 9 3 0 . 0 0 7 0 0 - 0 . 0 5 8 2 6 0 . 0 8 1 0 4 - 0 . 0 0 5 2 1 -0 . 0 1 1 8 2 - 0 . 0 0 3 3 7 - 0 . 0 0 0 8 5 - 0 . 0 1 6 2 6 - 0 . 0 1 5 2 4 0. 0 0 1 1 0 0 . 0 0 3 35 -0. 0 0 0 1 7 - 0 . 0 0 3 1 5 0 . 0 1 0 6 5 • 0 . 0 0 4 7 1 - 0 . 0 4 3 6 7 0 . 0 0 0 0 1 - 0 . 0 1 2 3 1 - 0 . 0 0 0 0 2 - 0 . 0 1 1 9 6 - 0 . 0 0 4 4 6 - 0 . 0 0 6 1 3 VARIABLE 3 0 . 7 3 0 5 4 0 . 0 6 1 5 4 0 . 2 5 7 6 0 0 .01385 • 0 . 5 7 5 5 3 -0 . 0 3 5 0 7 0 . 0 0 7 3 8 0 . 0 2 8 9 5 0 . 0 4 0 5 5 • 0 . 0 0 0 1 7 - 0 . 0 7 1 2 7 0 . 0 2 1 0 5 0 . 2 2 4 2 1 0 . 0 0 3 2 2 -0 . 0 2 7 1 8 - 0 . 0 1 9 5 1 -0 . 0 5 3 9 0 0 . 0 0 8 6 6 • 0 . 0 1 0 0 5 -0 . 0 2 4 7 8 - 0 . 0 1 5 3 2 — V A R I A B L E 0 . 9 2 5 3 3 - 0 . 0 1 0 9 0 0 . 0 0 4 2 8 0 . 0 0 5 0 5 - 0 . 0 0 3 7 6 - 0 . 0 0 1 8 0 -0 . 0 0 0 8 3 - 0 . 0 0 0 0 0 0 . 0 0 0 0 0 - 0 . 3 3 6 2 6 - 0 . 0 0 0 6 3 -0 . 0 0 4 9 0 - 0 . 0 2 5 5 0 -0. 0 4 6 2 6 0 . 0 0 0 1 6 - 0 . 0 9 9 4 9 - 0 . 0 1 3 2 5 - 0 . 0 0 0 9 1 0 . 1 0 1 6 5 0 . 0 2 9 8 6 0 .00031 - 0 . 0 2 3 9 5 0 . 0 5 6 2 3 0.00081 0.03426 0.01159 0 . 0 0 0 1 3 - 0 . 0 3 1 3 2 0 . 0 1 6 9 2 0 . 0 0 0 8 6 0 . 0 0 2 7 6 -0 . 0 0 7 7 7 0 . 0 0 1 0 4 I VARIABLE 5 .. 0 . 7 6 3 5 6 - 0 . 0 4 6 0 2 0 . 0 0 2 1 6 _a..5J_St£L6_ - 0 . 0 0 8 8 5 - 0 . 0 0 1 9 0 J1_2JEL3J_3_ - 0 . 1 1 4 5 8 0 . 0 8 3 79 0 . 0 1 1 1 1 -0 .06109 -0 . 0 0 6 9 1 0 . 0 1 4 8 2 ^ - 0 . 0 5 0 1 4 0 .00129 • 0 . 0 1 4 0 5 0 . 0 0 0 0 3 0 . 0 4 4 1 0 0 . 0 0 0 4 9 0 . 0 4 4 6 8 - 0 . 0 0 0 6 7 -0 . 0 2 1 8 1 -0 .000 11 0 . 0 2 5 6 4 0 . 0 0 5 3 1 _0..J)J3_36.2. - 0 . 0 1 1 6 2 VARIABLE 6 0 . 6 8 9 6 1 . _ _ ] . 0 . 0 6 5 4 4 I 0 . 0 0 6 2 6 _ AR T AR1 F _ _ 0 . 2 8 2 6 4 ._Q_.Si.l5J5±. - 0 . 0 0 7 6 7 - 0 . 6 1 5 4 0 -0. 010913 -0.0 1 0 8 4 -0. 0 0 3 5 6 0 .07570 - 0 . 0 1 6 0 7 -0.07836 0 . 0 4 5 5 4 0 . 2 0 2 3 6 -0 . 0 1 5 4 3 - 0 . 0 6 1 9 1 - 0 . 0 1 0 6 2 •0 .02769 • 0 . 0 0 3 6 2 - 0 . 0 1 1 4 4 0 . 0 2 5 1 7 - 0 . 0 0 2 3 7 - 0 . 0 0 2 2 2 - 0 . 0 0 0 2 9 - 0 . 0 0 0 3 3 - 0 . 0 0 0 0 6 0.92979 - 0 . 0 0 2 3 0 - 0 . 0 1 0 8 0 - 0 . 3 5 1 5 1 0 .01477 0 .00611 - 0 . 0 5 8 8 2 - 0 . 0 1 8 9 8 - 0 . 0 0 1 3 6 0 .00304 0 .00616 0 .00227 0 .06975 0 .01505 -0 .00111 0.03302 - 0 . 0 1 0 8 8 0 .00040 -0 .00565 -0 .01828 -0 .00075 0 .02068 0 .00899 0 .00016 - 0 . 0 1 6 9 6 - 0 . 0 1 0 0 9 0 .00779 \\ VARIABLE 8 0.77160 - 0 . 5 6 4 4 1 0 .26019 - 0 . 0 3 0 3 0 0 .07995 0 .06508 -0 .06399 0 .02387 - 0 . 0 0 8 7 7 - 0 . 0 0 2 2 9 J 0 .00160 - 0 . 0 0 8 5 0 - 0 . 0 0 3 6 9 0 .00750 - 0 . 0 1 9 9 2 -0 .007 32 0 .00846 0 .00096 0 .02068 - 0 . 0 0 1 6 4 -0 .01184 - 0 . 0 0 0 3 3 -0 .02123 0.00062 0 .00792 - 0 . 0 1 3 2 1 0 .00966 \\ VARIABLE 9 0 .69984 - 0 . 0 0 8 7 9 0 .26615 0 .04258 - 0 . 6 4 5 6 8 -0.0065*6 0 .06646 -0 .00208 0 .00949 -0 .00493 - 0 . 0 4 8 7 0 - 0 . 0 0 2 6 7 0.11145 -0 .00222 0 .00286 0 .00565 0 .01747 - 0 . 0 1 3 97 -0 .0 1937 0 .00004 - 0 . 0 0 8 8 1 - 0 . 0 0 1 3 8 0 .01174 0 .00368 -0 .00001 -0 .00018 0.00031 VART ABI F 10 .... 0.88763 - 0 . 0 3 5 3 0 0 .00115 - 0 . 4 5 3 3 5 - 0 . 0 0 4 5 5 0 .00880 0.03061 0 .00747 0 .00367 0 .01694 0 .00149 - 0 . 0 0 2 6 7 0 .04201 0 .00534 0 .00137 0 .00912 -0 .02098 0 .00075 0.00109 0.00738 0 .00026 - 0 . 0 1 4 4 2 - 0 . 0 0 9 3 9 0 .00373 0 .01332 ~-6T03121 0 .00750 VARIABLE 11 0.75393 - 0 . 5 9 0 8 3 0 .27201 0 .01474 0 .05096 0 .01973 -0 .03715 0 .00981 0 .006 23 -0 .01530 - 0 . 0 3 4 9 1 -0 .00231 - 0 . 0 3 8 9 4 0 .00966 0 .00649 0 .00512 0 .00499 - 0 . 0 0 3 0 0 -0 .00570 0 .00179 0 .00288 -0 .00066 0.00696 -0 .00022 - 0 . 0 1 8 9 2 0 .00689 0 .00826 VARIABLE 12 0.71986 -0 .01529 0 .18874 0 .09117 - 0 . 6 4 0 4 3 0 .005 70 0.01278 - 0 . 0 0 8 8 9 -0 .00724 0 .03194 -0 .02500 - 0 . 0 7 299 0 .10385 0 .00409 - 0 . 0 7134 0 .02188 - 0 . 0 0 5 2 7 0 .02276 -0.05561 0 .00112 0.00989 0 .00120 -0 .00246 - 0 . 0 0 0 1 4 -0 .00018 - 0 . 0 0 0 2 4 -0 .00008 VARIABLE 13 -0.85345 0 .00014 0 .01648 -0 .49398 - 0 . 0 5 2 9 6 0 .00256 0 .07192 0.0141\"6 - 0 . 0 0 1 1 4 0 . 0 6 0 4 7 0 .02747 0 .00580 0 .01648 -0 .03915 -0 .00291 - 0 . 0 3 3 5 8 0 .01491 0.00000 0.03408 0 .01821 -0 .00001 - 0 . 0 7 3 3 2 - 0 . 0 1 9 8 8 0 .05653 0 .01137 -0 .03004 -0.00251 VARIABLE 14 - 0 . 4 5 1 0 9 - 0 . 6 7 4 0 1 0 .00916 0 .00451 -0 .20192 -0 .26900 0 .28302 - 0 . 2 1 6 8 2 0 .26859 0.16204 -0 .03166 - 0 . 0 0 1 5 7 0 .01176 - 0 . 0 0 0 6 4 - 0 . 0 3 7 9 7 -0 .00033 0 .00658 - 0 . 0 0 0 6 2 0 .02357 0 .00023 - 0 . 0 1 2 9 6 -0 .00000 -0 .00656 0 .00000 - 0 . 0 0 3 8 9 -0 .00383 0 .00029 VARIABLE 15 - 0 . 4 1 4 7 8 0 .08326 - 0 . 4 7 7 9 0 0 .06178 0 .2788 5 - 0 . 0 1 8 3 7 - 0 . 3 2 3 8 6 -0 .02566 - 0 . 0 6 9 3 5 -0 .02320 - 0 . 2 7 4 5 0 - 0 . 0 0 0 4 2 0.34503 0 .00817 0 .44770 0 .00403 0 .03054 0 .00369 -0 .06229 0.002 05 0 .00126 0 .00292 0 .00024 0 .00043 -0 .00021 - 0 . 0 0 0 0 0 -0 .00000 . VARIABLE.1 6 - 0 . 4 6 7 5 2 -0 .24186 - 0 . 0 0 3 4 9 - 0 . 7 3 7 0 9 0 .05341 - 0 . 0 0 2 4 6 - 0 . 0 5 5 1 4 0 .06040 -0 .00176 -0 .09182 0 .00198 0 .00006 -0 .17878 - 0 . 0 1 8 1 9 -0 .00013 - 0 . 2 0 8 5 3 0 .01082 -0 .00000 0 .18866 0.00473 0.00000 - 0 . 1 1 3 7 5 - 0 . 0 0 2 1 7 - 0 . 1 7 0 6 9 - 0 . 0 0 6 6 6 -0TO8963\"\"--0 .00031 VARIABLE 17 0.33052 - 0 . 0 8 6 4 9 0 .02707 0 .17770 - 0 . 5 6 0 6 7 0 .63572 0.32851 0 .14148 - 0 . 0 0 1 4 5 0 .04198 - 0 . 0 2 5 9 8 0 .00249 - 0 . 0 0 0 0 1 - 0 . 0 0 1 2 6 0.02915 - 0 . 0 0 0 0 1 0 .01464 - 0 . 0 0 0 0 9 0 .02930 - 0 . 0 0 0 0 7 0 .01008 0 .00000 0 .00032 -0 .00000 - 0 . 0 0 1 5 4 - 0 . 0 0 0 9 6 -0 .00004 VARIABLE 18 - 0 . 6 4 8 1 9 0 .04976 - 0 . 4 2 3 0 5 0 .04312 0 .06258 0 .10329 0 .28758 - 0 . 0 2 5 0 6 0 .40917 0 .02562 0 . 19115 0 .01765 0 .13049 -0 .00580 - 0 . 0 3 5 4 0 - 0 . 0 0 1 2 0 0 . 17443 -0 .00027 -0. 19703 -0 .00270 - 0 . 0 0 4 4 3 - 0 . 0 0 1 1 0 -0 .00054 - 0 . 0 0 0 1 9 0 .00012 -0 .00000 0 .00000 VARIABt F 19 0.81124 0.0 2318 -0.00396 -0.37972 -0.06766 -0.00252 -0.176 26 0.06500 -0.00160 0.31683 0.02124 -0.00196 -0 .16765 -0.11003 0.00093 -0.06469 -0.00314 0.00000 -0.04897 0 .00402 0.00000 0.04316 0.02857 0.08242 •0.00252 0.00664 -0.00423 VARIABLE 20 0.73313 -0.14338 0.35921 -0.13126 -0.39126 0.00298 -0.24299 -0.16 361 -0.00674 0.03216 0.10767 -0.00379 0.19164 •0.00051 0.04708 -0.00031 •0.06516 0.00024 -0.02114 -0.00011 0.01137 -0 .00000 0.01426 0 .00000 -0.00857 -0.00018 -0.00109 VARIABLE 21 -0.17188 -0.02234 -0.40000 0. 10519 0 .15285 -0.03169 0.69339 -0. 02744 0.47169 -0.02533 0.06747 -0.00286 0. 13513 0.01371 0.07157 •0.00103 -0.10954 0.00015 0.17214 -0.00043 0.00269 0.00032 -0.00016 0.00020 -0.00011 0.00000 -0.00000 -VAR LA B-L-E—22— -0.13705 0.07498 0.00058 -0.33049 -0 .02652 -0.00041 -0.02415 0.019 56 0.00070 0.71053 0.02038 0.00035 -0.39152 0.07068 -0.00020 -0.40279 0.01328 0 .00000 -0 .153 78 •0.01180 -0.00000 0 .08695 -0.00086 -0.07192 0.00451 •0.04602 0.00180 VARIABLE 23 Jl._5_5A4.5_ -0.00965 0.00319 -_Q_._6_8_120_ 0.00185 0.00332 JX«t4_3728_ 0.03036 0.00116 0.05341 0.00029 0.00075 0.02561 - 0 . 10537 0.00874 0.00071 -0.00372 0.00007 0. 14219 -0 .00279 -0.00003 -0.03297 -0.00107 -0.00592 0.01147 -0 .00682 -0.00277 VARIABLE 24 0 .54119 -0-..0.0-L0.2„ -0.00244 0.65188 :0.UA3JL2_ -0.00023 0.34605 _0_.JDX58'9_. -0.00151 0.18764 -0. 11879 0.00007 -0.08811 0.00206 -0 .00015 -0.09502 •0. 02076 -0 .00002 0.24899 0.01979 0.00001 -0 .09869 -0.00124 -0.0 349 7 -0 .00538 •0.04087 -0.00030 V AR T ARI F 2 5 0.59167 0.03560 _n0„.JXO„O92_ 0.51008 -0.01646 i0.000.0 2. 0.42278 0. 16374 0.00069 -0 .23130 0.03846 0.00011 0.20895 0.03343 -0.00030 -0. 16104 0.00764 -0.00002 0.18043 -0 .00624 0.00001 -0.00600 0.00908 -0.05994 0.00611 0 .14316 0.00036 VARIABLE 26 0.46655 0.72319 0.44918 0.15111 -0.019 32 -0.07781 0.05786 -0.02998 0.03799 -0.09335 -0.00917 0.01492 0.08593 0.00318 -0.04015 -0.00034 0.06006 -0.00255 -0.00402 0.00027 -0.00530 -0 .00003 0.00868 0.00002 0.00049 -0 .02719 -0.00684 VARIABLE 27 0.47350 -0.12231 0.74118 0.04570 0.40702 -0.02 854 0.14013 -0. 02644 -0.04162 -0.02629 -0.03824 0.02317 -0.02267 -0 .07736 0.07045 -0.00000 0.07747 0.02036 -0.01484 -0.00314 -0.00082 0.00005 0.00040 0.00039 -0.00033 -0.00001 0.00000 VARIABLE .28. 0.28252 -0.08290 -0.01613 0.85191 0.03801 -0.00716 0.36183 -6.0215\"2 -0. 00215 0. 156 94 0 .04602 0.00095 0.00147 0.00560 -0.00028 -0.04138 -0.00262 0 .00000 -0 .04909 0.055 91 -0 .00000 0 .09180 -0.0046 3 0 .10326 0.01313 •0.02936 0.01307 VARIABLE 29 0.474.16 -0.12115 0 .00614 .0..27294_ 0.00329 0.00271 -A.. 71518_ 6. 07138 -0.00285 -0.00824 -0.05150 •0.00075 0.04813 0.02855 -0.00012 -0.08239 0 .01082 -0.00000 -0.245 77 0 .01400 0.00000 0.27425 -0.01299 0.12541 •0.01365 0_.0_68 01 -0. 00478 ITERATION CYCLE 0 1 2 VARIANCES 0.146480 0.460208 0.498346 3 4 5 6 7 8 0.501713 0.502589 0.502614 0.502614 0.502614 0.502614 0.502614 ROTATED FACTOR MATRIX { 27 FACTORS) VARIABLE 1 0.96682 0.01495 -0.00200 0.06288 -0.00104 -0.01467 -0.22594 0.02656 -0 .00 164 -0 .02900 0.00359 0.00097 0.00165 0.00820 0.01116 0.02715 -0.01283 -0.00000 0.05941 -0.006 36 0.00001 0.03944 -0.03118 -0. 01299 -0.00758 0.02688 -0.00450 VARIABLE 2 0.99344 0.00682 0.02852 -0.01585 0.02433 0.01164 0.07473 0.04100 0.019 29 0 .0 1827 0.0101.4 -0.00650 VARIABLE 3 0.24727 0 .00577 -0.00096 -0.02221 0.01791 0.00166 -0.00219 -0.00117 0.00734 -0.00155 •0.02923 -0.00002 0.20952 -0.02490 -0.93085 0.03023 -0 .05894 -0.00395 -0.05973 0.00165 0.05619 0.03144 -0. 00331 0.00004 -0.02784 0 .00613 -0.03505 0.00446 0.00340 -0.00604 -0. 10943 0.00403 -0.00346 0.03783 -0.03460 0.01113 -0.00024 -0.00340 -0.00002 0.00043 •0.00015 0.00011 _V„ARJAB.L.E_ 0.90640 -0.01042 0.00154 0.09730 0.00144 -0.00063 -0.38689 0.00260 -0.00249 -0.09119 -0.01406 0.00002 -0.05006 0.0 38 10 0.00046 0.00367 0.03523 0.00086 -0.00938 •0.00336 -0.00011 -0 .01503 0.05721 -0 .03126 0.00152 0 .02681 0.00659 VARIABLE 5 0.99234 -0.01873 -0.00159 0.02181 0.00505 -0.00210 0.01690 -0 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-0.01440 0.06184 0.00066 -0.09857 0 .00185 0.0 3047 -0 .00080 0.02888 -0 .00487 0.00287 0.00192 -0.01496 -0.00245 0.0 130 7 -0.00097 -0.00102 -0.00012 0.00008 JV:AR.LAB.L.E_LO._ 0.95230 -0.03642 0.00971 0 .03798 0.00152 0.01023 -0.28686 0.00 248 0.00147 0.02204 -0 .00698 -0.00644 0.00369 -0 .00458 -0.003 27 0.07188 •0.01936 0.00090 -0.03463 0.00575 0.00011 -0.00617 -0. 01441 -0 .00206 0.00955 -0 .00674 0.00081 VARIABLE 11 0.99530 -0.02782 0.01152 0.00308 -0.01446 0.01170 0.01510 0.01045 0.002 39 0.03716 •0.01166 -0.00755 0.04342 -0.01411 -0 .00371 0 .05832 0.01045 -0.00066 0 .00778 0.00336 0.00016 -0.01325 -0.01200 0.00338 0.01045 0.00090 -0 .00088 VAR TABI F 1 ? 0.26817 -0.03796 _n0_..0-0_0_93_ 0.10967 0.04385 JL.0002_7_ -0.93233 -0.02 054 L0_.JL0J_?J. -0.03201 0 .00984 0.00018 -0.10595 0.02391 0.00024 0.06568 -0.08840 -0.00002 -0.12865 0.00880 0.00007 0.01665 •0.01241 -0.01555 0. 00143 -0.02340 0. 005 03 VARIABLE 13 0.95505 0.02941 -0 .23467 0.07456 0.01308 0.06427 -0.04002 -0.09603 0.04470 -0.03892 -0 .01621 0.03949 -0.02306 0.00539 0.01264 -0.000 81 •0.01191 0 .00323 •0.06418 -0 .00065 0.02434 -0.00003 0.01534 •0.00017 -0.00355 0.00309 -0.00201 VARIABLE 14 0.00746 -0 .06727 -0.60275 0.00301 0.32194 0.002 7\"4 0.2018 5 -0.00371 0.05985 -0.00181 •0.01273 0.00045 0.21239 0.00032 -0.65986 0.00026 -0.05251 -0. 00008 -0.02351 0.00004 0.00035 0.00014 0.00002 -0 .00012 -0.00004 0.00001 -0.00001 -VAR.I-ABL.E_L5— 0.00794 -0 .03766 -0.00003 -0.34124 -0.01477 -0.00014 0.44154 0.00 723 0.00004 -0. 00431 0.00091 -0 .00003 -0.02608 0.00194 -0 .00004 -0 .03747 0.00005 -0.00001 0 .82019 0.00013 -0.00000 -0.10823 -0.00015 -0.01394 -0 .00011 -0.00022 -0.00002 VARIABLE 16 JX..0.263SL. -0 .46447 0.00017 -0..J-253-.0-. •0.01079 0.00018 JL..3J.8.2.L 0.00574 0.00001 0.17644 -0.00557 -0.00004 0.01599 -0.02447 0.23642 0.00364 0.00001 -0.00042 0.00000 •0.000 10 0.00000 -0.24091 0.00017 -0.09824 - 0 . 00024 0.00987 -0.00002 VARIABLE 17 0.23090 0.0025.9 -0.00001 0.06195 J0_.OJDJ94 5-_ 0.00003 -0. 08327 -0.00501 -0.00011 0.03194 •0.00161 -0.04473 •0.00145 0.96537 -0.00034 -0 .023 56 -0.00022 0.00417 -0.00016 •0.01048 -0.00006 0.00003 -0.00006 0.00000 0.00000 0.00660 0.00001 VARIABLE 18 -0.22401 0.01114 _..0..0.0.0.2.2_ -0.47492 -0.04429 -0.00001 0.41593 -0.03092 -0.00002 -0 .04223 0.00167 0.00003 0.58644 -0 .00172 0.00001 •0.06405 -0.00048 -0.00001 0.003 83 0.00080 -0.00000 -0.07939 -0.00034 -0.0501 1 0. 00006 -0 .43530 0.00009 VARIABLE 19 0.77195 0.00552 -0 .43 504 0.36336 0.02536 0 . 17298 -0.09599 -0 .04037 0.07342 -0.01411 0 .05341 -0.00026 -0.00836 -0.00009 0.00212 0.00011 •0.01467 -0.00019 •0.18036 0.00002 0.00291 0.00000 -0.001.34 0.00000 -0.00227 0.00012 0.00007 VARIABLE 20 0.72345 0.01985 0.30221 0.37013 0 .04364 0.01263 0.11550 0.01262 -0.42231 0 .00141 0.15043 -0.00098 •0.15470 •0.00050 -0.01832 •0.00003 -0 .04136 -0.00026 0.07267 0.00012 -0 .00022 0.00003 -0 .00006 0.00001 0.00005 -0.00000 0.00000 -VAR.LABLE_2-1_ 0.12376 -0.00443 -0.00001 -0.15449 0.00866 -0.00012 0.21036 0.003 73 0.00010 0.21676 0.00098 0 .00002 0.93064 -0.00036 -0.00017 -0 .02470 0.00014 -0.00000 -0 .02808 -0.00014 -0.00001 -0.00967 -0.00056 •0.00875 0 .00021 0.04107 0.00001 VARIABLE 22 0 ..02662 -0.02368 0.00031 -IL..17-2 50_ 0.00854 0.00030 0.09221 -0. 003 95 0.00019 0.96364 0.16344 -0.00038 0.00020 0 .00354 -0.00014 0.02336 -0.00013 -0.00000 0.00714 0.00030 -0.00001 -0.06560 -0 .00036 0 .00070 0.00007 _0 ,L0_0 7 2 3^ -0.00016 VARIABLE 23 0 .13351 -0 .02947 - 0 . 0 0 2 7 1 0 .97154 0 .01561 0 .00125 - 0 . 1 2 1 6 4 0 .0 66 39 0 .00163 - 0 . 0 8 1 7 5 - 0 . 0 2 1 0 5 0 .00027 -0 .07387 0 .00359 0 .00059 0 .00490 0 .00158 0 .00004 -0 .01423 0 .00427 -0 .00011 -0 .00736 -0 .00545 - 0 . 0 6 6 3 0 - 0 . 0 1 2 3 0 0 .01967 - 0 . 0 0 0 4 2 VARIABLE 24 ) 0.09701 - 0 . 0 5 3 8 5 0 .00054 0 .92269 - 0 . 0 6 9 6 7 0 .00004 -0 .19166 0 .02481 - 0 , 0 0 0 1 5 0 .04211 - 0 . 2 0 7 3 2 - 0 . 0 0 0 0 6 - 0 . 0 4 8 5 0 - 0 . 0 0 9 6 1 - 0 . 0 0 0 0 1 0 . 12116 0 .00137 - 0 . 0 0 0 0 2 - 0 . 0 5 0 4 2 6 .00481 0.00002 - 0 . 0 7 5 3 8 0 .00080 - 0 . 1 5 4 2 0 - 0 . 0 0 0 3 6 0 .01091 0 .00006 VARIABLE 25 0 .27525 0 .81557 - 0 . 1 1 6 7 8 - 0 . 3 1 2 1 8 -0 .09761 - 0 . 1 4 8 2 8 0 .11228 - 0 . 0 2 0 7 9 - 0 . 0 5 2 7 8 0 .09938 -0 .01944 0 .00021 \" 0 .02380 ' - 0 . 0 0 0 0 6 0 .29936 - 0 . 0 0 0 0 8 - 0 . 0 0 9 7 2 -0 .00000 - 0 . 0 0 0 9 3 0 .00003 0 .00122 0 .00000 0.00132 0 .00002 - 0 . 0 0 0 3 1 -0 .00000 - 0 . 0 0 0 1 3 VARIABLE 26 0 .04550 - 0 . 0 0 7 0 2 0 .98168 0 .05041 - 0 . 0 7 0 0 0 -0 .05911 0 .00568 0 .08098 - 0 . 0 6 0 9 5 0 .00877 0 .02059 -0 .00249 -0 .06671 0.03098 0 .03109 - 0 . 0 0 2 9 7 - 0 . 0 6 2 3 2 - 0 . 0 2 7 9 2 -0 .03595 0 .00077 - 0 . 0 0 2 2 1 1 -0 .00117 - 0 . 0 0 1 9 2 0 .00008 0 .00005 - 0 . 0 0 0 0 0 0.00009 VARIABLE 27 0 .03525 - 0 . 0 0 1 3 7 - 0 . 0 0 1 1 1 0 .96825 0 .02383 0 .00001 - 0 . 0 8 6 8 0 - 0 . 0 7 9 8 1 - 0 . 0 0 0 2 7 - 0 . 0 0 5 1 8 0 .03068 0 .00007 - 0 . 0 8 2 6 3 - 0 . 0 0 4 8 9 0 .00002 0 .05160 0 .00813 -0 .00001 -0 .08534 -0 .09304 -0 .00000 0 .06859 0 .00065 0 .12138 0 .00188 0 .02734 0 .00064 , VARIABLE 28 - 0 . 1 8 0 6 3 „__0.. 95293 - 0 . 0 5 8 9 1 - 0 . 0 0 7 0 5 - 0 . 0 5 8 0 4 0 .00212 -0 .08895 0 .09751 0 .13039 - 0 . 0 0 5 6 2 0 .05268 \" - 0 . 0 0 5 4 2 - 0 . 0 6 8 6 7 0.07401 0 .00118 -0 .00849 0.05301 0 .00972 0 .04284 - 0 . 0 0 1 7 4 0 .00604 0 .00128 - 0 . 0 0 0 7 2 - 0 . 0 0 0 1 7 - 0 . 0 0 0 1 8 - 0 . 0 0 0 0 0 0.00001 VARIABLE 29 0 .04659 0 .02304 - 0 . 8 3 7 2 2 0 .03761 - 0 . 1 4 7 0 8 -0 .09260 -0 .09046 0 .21245 0 .43992 0 .04986 0 .11873 - 0 . 0 2 8 5 4 - 0 . 0 1 6 3 2 0 .00965 - 0 . 0 0 5 9 5 - 0 . 00006 -0 .00096 -0 .00018 - 0 . 0 0 0 2 6 - 0 . 0 0 0 1 1 - 0 . 0 0 0 3 7 - 0 . 0 0 0 1 4 0 .00002 -0 .00001 -0 .00005 -0 .00002 0.00001 CHECK ON COMMUNALITIES VARI A8LE IQB-IGJNAL FINAL DIFFERENCE . . . 1 0 .99994 0\".99991 0 .00003 2 0 .99993 6 .99991 0.00002 3 0 .99993 0 . 99990 0 .00003 4 0 .99994 0 .99991 0 .00003 5 0 .99993 0 .99991 0.00002 6 0 .99993 , O\". 99990 0 .00 003 , . „ 7 0 .99994 6\". 9999 1 0.00 00 3 8 0 .99994 0 .99991 0.00002 9 0 . 9 9 9 9 3 0 .99990 0 .00003 10 0 .99994 0 .99992 0 .00003 11 0 .99994 0 .99992 0.00002 12 0 . 9 9 9 9 3 0 .99990 0 .00003 . 13 0 .99995 0\". 99992 0 .00003 14 0 .99994 0 .99989 0 .00004 15 0 .99993 0'. 99989 0 .00004 16 0 .99993 0 .99989 0 .00004 17 0 .99993 6 . 99990 0 .00003 , -13 J3.99993 0 .99988 0 .00004 ; ; 19 0 .99994 0 .99990 0.00003 20 0 .99994 0 .99990 0 .00004 21 0 .99992 0 .99988 0 .00004 J 22 23 24 25 26 2 7 0 .99992 0 .99994 0 .99993 0 .99993 0 .99994 0 .99994 0 .99989 0 .99991 0\". 99990 0 .99989 0 .99991 6.99990 0. 00003 0 .00003 0.00003 0.00004 0 .00003 0 .00003 / 28 29 0 .99994 0 .99994 0 .99991 0 .99990 0 .00003 0 .00004 THE PERCENTAGE OF THE TOTAL VARIANCE OF THE ORIGINAL STANDARDIZED VARIABLES WHICH IS ACCOUNTED FOR IN THE FACTOR SPACE IS 100 .0 REGRESSION EQUATIONS FOR COMPUTING FACTOR SCORES 0 .07219 0. 15848 - 0 . 0 3 3 4 9 0 .17069 0 . 0 - 0 . 0 0 6 8 1 - 0 . 0 2 6 5 2 0 .10647\" 0 .2404 5\" 0 .07970 - 0 . 0 0 1 8 7 - 0 . 1 2 1 5 4 0 .17242 -0 .01834 - 0 . 16050 0. 0 -0 .0 1392 - 0 . 1 6 4 9 3 -0 .20511 -0 .04961 -0 .03642 0 .36826 0 .00603 0 .01447 0 . 0 0 .06006 -0 .01966 0 .07372 - 0 . 0 0 3 8 6 0 .02025 - 0 . 0 1 5 0 3 rJ3_Jj3_105_ - 0 . 05409 0 .06013 0 .0 -0 .11079 -0 .02963 0 . 0 - 0 . 0 7 1 7 0 0 .06033 0 .04616 0 . 0 0 .03225 0 .01572 0 .29179 0 .03269 0 . 13872 0 .05494 -0 .0082 2 - 0 . 0 3 0 4 3 0 .05037 - 0 . 01256 0 .21568 0 .02238 0 .20395 - 0 . 0 1 3 0 8 - 0 . 0 0 2 1 8 -0 .03526 0 .07991 0 .84662 - 0 . 0 4 0 2 8 0 . 0 - 0 . 2 848 8 0 .05431 -0 .78101 - 0 . 0 3 1 1 6 0 .64307 - 0 . 10455 0 . 0 -0 .00995 -0 .43188 0 .02166 0 .45117 - 0 . 0 2 3 6 7 0. 0 - 0 . 0 2 1 7 7 - 0 . 8 7 9 6 4 0 .00604 - 0 . 0 8 4 1 4 - 0 . 0 1 3 6 3 - 0 . 5 5 6 6 4 \" 0 .20638 0 .22806 0. 27488 0.07788 0 .01042 - 0 . 1 2 3 6 4 0 .09328 0 .20608 ..._-0.._98LOLl_ - 0 . 11034 0 . 0 1.12481 - 0 . 0 2 1 3 0 0 .02307 - 1. 33105' - 0 . 1 9 3 3 3 - 0 . 1 0 0 1 6 0 .37016 0 .07823 0 .02217 0 .44963 0. 0 -0 .03235 0 .54715 0 .47359 -0 .03302 0 .15401 - 0 . 3 3 0 0 3 0 .01478 - 0 . 0 0 3 3 4 0 .0 - 0 . 0 4 8 51 - 0 . 0 2 3 2 7 - 0 . 16884 0. 00028 0.G0620 - 0 . 0 6 6 2 2 0 .05339 0 .04562 -0 .09991 0 .0 0 .31030 - 0 . 2 5 7 0 6 0 . 0 0. 11455 -0 .12645 1.09472 0 .0 - 0 . 2 2 5 8 9 0 .00220 - 0 . 4 2 5 1 9 ' 0 .01102 0 .17365 0.07936 0.16879 0 . 01570 0 .24411 0 .04489 0 .08470 0 .11492 0 .02290 -0 .04308 0 .07993 0 .00505 - 0 . 0 1 2 1 2 0 .04399 - 0 . 0 3 7 1 9 0 .0 - 0 . 0 1 2 7 1 - 0 . 0 2 1 7 4 - 0 . 0 7 2 4 5 0 .00874 0 .00972 0.01242 0 .0 0 .01508 - 0 . 0 0 1 0 5 1.06727 -0 .03841 0 .02012 0 . 0 - 0 . 0 2 5 9 2 -0 .09666 - 0 . 0 2 1 4 5 0 .03662 - 0 . 0 3 4 7 1 - 0 . 1 7 8 3 9 0 .03415 0 .07495 0 .05930 0 .00956 - 0 . 0 0 9 2 4 0 .02849 - 0 . 0 4 7 0 6 -0 .45932 0. 12001 - 0 . 0 0 1 2 4 0 . 0 0 .03849 0 .14020 - 0 . 0 2 0 9 8 0 .39445 0 .36888 - 0 . 1 6 9 4 6 - 0 . 0 3 4 3 7 - 0 . 3 2 3 8 5 1.38310 - 0 . 1 1 4 3 2 0 .0 - 0 . 0 7 4 8 8 -0 .07157 0 .19328 0.02011 0 .02282 - 0 . 1 9 9 4 6 0 .03649 0 .05626 — oTo 0.02332 0 .07852 0 .43932 0 .04855 _ - 0..-0.1A22_ _ -..0_. 0.1343 - 0 . 0 2 6 7 9 - 0 . 0 1 0 7 0 0 .04578 0 . 0 - 0 . 18872 0 .13599 0. 0 . - 0 , 0 3 674 . 0 .03429 - 0 . 0 5 0 2 2 0 . 0 0 .30533 - O . O O U O 0 . 2 2 2 4 4 ' - 1 . 7 6 9 2 3 - 0 . 19792. ' 0.33701 - 0 . 1 7 1 8 1 0 .18130 - 0 . 3 0 5 5 7 -0 .01923 - 0 . 19101 0 .06467 - 0 . 1 4 5 7 7 C ' 0 5 5 6 3 - 0 . 1 6 9 3 4 0 .03909 - 0 . 0 1 3 0 3 1. 11394 0 .02863 0 . 0 - 0 . 4 2 4 4 8 - 0 . 0 1 0 5 4 ' - 0 . 9 8 4 8 6 0 .56915 • 0 .84869 -0 .12368 0. 0 0 .54657 -1 .28345 0 .34506 1 .04907 0 .35671 0 .0 - 0 . 0 5 8 7 2 - 1 . 2 5 6 2 0 0 .23341 0 .24023 - 0 . 3 6 9 7 7 0 .63940 ' 0 .13022 0 .08499 -0 .02654 0.08539 0 . 16385 2 .44150 0 .02828 0 .23486 1.26761 - 0 . 1 0 4 8 7 0 . 0 - 0 . 4 8 9 1 8 - 0 . 1 0 4 0 0 0 .00584 - 0 . 5 8 6 6 9 ' - 0 . 3 5 4 9 8 0 .25749 0 .00831 0 .21394 - 0 . 0 9 8 5 3 -0 .16367 0 .0 - 0 . 1 4 8 7 7 0 .06459 -0 .12573 - 0 . 1 0 0 7 7 -0 .08503 0 . 0 8 6 4 3 - 2 . 38535 - 0 . 1 2 1 2 3 0 . 0 - 0 . 0 1 8 7 9 - 0 . 3 6 5 1 7 - 0 . 3 1 4 8 7 - 0 . 3 0 6 1 7 0 .04572 - 0 . 0 2 2 5 2 0.01071 0 . 0 0 0 2 1 0 . 0 3 6 3 6 0 . 0 0.05162 0 .00981 0 . 0 0 .10396 J - 0 . 0 2 7 9 8 -0 .13870 0 . 0 0 .32770 0 .01562 - 0 . 4 1 1 8 7^ 0 . 6 0 6 3 7 - 0 . 1 4 1 6 3 0 .38500 - 0 . 0 7 2 6 5 -2 .40857 - 0 . 21359 -0 .07780 - 0 . 2 3 7 2 0 - 0 . 1 9 4 0 3 - 0 . 2 6 4 5 1 - 0 . 0 2 2 0 2 -0 .48566 - 0 . 08900 - 0 . 2 8 9 0 7 - 0 . 9 3 064 - 0 . 2 2 3 3 2 0 . 0 0 .23942 -0 .24496\" 0 .45096 - 0 . 1 6 3 4 2 - 0 . 7 6 4 8 9 0 .69624 0 . 0 0 .25767 0 . 12724 - 0 .2 4 0 2 6 - 0 . 5 9 0 7 0 0 .60383 0 . 0 - 0 . 0 5 6 0 2 0 .43788 2 .88005 1.20183 - 0 . 6 1 2 3 4 0 .65952 - 0 . 03003 -0 .32574 -0 .37925 - 0 . 15213 - 0 . 0 7 9 1 7 0 .57092 - 0 . 1 5 842 - 0 . 1 8 9 7 0 - 0 . 5 1 6 6 6 0 .02742 0 . 0 1.19035 - 0 . 0 5 4 4 9 - 0 . 1 8 7 9 3 1.02413 0 .00717 - 0 . 18030 - 0 . 9 6 1 7 7 0 .01503 - 0 . 64891 2.84328 0 . 0 0 . 01432 - 1 . 1 4 5 2 3 -1 .01799 0 . 70028 - 0 . 62505 0 .61995 0 .72080 - 0 . 4 8 7 2 4 0 . 0 0 .10091 0 .31840 0 .01584 - 0 . 1 8 2 4 0 0 .14230 - 0 . 0 3 0 2 4 0 .23445 ' 0 .55887 - 0 . 4 4 6 8 8 0 . 0 1.69815 - 1 . 2 6 2 8 5 0 . 0 0 . 5 7 3 1 0 - 0 . 33685 - 0 . 5 2 2 0 3 0 . 0 0 .68515 0 . 16750 - 1.00744 0 .27442 - 3 . 83030 -0 .43454 1.27257 0 .0 2464 1.82009 0.41281 0 .90925 - 0 . 3 8 8 0 2 0 .86334 0. 20676 - 1 . 6 7 2 3 5 - 1 . 2 4 4 0 0 0 .60412 0 .70544 0 .4563 6 0 . 0 0 .22086 0 .35230 0 .98704 0 .75290 - 0 . 2 5 6 1 7 - 0 . 52123 0 . 0 - 0 . 53521 1.44470 0.80442 - 0 . 3 6 9 1 4 0 .43513 0 . 0 - 5 . 5 8 3 4 6 0 .41384 0 .04335 - 0 . 2 7 7 2 4 2. 10050 - 1 . 0 8 2 9 2 0 .57175 0 . 3 1 7 8 0 0 . 2 7 3 5 9 0.06326 - 0 . 0 2 8 3 4 1. 18888 - 0 . 0 2 5 3 6 24 .82422 - 0 . 2 4 9 8 9 1.34770 0 . 0 0 .00582 2 .27674 - 0 . 1 4 4 7 1 1.91804 10 .51530 0 .31948 - 0 . 4 9 8 6 1 - 1 0 . 2 7 2 2 3 -0 .85211 - 1 . 6 6 7 1 7 0 . 0 1.50692 - 0 . 0 2 4 4 3 5. 12517 0 . 3 5 3 5 6 - 0 . 9 5 5 0 9 - 3 . 0 9 5 5 6 0 .92740 1.16922 0 . 0 - 1 . 8 5 6 6 4 1.74444 - 2 7 . 8 0 1 2 1 1. 52595 - 0 . 0 0 5 5 6 0 .24859 - 0 . 4 3 6 7 5 . - 0 . 0 0 7 1 7 - 0 . 15646 0 . 0 -0 .2175 5 0 .45263 0 . 0 - 4 . 4 2 0 9 6 3 .90921 0 .68951 0 . 0 - 1 . 0 5 2 7 0 - 0 . 1 1 5 2 1 2 . 30533\" 0 . 2 5 3 2 0 1.08576 - 0 . 0 9 3 4 6 -1 .45187 0 . 9 0 0 0 7 3 .11372 0 .22420 ' -7 .9940 3 - 0 . 52481 3 .24147 0 .15404 2 .29206 0 .60571 - 2 . 38597 - 1 2 . 0 1 2 7 3 - 3 . 4 4 3 3 7 0 . 0 - 1 . 1 6 8 4 0 - 1.59580 - 0 . 1 8 0 1 0 - 1 . 21335 12.17865 0.74341 0 .0 - 0 . 6 4 0 5 2 - 3 . 7 2 4 8 7 0.24750 - 0 . 7 7 8 3 3 0 . 14597 0. 0 4 .25171 9 .08600 - 1 . 0 0 4 1 3 0 .21711 0 .29124 - 1 . 5 3 1 6 9 - 0 . 4 0 9 4 5 1.88266 0 .68227 0 . 51811 - 1 . 18462 -1 .34780 1.05171 1.45645 - 0 . 8 0 6 9 8 1.55669 0 . 0 1.00258 1.72724 - 1 . 6 6 8 2 8 - 6 . 0 0 6 5 6 \" 6 .48324 -0 .16651 0. 72807 - 7 . 50906 0 . 06522 1. 74429 0. 0 0 .94988 - 1 2 . 8 5 2 9 4 6 .38090 - 0 . 7 5 6 4 2 2 .55054 - 2 . 9 3 7 7 9 1. 28469 14.14331 0 . 0 - 0 . 66195 - 5 . 8 7 9 7 9 - 0 . 9 4 0 0 7 1.89542 _ 0 .27973 1.84016 - 1 8 . 72362 33 .47461 -27 .41634 0 . 0 8.69985 - 9 . 2 0 5 5 4 0 . 0 5 .99319 - 5 . 6 0 3 8 6 0 .40069 0 . 0 1.21242 3 .25682 4 . 0 9 6 7 8 ' - 0 . 4 6 4 3 7 - 2 . 1 8 7 0 6 0 .57868 -1 .02162 - 0 . 8 2 4 4 9 -1 .50518 0.94973 -2 .02501 - 2 . 2 3 6 2 4 1.74904 - 2 . 0 9 2 4 6 - 2 . 3 5 7 9 7 -1 .67023 - 0 . 3 1 1 5 5 - 1 4 . 8 2 0 6 6 - 0 . 2 3 5 0 1 0 . 0 - 3 . 1 8 0 5 9 18. 86780\" -3 .67038 - 1 . 9 9 4 8 4 3.51379 1.35329 0 . 0 - 2 . 2 5749 -7 .87424 0.96409 - 5 . 0 8 7 0 3 - 1 . 9 8 7 5 4 0. 0 - 6 . 8 1 7 1 5 14.67192 - 0 . 2 7 0 4 0 1.70799 1.22496 - 0 . 4 5 8 1 0 . - 1 . 5 0 8 9 2 0 .32026 0.13366 2.90469 - 3 . 8 0 0 9 5 1.02761 J 3 . 6 4 1 4 7 5. 4 4 1 7 7 0 . 2 6 8 7 6 - 3 2 . 2 4 7 1 0 0. 0 - 0 . 4 7 8 6 1 - 0 . 0 9 2 7 1 1 . 6 7 4 7 3 5 . 6 2 0 4 0 - 2 0 . 3 4 1 1 9 - 0 . 7 4 6 0 3 - 0 . 4 1 3 5 6 1 0 . 0 9 0 4 2 3 . 3 7 9 7 7 - 0 . 8 5 4 0 0 0 . 0 - 2 . 3 8 4 7 2 - 0 . 4 4 4 9 8 1 . 6 2 4 9 2 - 1 . 6 3 2 6 3 - 0 . 6 6 0 9 3 1 3 . 6 8 8 1 1 - 1 . 2 2 2 9 1 - 4 . 0 5 8 6 0 0 . 0 - 2 . 2 5 3 2 8 1 . 8 1 4 7 4 1 6 . 6 7 0 3 5 - 0 . 5 7 1 7 0 4 . 1 9 1 7 1 - 7 . 0 7 5 7 1 - 1 7 . 9 6 0 8 6 - 5 2 . 2 0 5 0 2 4 2 . 2 4 1 9 4 0 . 0 1 3 6 . 0 3 2 8 5 - 1 1 8 .8 1 0 7 3 0 . 0 - 3 1 . 3 3 0 2 5 ) 2 3 . 8 5 2 7 2 0 . 5 1 1 7 6 0 . 0 3 . 5 6 6 0 8 2 5 . 2 7 9 4 0 - 1 3 . 8 4 7 9 6 - 3 . 8 6 0 0 4 1 . 9 8 3 2 0 2 . 7 5 3 2 2 8 . 8 5 8 7 2 - 4 . 0 1 2 7 1 - 5 . 9 8 8 1 5 - 0 . 6 3 2 3 7 5 . 2 7 8 4 5 - 1 . 9 4 5 2 4 - 0 . 9 5 8 0 4 - 1 4 . 8 3 3 2 8 - 1 1 . 5 3 4 6 3 0 . 9 6 9 8 2 - 1 2 . 8 0 0 1 9 - 4 7 . 8 3 9 3 6 1 . 3 2 2 1 7 0 . 0 - 2 . 4 0 1 0 7 ' 5 8 . 2 2 4 2 0 - 3 2 . 1 8 1 9 5 - 5 . 0 0 9 1 7 1 5 . 1 6 5 2 5 3 . 6 4 4 6 8 0 . 0 4 . 1 6 9 6 4 4 6 . 0 4 9 5 3 -0 . 2 0 9 1 5 1 0 . 3 5 4 3 5 - 1 . 0 5 0 8 7 0. 0 - 1 6 . 4 1 3 2 4 - 2 3 . 2 1 5 7 0 2 . 8 4 2 9 9 2 . 2 1 4 8 8 2 . 4 9 5 0 3 - 6 . 3 9 4 5 5 5 . 3 0 2 7 7 3 . 2 3 4 4 5 - 1 6 . 2 2 4 2 7 4 . 3 1 2 8 1 1 1 . 4 9 6 4 2 - 0 . 1 6 9 1 8 8 0 . 7 6 5 5 2 4 . 3 1 1 6 6 - 0 . 3 8 7 1 8 - 6 0 . 1 4 3 9 7 0 . 0 - 1 . 4 3 6 6 9 - 1 2 . 8 4 5 8 0 - 1 0 . 0 5 2 4 7 3 . 3 8 9 4 0 - 1 7 . 4 3 9 9 6 0 . 7 1 0 1 9 1 . 3 0 5 4 2 2 0 . 0 8 3 2 7 - 1 . 7 7 6 8 4 - 1 . 7 8 9 9 4 0. 0 0 . 9 3 1 6 3 - 4 . 0 4 4 9 2 4 . 9 0 7 2 1 - 0 . 6 3 4 8 5 -1 . 8 8 2 6 9 - 1 7 . 8 5 8 4 7 1 . 4 5 7 3 9 3 . 2 4 1 7 3 0 .0 4 . 7 5 5 9 9 - 1 . 9 1 9 6 3 - 3 . 1 7 4 5 3 0 . 1 3 8 1 9 5.. 4 3 8 2 4 - 7 . 3 4 3 5 4 - 2 . 1 2 8 8 8 - 1 3 . 3 0 0 5 8 4 . 3 6 5 4 6 0 .0 2 8 . 5 1 6 3 1 - 1 8 . 7 8 5 2 6 0 . 0 - 1 2 . 2 5 7 7 5 1 6 . 0 3 7 5 7 0. 1 1 4 8 7 0 .0 0 . 3 8 0 1 5 1 . 8 7 3 0 4 - 1 0 7 . 3 7 5 1 2 ^ 0. 1 7 8 6 1 2 8 . 7 0 4 9 0 0 . 0 3 1 7 7 3 3 . 2 4 9 9 1 1 . 4 0 5 7 2 4 2 . 8 3 0 4 7 0 . 3 7 0 0 9 1 0 . 9 3 0 3 2 0 . 9 2 8 1 7 - 1 . 2 6 2 3 2 - 5 . 7 1 6 1 6 1 . 0 8 6 1 4 1 . 8 7 4 4 7 4 . 7 8 6 3 4 12.-22 5 0 6 - 6 . 2 2 5 5 1 0 . 0 2 . 2 0 3 2 3 - 4 . 3 9 1 9 5 - 5 . 3 6 3 8 6 0 . 9 0 5 1 0 - 0 . 5 7 2 4 1 - 0 . 4 8 8 5 5 0 . 0 1 . 6 1 4 4 5 1. 9 3 8 8 9 0 . 2 8 6 0 9 2 . 1 2 7 2 3 1 . 2 1 1 4 8 0 . 0 - 1 . 7 8 7 4 3 - 5 . 4 0 2 2 6 1 . 3 8 8 6 1 - 0 . 0 8 4 8 3 - 0 . 4 2 9 3 6 - 8 4 . 3 4 3 5 7 ' 2 2 . 8 5 6 4 5 2 5 . 4 1 5 0 4 3 6 . 1 5 4 0 2 7 . 9 0 4 0 5 - 1 . 6 0 4 5 2 2 . 8 3 2 2 6 FACTOR SCORES ON ROTATED FACTORS SUB J ECT 1 — - 1 . 9 4 8 3 6 0 . 2 9 0 5 5 0 . 0 4 7 0 4 4 . 2 3 1 9 7 - 0 . 0 2 7 8 0 0 . 0 1 8 1 4 1 . 1 9 2 0 4 - 0 . 7 0 8 9 4 - 0 . 0 0 2 1 5 0 . 2 1 7 3 6 0 . 4 5 0 1 0 - 0 . 0 6 0 7 6 0 . 1 2 5 2 6 0 . 0 0 7 7 0 - 0 . 0 1 4 9 7 0 . 1 3 0 8 3 - 0 . 0 0 7 8 2 0 . 0 0 3 3 2 - 0 . 3 9 5 9 5 0 . 5 2 1 4 6 0 . 0 0 5 9 8 0 . 4 3 7 8 7 0 . 1 1 7 4 4 0 . 7 0 1 7 1 0 . 3 2 7 8 7 - 0 . 1 2 8 9 9 - 0 . 0 1 4 6 9 SUBJECT ___.____.0..A3.0-9J4_ 2 - 0 . 4 6 3 0 6 - 4 . 2 0 2 1 6 0 . 5 0 0 8 6 - 0 . 0 8 3 5 6 - 0 . 5 4 5 3 1 - 0 . 4 9 9 3 7 1 . 2 8 5 1 9 2 . 7 0 5 5 7 0 . 2 6 0 9 6 0 . 5 5 2 5 8 - 0 . 6 7 1 1 2 - 0 . 1 2 9 3 8 - 0 . 3 7 2 0 2 - 0 . 9 0 0 1 1 0 . 1 4 6 5 6 0 . 3 6 7 0 7 0 . 1 0 4 0 8 0 . 1 0 3 5 9 0 . 0 5 1 2 7 - 0 . 4 6 2 2 9 0 . 0 0 6 0 0 0 . 0 1 1 5 4 - 0 . 0 4 6 3 4 0 . 1 4 9 0 2 0 . 1 4 7 6 7 0 . 2 6 2 9 0 SUBJECT 1 . 6 6 8 9 5 - 0 . 0 9 3 . 1 5 3 - 0 . 2 6 5 6 2 0 . 3 0 4 4 2 -0 . 0 3 4 2 4 -0.3367'6 0 . 3 6 8 4 9 - 0 . 5 9 1 8 1 0 . 0 1 5 3 0 - 0 . 5 2 2 0 7 4 . 9 0 6 8 2 - 0 . 3 5 4 8 2 - 0 . 4 7 8 6 0 - 0 . 1 4 2 4 1 0 . 4 1 1 9 4 - 0 . 2 0 2 4 8 0 . 3 2 8 7 7 0. 1 8 8 3 9 0 . 1 8 2 3 9 - 0 . 1 6 5 1 9 - 0 . 5 9 3 2 0 0 . 0 3 8 2 9 - 0 . 3 6 2 4 8 0 . 0 6 7 5 4 0 . 5 3 1 3 4 - 0 . 0 7 4 8 9 0 . 0 1 1 0 0 SIIR.lFf.T 4 0 . 4 0 7 6 9 - 0 . 2 1 3 1 9 0 . 3 8 7 3 7 0 . 5 2 1 5 0 - 0 . 6 4 2 5 4 0 . 3 2 2 6 5 - 2 . 8 2 1 2 4 0 . 3 8 1 1 9 - 0 . 0 9 2 0 6 - 0 . 4 1 6 0 7 - 0 . 5 3 4 4 3 - 0 . 2 7 5 7 9 0 . 3 2 5 7 0 - 0 . 4 0 4 9 2 - 0 . 1 4 3 4 8 0 . 0 9 4 8 8 2. 1 9 1 6 1 - 0 . 0 1 1 2 5 0 . 5 4 1 5 3 - 0 . 1 5 4 9 1 0 . 0 2 6 6 6 - 1 . 5 7 5 8 3 0 . 5 4 6 6 4 - 3 . 0 2 9 1 9 0 . 0 5 2 1 7 0 . 1 5 3 6 0 - 0 . 1 4 6 5 4 SUBJECT 2 . 2 4 1 3 1 5 - 0 . 0 9 1 6 8 0 . 0 0 1 8 0 - 1 . 5 4 2 0 6 - 0 . 2 7 0 7 0 - 0 . 9 0 4 1 0 0.2 9 2 8 0 0 . 7 3 3 9 4 - 1 . 6 6 7 1 7 0 . 6 6 6 7 3 0 . 2 9 1 5 3 - 1 . 4 9 9 9 3 0 . 8 9 4 0 8 - 0 . 6 9 7 1 9 - 0 . 6 2 3 7 1 - 0 . 0 4 3 4 5 1 . 6 4 4 0 0 0 . 7 2 8 3 2 1 . 9 9 1 8 2 0 . 0 4 6 9 6 - 2 . 1 4 8 9 7 0 . 0 5 7 3 4 - 0 . 1 0 0 3 3 -0 . 0 3 7 2 9 - 0 . 2 8 2 6 6 - 0 . 4 8 4 7 2 0 . 4 4 3 4 4 SUBJECT 0 . 3 2 4 3 5 0 . 1 8 7 0 7 6 0 . 3 2 1 2 2 0 . 2 3 1 4 9 0 . 1 5 8 3 8 3 . 9 8 6 4 2 - 0 . 9 7 3 5 7 - 1 . 1 3 8 7 4 - 0 . 3 9 0 8 1 - 0 . 1 4 4 3 5 - 0 . 3 8 3 2 7 0 . 3 8 4 6 3 1 . 7 1 6 4 1 - 0 . 7 0 1 6 9 1 . 0 4 5 3 5 - 0 . 7 6 4 7 8 1 . 2 6 3 5 0 0 . 3 9 1 4 3 1 . 1 7 6 8 0 - 0 . 6 5 3 5 0 J - 0 . 0 0 1 7 5 - 0 . 3 6 4 2 9 0 .11268 0 .70490 0 .46557 - 0 . 3 1 2 3 6 -0 .23635 SUBJECT 7 0.48085 0 .33132 -0 .09988 -0.01115 -1.49080 1.68790 -0 . 10351 0. 8704\"6 -1 .43527 2 .14975 -0. 12910 0 .45087 -1 .10869 -1 .22924 0 .20076 -0.55057 -2 . 19880 0 .47100 -0.34604 0 .39643 0.58597 -0.92540 -0.07223 •0 .38190 •0 .77100 0 .26049 0 . 22914 SUBJECT 2 .90 5 88. - 0 . 4 3 3 6 9 0 .61940 ___0. 2779 5 -0.22560 1. 11527 1.00236 -0 .806 54 -0.34445 •0. 65831 0 .03756 -1.33400 -0 .66914 0.19991 -0.136 32 -0 .91881 1.94108 0 .11239 -0 .70686 •0.61322 0.21596 0 . 2 0 7 0 7 1.99757 1.8586 2 -0 .17520 • 0 . 0 5_5_85 6. 16066 SUBJECT 9 - 0 . 2 4 8 9 0 0 .06660 0 .24403 0 .15305 0 .0365 6 -0 .37548 0 .38103 -0. 42935 1.35347 1.52688 :2._911.43. 0 .46934 -0.14012 1 .68948 0 .69541 -0.234 60 -0 .32461 0 .20815 1.26433 -0 .52676 -0 .12368 0 .76086 1.98098 •0 .37990 1.22112 -0 .24624 1.23819 SUBJECT 10 0 .02783 - 0 . 1 3 4 7 7 - 1 . 6 6 6 6 3 •0 .28798 •1 .21262 0 .04488 0 .37201 0 .90077 -0.36837 0 .75073 1.00502 -1.54560 -0. 36485 0 .90733 0 .08738 -0.23466 0 .67938 0 .20997 -0 .18138 -0.52530 0 .21177 0 .35071 -0.48972 -0.25006 2 .61440 - 1 . 16958 0 .58330 SUBJECT 11 - 0 . 8 4 9 8 5 -0.08012 0 .12764 - 1 . 2 4 9 0 6 0 .73031 0 .05727 1.21426 - 2 . 3 2 6 7 0 1 .10049 1 .53547 - 0 . 7 2 3 8 3 -1 .11328 I . 19566 0 .80818 0 .11179 0 . 0 3620 0 .89626 •0 .83104 -1 .09151 0 .07707 -0 .58663 -0 . 02010 0.821 14 0.03708 1.28628 - 1 . 2 6 6 0 1 0 .23971 SUBJECT 12 0 .48180 0 .54197 •0 .20987 1.98697 0 .26604 0 .80980 2 .75519 1.08214 -0.61183 •0 .63811 -0.50718 -0.21301 -0.77665 -0.37105 •1 .07373 1 .72274 •0 .39392 1 .179 83 0 .25077 •1 .16899 - 0 . 1 6 1 3 0 - 1 . 1 2 0 3 1 0 .87820 0 .61842 -0 .27102 -0 .49105 -0 .51384 SUBJECT 0 .90554 0 .84448 0 .05270 13 -0.08030 0 .75696 -2.14677 0 .45135 -0. 3135\"0 0 .13949 1.1480 3 0 .16935 •1 .50050 -0.70157 -1 .67103 •0 .83334 •0 .54309 1 .09004 0 .25738 0.52775 0 .11165 0.14422 -0. 16138 •2 .49011 0 .2 056 8 -1 .98446 -0 .02155 1. 2 7861 SUBJECT 14 0 .29475 -0 .96721 1.26358 •0 .25820 0 .81079 0 .00002 0 .22335 -0.77564 1 .10957 0 .00586 0 .43534 - 0 . 3 0 9 3 8 -0 .02134 -0 .23064 0 .39638 0 .62782 1.39561 •0 .29788 0 .09120 1.28090 -0 .21288 - 0 . 3 6 5 2 6 - 0 . 1 4 2 8 3 - 0 .06668 2 .35322 i_9689.1_ 1 .05161 SUBJECT 15 -0 .71481 2 .05491 -0.32854 0 .38482 0 .08856 0 .44063 -2.21362 -0.77072 •0 .32399 -1.72409 •0 .04894 -1 .23609 -1.01208 -0 .15276 0 .63524 1.46460 1 .30675 - 1 . 0 4 1 7 5 - 1 . 4 0 8 2 3 - 0 . 4 8 3 4 0 - 0 . 3 2 0 2 4 0 .44326 0.38021 •0 .70686 1.12028 -0 .89427 1.51810 SUBJECT 16 - 0 . 2 1 0 7 1 - 2 . 7 0 5 5 6 0 .46112 0 .10029 1.99276 0 .77298 -0 .55230 0 .47797 0 .36787 •0 . 56536 •1 .26476 -0.19116 -0.28598 0 .46118 -0.09021 -0.35127 -0.93594 -0 .14870 -1 .32320 •0.41243 -0 .231 19 -0 .91015 -1 .59705 0 .24014 -0 .1 7242 •2 .55721 0 .94773 SUBJECT 17 0 .74309 -0.04745 0 .25145 - 0 . 3 2 4 0 5 1.10572 •0 .35832 0.25592 - 0 . 2 4 5 2 6 0 .26732 - 0 . 0 2 1 2 4 - 1 . 0 5 6 8 3 - 0 . 2 4 1 1 3 1.65326 •1 .42831 SUBJECT 18 - 0 . 4 9 1 8 4 1.30130 -0.05688 0 .25131 •0 . 54433 0 .62849 -1 . 67929 •0 .52885 -0.27724 -3.14928 -1.32045 -0.00587 1 .26844 0.01277 0 .20369 -0 .34260 -0. 32538 -0.60590 1.23934 1.59102 -0.02945 0 .41472 -0 .11326 -0.33734 0 .04834 -2 .03513 0 .26595 0 .81265 0 .67642 -0 .50454 - 2 . 01817 1.17038 •1.31755 - 0 . 6 6 9 3 6 - 1 . 6 1 6 8 6 - 1 . 7 8 2 1 6 - 0 . 0 3 2 5 1 1.45805 -0 .05928 0.29041 SUBJECT 19 0.12080 0 .91628 1.23834 - 0 . 3 8 9 1 8 1.30978 0 .84304 0 .14312 - 1 . 2 5220 - 1 . 7 7 5 1 9 0 . 0 7 7 2 1 - 0 . 7 9 4 0 8 1.83305 - 0 . 8 7 0 7 3 0 .52307 - 0 . 5 6 2 0 0 - 0 . 3 2 6 0 4 1.13491 - 0 . 1 4 0 2 7 0 . 00757 1 .48302 0.19076 0 .61947 - 1 . 1 5 7 6 3 - 0 . 1 6 0 9 1 - 0 . 0 0 6 6 9 0.50671 - 1 . 2 4 1 2 3 ) SUBJECT 20 -0 .88155 0 .13847 0 .38862 - 0 . 4 7 1 4 8 - 0 . 7 6 1 1 6 - 0 . 0 7 6 2 9 - 0 . 5 1 1 4 8 -0 .66534 0 .08073 1.45330 - 0 . 8 9 4 0 6 0 .47777 - 0 . 7 5 7 8 2 - 0 . 1 4 5 1 3 - 1 . 1 3 0 5 3 - 0 . 3 2 3 3 9 0 .12073 1.02322 - 0 . 4 8 7 1 0 - 0 . 5 4 2 8 6 - 0 . 2 9 4 7 6 0 .07749 - 4 . 2 9 7 3 1 0 .09397 - 0 . 5 1 6 0 5 - 0 . 0 3 010 - 0 . 7 3 3 9 7 SUBJECT 21 -0 . 5 1 9 9 3 _ _ J3.J_0J-.2J. . ... - 0 . 3 6 7 0 8 - 0 . 6 4 0 7 3 -0 .31847 0/8999% -0 .34616 1.91278 - 0 . 6 8 7 3 8 1.28605 0 .86278 - 0 . 5 0 1 4 0 - 0 . 7 8 6 4 2 0 .37457 0 .24472 0 .09793 - 0 . 2 2 1 3 7 - 1 . 2 8 1 8 1 - 0 . 0 7 3 8 9 - 1 . 4 6 8 7 1 3 .05837 - 0 . 7 2 8 2 4 1.74634 - 0 . 8 9 8 2 3 0 .29664 0 .00450 - 0 .1 5 0 0 3 SUR.) EOT ?? -0 .39019 0.39311 _ ' -0...71.78.0 .. -0 .32310 0 .57509 , O . J 7369 0 . 33321 -0 .24772 1. 25582 - 0 . 7 1 8 2 8 0 .00450 0 .65908 - 0 . 4 9 4 7 7 0 .03459 0 .54509 - 0 . 11715 1.05925 0 .57711 - 0 . 2 6 2 0 0 0.532 36 0.36304 - 0 . 5 9 8 7 0 , - 0 . 9 2 9 4 2 0 .21095 1.15139 - 0 . 3 3 9 1 4 - 1 . 0 5 0 8 9 SUBJECT 23 - 0 . 2 9 3 5 5 - 0 . 2 1 5 5 4 0.25096 -0 .41433 -0 .68668 -0 .20811 - 0 . 9 4 2 79 0 .30045 - 0 . 0 7 4 0 4 - 0 . 542 75 0 .25539 - 0 . 8 2 2 9 9 - 0 . 4 3 0 2 8 1 .94314 0 . 9 6 6 7 0 - 0 . 2 29 33 - 0 . 2 2 8 2 1 - 0 . 3 5 4 5 9 0 .12932 0.3TB3 80 - 0 . 3 1 5 3 6 - 0 . 0 1 1 9 7 0.94188 0.21826 0 .13534 - 1 . 13386 - 1 . 3 8 2 3 6 SUBJECT 24 -0 .84599 0 .3 7053 -0 .17746 -1 .47633 0 .42511 -0 .570 23 - 0 . 2 1 1 1 0 -1 .11327 - 0 . 8 2 7 2 8 0 .50630 -0 .06917 0 .01175 -1 .06454 0 .50398 - 0 . 4 0 1 4 6 - 1 . 0 3 0 0 1 - 0 . 5 7 8 8 9 - 0 . 0 7 8 2 8 1.59448 0 .49349 - 1 . 1 7 0 4 5 - 0 . 6 6 5 6 1 0 . 6 5677 -1 .00022 1 .61808 -0 .40728 - 0 .39760 SUBJECT _ 25 - 0 . 5 9 5 3 6 0 .0 7033 0 .05747 - 0 . 2 7 7 5 9 - 0 . 3 3 1 5 9 0 .98344 0 .16362 - 0 . 5 6 1 0 6 - 0 . 3 5 7 9 3 0 .25432 0 .51588 1.14546 - 0 . 8 449 3 0 .63694 - 1 . 14475 - 0 . 0 9 1 9 8 0 .46594 - 0 . 2 1 1 3 6 1.03493 0 . 1 8 0 4 3 - 0 . 1 9 1 9 5 0 .01929 - 0 . 2 8 8 1 7 - 0 . 0 9 0 1 5 0 .58380 - 0 . 0 7 8 8 4 0.57768 SUBJECT 26 --L.jD.2al4 - 0 . 3 1 7 6 7 0 .30760 - 0 . 3 9 8 2 7 - 0 . 6 6 5 2 4 0 . 01575 - 0 .08874 2 .10721 - 0 . 8 9 6 0 4 - 0 . 7 7 9 78 - 2 . 4 0 1 9 0 - 1 . 4 3 3 7 0 -0.2.3273 - 1 . 4 1 5 6 7 - 0 . 1 4 9 27 - 0 . 4 0 3 4 3 0 .78873 1.28933 - 1 . 6 3 1 8 5 0 .58221 1.12444 -0 .06582 0.68644 0 .01081 1.31369 -1 .1232 8 - 0 . 3 7 8 4 4 SUBJECT 27 - 0 . 9 9 6 7 3 - _ 0 . . 3_7_6.8A. - 0 . 1 9 3 2 6 -0. . 12681 0 .14481 0/41847 - 0 . 1 8 1 5 1 1.02248 - 0 . 6 1 9 65 1.27792 1.535 5 8 0 .38198 1.67767 0 . 1 9 1 5 8 - 0 . 8 4 1 1 9 0 . 3 3 3 3 3 0 .41900 0 .06949 - 0 . 5 6 3 1 1 1.74987 -0 .12694 0 .16105 0 .20138 0 .55832 - 2 . 1 3 8 1 2 0 .28829 0 . 04571 SUBJECT 28 .... - 0 . 6 2 1 3 2 0 .74354 0.024.70 - 0 . 3 1 6 1 9 -0 . 30915 1.38329 0 .30300 - 0 . 7 4 2 6 1 1.07703 - 0 . 3 6 5 4 1 - 0 . 0 6 3 4 5 - 1 . 4 5 2 4 8 -0 . 74167 - 0 . 2 2 0 2 2 -0 .30761 -0 .08048 0 .20271 -0 .80002 0 .16523 0 .03456 -0 .72422 0 .59325 0 .00260 - 0 . 5 2 843 - 0 . 1 4 0 3 2 - 0 . 0 5 1 5 5 0 .128 86 SUBJECT 29 1.16062 - 0 . 1 1 0 5 6 0 .43903 -0 .15417 1.65128 - 0 . 3 7 9 8 8 0.162 44 - 0 . 8 1 7 6 2 0 .81133 - 1 . 4 1 1 1 7 -0 . 04879 1.08558 - 2 . 4 3 7 6 5 - 0 . 2 7 7 4 7 0 .005 09 0 .3 5960 1.00679 2 .29142 - 0 . 6 4 4 0 5 1.27859 0.13856 - 0 . 3 5 6 0 0 0 .47795 - 0 . 4 9 5 2 2 - 0 . 5 1 4 2 7 - 0 . 2 4 5 2 6 1.19496 SUBJECT 30 -0 .17354 -0 .78634 - 0 . 0 4 0 4 2 0 .39149 - 0 . 0 8 5 3 9 -0 .950 06 0 .73369 0 .62168 1.06481 - 0 . 3 3 1 9 1 - 0 . 1 3 9 8 9 - 0 . 9 3 2 4 7 2.97536 - 0 . 5 3 9 6 0 1 .16998 - 0 . 4 5 6 8 1 -0 .44010 0 .61859 - 0 . 7 1 7 5 1 - 1 . 1 0 3 4 7 1.125 51 0 .46121 -1 .35493 - 1 . 8 4 0 0 3 1.41563 0.15996 0 .42890 SUBJECT 31 0.05366 1 .78112 - 0 . 8 7 8 7 3 •0 .11768 0 .69122 1.66016 0 .23303 -0. 11333 1 . 8 7 2 9 0 -0.00553 0 .03039 0 .47758 2 .91168 •1 .07610 -0 .55276 -0 . 14347 0 . 16 593 -0 .14897 -0 .42892 - 1 . 16468 -0.32318 1.12365 -0.47819 - 0 . 6 1 5 3 0 -0 .55170 -0. 54517 -0 .34734 SUBJECT 32 -0 .58342 •1 .01744 0 .47574 -0 .16196 0 .31208 - 0 . 0 2 3 9 2 0 .26544 1 .22912 - 1 . 6 6 4 9 8 1.04528 0 .38037 - 0 . 4 8 9 2 8 2 .54606 1.37436 • 0 . 92118 - 0 . 0 5 2 5 1 0 .74474 0.29832 •1.89633 0.21694 0 .41139 0 .89663 - 0 . 0 4 9 9 4 -0.38885 - 0 . 4 4 0 0 0 1 .85882 1.09172 MEANS OF THE FACTORS - 0 . 0 0 0 0 0 - 0 . 0 0 0 0 0 G.00001 - 0 . 0 0 0 0 1 0 .00002 0 .00004 0 .00000 0 .00002 -0. 00000 •0 .00003 0 .00001 C.00003 -0.00000 0 .00001 •0 .00003 0 .00000 -0. 00000 0 .00000 0 .00000 - 0 . 0 0 0 0 8 - 0 . 0 0 0 0 5 0 .00001 __P_L°OOO_L -0.00(317 - 0 . 0 0 0 0 1 o • o o o o i -6 .00004 STANDARD DEVIATIONS OF THE FACTORS 0 .99226 0 .99827 0 .99980 0 .99710 0 .80052 0 .99994 0 .98878 1.00013 0 .99850 0 .99979 0 .99744 0.99882 1.00011 0 .99988 0 .99993 0 .28552 1.00010 0.30033 0 .99804 1.00021 1.00676 0 .99955 __A0_QP6_ 0.98600 0 .99982 J . .00082 1 .00034 CORRELATIONS OF THE FACTORS R0W._._1 _ _______ 1.00000 - 0 . 3 2 5 1 3 0 .02183 0 .02534 0 .01714 0 . 00211 -0 .00031 0 .00244 0 . 0 2 1 6 5 - 0 . 0 0 5 9 6 0 .00714 - 0 . 0 0 4 5 6 - 0 . 0 2 4 5 3 0 .00475 - 0 . 0 0 2 3 4 - 0 . 0 0 0 3 1 - 0 . 0 0 1 4 8 0 .00163 0 .00301 0 .00036 0 .00027 0 .00016 - 0 . 0 0 0 6 2 0 .00015 - 0 . 0 0 0 3 0 -0 .00109 0 .00061 ROW 2 -0_.J3__5_._3_ - 0 . 0 0 3 9 1 0 .00913 J . ooooo -0.01987 -0.00127 0 .18259 -0 .03593 -0 .00134 0 .03740 -0. 022 72 •0 .00146 0 .06644 - 0 . 0 1 0 1 9 0 .01750 -0.00111 0 .00108 0 .00377 - 0 . 00153 -0.008 10 0.00009 - 0 . 0 0 9 9 7 0 .00341 0 .03936 0 .01263 - 0 . 0 0 6 4 9 - 0 . 0 0 1 8 5 ROW 3 0 .02183 _ -0 .00314 . - 0 . 0 0 0 8 1 0 .18259 __.0_0_2_L0_ 0 .00018 1.OOOOO p.. 0.1155 0 .00049 •0 .01203 •0 .00261 0 .00041 -0.01357 •0 .00057 0 .00242 - 0 . 0 0 0 7 3 -0 .00266 0.00108 0 .00010 -0 .00686 0 .00465 - 0 . 0 0 0 1 0 -0 .00106 -0 .01212 -0 .00194 0 .00268 0 .00009 ROW 4 0 .02534 0 .00009 - 0 . 0 0 0 5 4 0 .03740 0 .00035 0 .00006 -0 .01203 0 .00348 -0.0000*9 1.00000 - 0 . 0 0 0 5 6 - 0 . 0 0 0 0 3 -0 .00360 - 0 . 0 0 0 1 7 - 0 . 0 0 0 2 5 0 .00118 -0 .00020 0 .00312 - 0 . 0 0 0 7 7 0 .00012 0.00217 - 0 . 0 0 0 3 0 - 0 . 0 0 0 3 3 - 0 . 0 0 1 8 4 - 0 . 0 0 0 4 1 0 .00084 0 .00002 ROW 5 0 .01714 0 .06644 - 0 . 0 1 3 5 7 - 0 . 0 0 3 6 0 1.00000 0 .00139 -0 .00159 -0 .00021 -0 .00396 0 .00087 - 0 . 0 0 0 8 8 - 0 . 0 0 0 4 3 0 .00098 0 .00007 0 .00352 - 0 . 0 0 0 1 8 - 0 . 0 0 0 8 6 0 .00006 - 0 . 0 0 0 3 3 -0 .00026 - 0 . 00021 0 .00310 0.00067 0 .00006 - 0 . 0 0 0 2 9 - 0 . 0 0 0 9 2 -0 .00009 ROW 6 0.00211 0 .00025 - 0 . 0 1 0 1 9 - 0 . 0 0 0 4 3 0 .00242 - 0 . 0 0 1 1 8 0 .00118 - 0 . 0 0 0 2 6 0 .00139 -0 .00001 1.00000 0 .00009 0 .00014 -0 .000 15 - 0 . 0 0 0 1 0 - 0 . 0 0 0 0 4 0 .00162 0 .00023 - 0 . 0 0 0 2 4 0 .00003 0 .00005 - 0 . 0 0 0 2 3 - 0 . 0 0 0 1 7 0 .00008 - 0 . 0 0 0 1 9 0 .00010 0.00052 _RO.W_ 7 - 0 . 0 0 0 3 1 -0 .00015 - 0 . 0 0 0 1 8 0 .01750 0 .00058 0 . 0 0 0 1 6 - 0 . 0 0 2 6 6 0 .00079 - 0 . 0 0 0 2 6 - 0 . 0 0 0 7 7 0 .00075 0 .00021 - 0 . 0 0 1 5 9 - 0 . 0 0 0 0 5 0 .00002 0 .00014 - 0 . 0 0 0 0 5 0 .00421 1 .00000 0.00008 -0 .00164 0 .00050 0 .00005 - 0 . 0 0 1 0 7 - 0 . 0 0 0 3 8 0 .00015 - 0 . 0 0 0 1 6 J ROW 8 0.00244 0.00012 0.00011 -0.00997 -0.00013 0.00023 -0.00010 0.00016 0 .00060 -0 .00030 -0.00035 0.00022 -0 .00021 -0.00003 0.00003 -0.00010 -0.00004 -0.00399 0.00050 0 .00003 -0.00197 1.00000 -0 .00006 -0.00006 -0.00004 0.00014 0 .00013 N ROW 9 / 0 .02165 -0.00041 -0_._0QO44_ 0 .03936 0.00055 .0.00022 -0.01212 0 .00277 0.00056 -0.00184 -0.00059 0.00025 -0.00396 -0.00019 -0.00002 0.00162 -0.00013 -0.01280 -0.00107 0. 00050 0.00624 -0 .00006 -0.00051 1 .00000 -0.00046 0.00065 0.00060 \\ ROW 10 -0.00596 -0.00649 0.00268 0.00084 0.00087 - 0 . 0 0 0 2 4 0.00015 0.00014 0.00065 1.00000 -0.00008 0.00008 ' -0.00004 -0.00008 -0.00039 -0 .000.56 -0.00002 -0.00019 -0.00006 0.00006 0.00010 -0.00356 -0.00008 0.00077 0.00006 0.00024 0.00013 ROW 11 0.00714 1.00000 -0.0 0391 0.00014 -0.00314 0 .00001 0.00009 0.00053 - 0 . 0 0 0 8 8 0.00009 0.00025 -0.00011 -0.00015 0.00019 0.00012 -0.00005 -0 .00041 -0.00018 -0.00008 -0.00005 -0.00023 0.00008 0.00008 -0.00014 -0.00003 0.00451 0 .00318 .^ROW- -12 . - _ -0.00456 0.00014 0.00039 -0.01987 1.00000 -0.00008 0.00230 -0.0OO51 0.00009 0.00035 -0.00033 0.00063 0.00098 -0.00008 -0.00014 -0.00043 -0.00010 0.00405 0.00058 -0.00005 -0.004 97 -0.00013 0.00006 0.00055 0.00017 -0.00004 0.00007 ROW 13 -0 .J3.2453 _ -0 ..03593 0.01155 0.00348 0.00352 -0.00118 0.00079 0.00016 0 .00277 -0.00039 0.00001 0.00052 -0.00051 -0.00017 1 .'00000 0.00038 0.00040 0.00009 - 0 . 0 0 0 2 3 -0.00002 0.00026 -0.00108 -0.00060 0 .00282 0.00041 0 .00046 0.00002 ROW 14 0.00475 0.00053 -0.02272 -0.0003.3 -0.00261 0.00040 -0.00056 1.00000 -0.00086 -0.00015 -0.00026 -0.00001 0.00075 0.00016 -0.000.35 -0 .00026 -0.00059 0.00013 -0.00002 -0.00030 -0.00009 -0.00019 - 0 . 0 0 0 3 5 -0.00015 -0.00013 0.00457 -0.00912 ROW 1 5 -0.00234 0.00009 - o . - . - a o . Q . o 4 -0.00111 -0.00008 -0.00112 -0.00057 -0.00023 0.00102 -0.00017 -0.00015 -0.00001 -0.00033 1 . 00000 0.00104 -0.00001 0.00016 0.00932 -0.00005 0.00016 -0.00114 -0.00003 -0.00010 -0.00019 0.00030 -0.00006 0.00034 ROW 16 -0.00031 0.00.377 -0.00073 -0.00020 -0 .00021 0.00009 -0.00005 -0.00004 -0.00013 0.00010 -0.00011 -0.00005 '-0.00010 -0.00131 0.00026 -0 .00 300 -0.00001 -0.00039 0.00016 - 0 . 0 0 7 0 6 1.00000 -0.09505 0.00018 -0.03318 -0.00096 0.00050 0.00383 ROW 17 -0.00148 0.00019 -0.00810 -0.00005 0.00108 -0 .00060 0.00012 0 .00016 0.00067 0.00016 -0.00015 0.00018 0.00008 1 .00000 0 .00003 0.00004 0.00050 -0.00055 -0.00008 0.00053 0.00018 -0.00008 0.00032 -0.00050 -0.00108 -0.00924 0 .01221 ^ROW- 18 . -0.00163 -0.00005 -0.00028 0.00341 0.00006 - 0 . 0 0 0 1 5 -0.00106 0.00041 -0.00030 -0 .00033 -0.00026 -0.00118 -0.00029 -0.00010 0.0C462 -0.00004 -0.00096 0.03582 0.00005 0 .00004 0.01812 -0.00006 1.00000 -0.00051 -0.00036 0.00006 - 0 . 0 0 2 1 6 ROW 19 0 .00301 0 .01263 -0.00194 -0.00041 -0.00092 0.00023 -0.000 38 -0.00004 -0.00046 0.00024 -0.00018 0.00007 0.00017 -0.00225 0 .00046 - o . o o o s i 0.00013 0.00068 0.00030 -0.00207 0.00050 0.04171 -0.00055 -0 .02330 -0.00036 1.00000 -0.00056 j ROW 20 0 .00036 -0 .00005 - 0 . 0 0 1 6 7 - 0 . 0 0 1 8 5 0 .00007 -0 .00385 0 .00009 0 .00002 -0.00641 0.00002 •0 .00030 -0 .00359 -0.00009 0 .00034 0 .00146 0 .00003 0 .00383 0 .20000 -0.00016 0 .00053 -0.08801 0 .00013 -0.00216 0 .00060 -0.00056 0 .00013 1.00000 ROW 21 0 .00027 •0 .00023 1.00000 0 .00913 0 .00039 - 0 . 0 0 0 5 0 -0.00081 0 .00052 0 .00118 -0.00054 -0.00009 0 .00061 -0.00043 -0 .00004 0 .00497 0.00005 -0.00005 0.05234 -0.00018 0.000 18 -0 .00463 0 .00011 •0 .00028 -0.00044 0 .00007 0 .00008 -0.00167 ROW 22 0 .00016 - 0 . 0 0 1 2 7 0 .00018 0 .00006 0 .00007 -0.00023 0.00016 0 .00023 0 .00022 - 0 . 0 0 0 0 8 0 .00008 - 0 . 0 0 0 5 0 •0 .00008 1.00000 -0 .00017 -0.005 83 -0.00019 0 .00005 -0.00112 0 .00246 -0.00131 -0.06912 -0.00008 0 .02735 - 0 . 0 0 0 1 5 - 0 . 0 0 2 2 5 -0.00385 ROW 23 - 0 . 0 0 0 6 2 0 .00008 - 0 . 0 0 1 3 4 0 .00009 0 .00049 0 .00038 •0 .00009 -0.00035 -0.00018 0 .00102 -0.00017 -0.00300 •0.00026 0.00032 0 .00060 -0.00030 0 .00056 -0. 00081 -0 .00056 -0 .00641 0 .00118 - 0 . 0 0 5 8 3 1.00000 •0 .00316 -0 .02011 -0.28885 -0.67946 J30>LJ_A. 0.00015 - 0 . 0 0 0 1 4 0.00061 - 0 . 0 0 1 4 6 0 .00063 0 .00005 0 .00041 0.0000'9 -0 .00316 -0.00003 •0 . 00015 1 .00000 0 .00006 •0 .00001 0 .00733 0 .00008 -0.00039 -0.09976 0 .00021 -0.00050 -0.18123 0 .00022 -0.00118 0 .00025 0 .00068 -0 .00019 •0 .00359 ROW 25 -0_.j30jD3.P_ - 0 . 0 0 0 0 3 0 .00497 0 .00108 •0 .00014 0 .00246 0 .00010 •0.00002 •0 .02011 - 0 . 0 0 0 2 5 - 0 . 0 0 0 2 6 - 0 . 0 0 0 1 9 0.00002 -0.00013 0 .00733 0 .00104 1.00000 -0.00706 -0.11209 -0.00108 -0.05645 0 .00003 0 .00462 - 0 . 0 0 0 0 2 - 0 . 0 0 2 0 7 0 .00006 0 .00146 ROW 26 - 0 . 0 0 1 0 9 0 .00451 0 .05234 -0.00153 _0.0 0j40._5_ -0.06912 -0. 00686 -0.00108 -0 .28885 0 .00312 0 .00457 -0 .09976 0 .00310 0.00932 0 .00010 -0.09505 -0 .11209 1.00000 0 .00421 -0.00924 0 .84306 -0.00399 0 .03582 -0 .01280 0 .04171 •0 .00356 0 .20000 ROW 27 0 .00061 0 .00318 rP._Q.0463 0 .00009 -0.00497 O.02735_ 0 .00465 0 .00282 -0.67946 0 .00217 -0 .00912 -0 .18123 0 .00006 -0 .00114 -0.05645 0.00052 -0 .03318 0 .84306 •0.00164 0.01221 1 .00000 -0.00197 0 .01812 0 . 0 0 6 2 4 -0 .02330 0 .00077 -0.08801 STOP 0 EXECUTION TERMINATED $SIG RFS NO. 019805 UNIVERSITY OF 8 C COMPUTING CENTRE MTSIAN0 59 ) JOB START: 16: 14: 18 03-25-70 APPENDIX G MULTIPLE REGRESSION OUTPUTS OF MODEL II $SIGNON PL AK TIM E= 5M PAGES=50 C0PIES=7 PRIO = V **J_A.SI SIGNON WAS : 16:12:38 03-25-70 USER \"PLAK\" SIGNED ON AT 16:14:23' ON 03-25-70 $RUN *TRIP 4=*SOURCE* EXECUTION BEGINS TRIP/360 IMPLEMENTATION 3/18/70 • • • • • • • • • • • • • • • • • _ • * « • • • • • • • • • * * 0 0 0 1 1 1 2 2 2 2 3 3 3 4 4 5 5 6 6 7 7 8 1 6 9 2 5 8 1 4 6 8 0 1 5 0 5 0 5 0 5 0 5 0 CONTROL CARDS 1. INMSDC 3 5 1 1 1 1 2 . 3. 4. STPREG STPREG PARCOR 2 1 2 5 6 6 1 233 33 5 . END NOTE : OUTDATED *INVR# OR #MULREG* ROUTINES HAVE BEEN • • • REPLACED BY THE • • • • « EQUIVALENT *S TPREG* • CONTROL CARD NO. I * INMSDC * FORMAT CARDS ( F 1 0 . 5 / F 1 0 . 7 , 3 0 X ,F1Q .7 ) INPUT DATA TRIPGN FACTOl FACT05 -1 .127 - 1 . 9 4 8 0 .1253 0 .48 70 - 0 . 4 3 09 - 0 . 8 3 5 6 D - 0 1 2 . 584 1.669 0 .1530D-01 1 .221 0 .4077 0 .3257 1.782 2 .241 - 0 . 2 7 0 7 0 . 3 360 0 .3243 - 0 . 3 9 0 8 0 .5620 0 .4808 - 1 . 109\" 2 .026 2 . 906 -0 .6691 -0 .2790 - 0 . 2 4 8 9 - 0 . 1 4 0 1 - 0 . 3 2 9 0 0 .2783D-01 - 0 . 3 6 4 8 - 0 . 9 9 1 0 - 0 . 8 4 9 8 0 .7303 0 .5010 0 .4818 - 0 . 6 1 1 8 1. 196 0 .9055 -0 .7016 -0 .6000D-01 0 .2947 0 .4353 - 0 . 8 5 1 0 - 0 . 7 1 4 8 - 0 . 3 2 4 0 \" 0_._4.63„0 - 0 . 2107 -0 .2860 ' 0 .8700 0 .7431 1. 106 - 0 . 6 8 7 0 - 0 . 4 9 1 8 1.239 - 0 . 1 3 0 0 D - 0 1 0 .1208 - 0 . 8 7 0 7 -0 .9440 - 0 . 8 8 1 5 - 0 . 7 6 1 2 - 0 . 3 9 8 0 - 0 . 5 1 9 9 - 0 . 6 8 7 4 - 0 . 5 0 2 0 - 0 . 3 9 0 2 - 0 . 4 9 4 8 - 0 . 4 1 1 0 - 0 . 2 9 3 5 - 0 . 6 8 6 7 - 0 . 9 3 9 0 - 0 . 8 4 6 0 - 0 . 8 2 73 - 0 . 5 7 3 0 - 0 . 5 9 5 4 - 0 . 8 4 4 9 - 1 . 1 5 6 -1 .020 - 0 . 6 6 5 2 - 1 . 040 - 0 . 9967 - 0 . 6 1 9 6 -0 ,8380 - 0 . 6 2 1 3 - 0 . 7 4 1 7 1.145 1.161 1.651 - 0 . 7 4 9 0 - 0 . 1 7 3 5 1.065 - 0 . 4 3 6 0 0 .5366D-01 2 .912 - 0 . 8 5 1 0 - 0 . 5 8 3 4 2 .546 32 OBSERVATIONS 31 DEGREES OF FREEDOM NAME MEAN S . D . TRIPGN-0 .3125D-04 0 .9999 FACT01-0 .3125D-06 0 . 9 9 2 3 FAC TO5 0 . 2188D-05 0 .9974 CORRELATION MATRIX VARIABLE TRIPGN FACTOl FACT05 TRIPGN 1 .0000 FACTOl 0 .9078 1.0000 FACT05 - 0 . 0 4 3 1 0 .0171 1.0000 ARRAY WRITTEN IN AREA 5 CONTROL CARD NO. ? * STPREG » J DEPENDENT VARIABLE IS TRIPGN RSQ = 0.8275 FPROB. = 0.0000 STD ERR Y = 0.4294 VAR . _ .CO EF F STD. .ERR , F-R.A.T.LO CONST. -0.3084D-04 0.0759 FACT01 0.9157 0.0777 138.7819 FACTO 5 -0 .0588 ' 0.0773 0.5786 < FPROB. 0.0000 0.4590 NO. OBSERVED CALCULATED RES I DUAL NO. OBSERVED CALCULATED RESIDUAL 1 . 2 . 3 . -1 .1270 0 .48700 2 .5840 -1 .7916 - 0 . 3 8 9 7 4 1.5274 0 .66459 0 .87674 1.0566 ) 4 . 5 . 6 . 1 .2210 1.7820 0 . 3 3 6 0 0 0 .35415 2 .0683 0 .31998 0 .86685 -0 .28634 0 .16023E-01 7 . 8 . 9 . 0 . 5 6 2 0 0 2 .0260 - 0 . 2 7 9 00 0 .50552 2 .7004 - 0 . 2 1 9 7 2 0 .56483E-01 -0 .67435 - 0 . 5 9 2 8 4 E - 0 1 10. 11 . ] 2 . - 0 . 3 2 9 0 0 - 0 . 9 9 1 0 0 0 .50100 0 .46916E-01 - 0 . 82123 0 .47716 -0 .37592 - 0 . 1 6 9 7 7 0 .23839E-01 13. 14. 15. 1.1960 - 0 . 6 0 0 0 0 E - 0 1 - 0 . 8 5 1 0 0 0 .8704 7 0 .2442 7 -0 .63555 0 .32553 - 0 . 3 0 4 2 7 - 0 . 2 1 5 4 5 16. 17 . 1 8 . 0 .46300 0 .87000 - 0 . 6 8 7 0 0 - 0 . 1 7 6 1 6 0 .61540 - 0 . 5 2 3 3 3 0 ,63916 0 .25460 - 0 . 1 6 3 6 7 19. 2 0 . 2 1 . ' - 0 . 1 3 0 0 0 E - 0 1 . - 0 . 9 4 4 0 0 - 0 . 3 9 8 0 0 . 0 , 16181 - 0 . 7 6 2 5 3 -0*14357 2 -0 .17481 - 0 . 1 8 1 4 7 0 .37717E-Q1 2 2 . 23 . 24 . - 0 . 5 0 2 0 0 - 0 . 4 1 1 0 0 - 0 . 9 3 900 - 0 . 32 824 - 0 . 2 2 8 4 5 -0\". 7260 7 - 0 . 1 7 3 7 6 - 0 . 1 8 2 5 5 -0 .21293 2 5 . 26 . 27 . - 0 . 5 7 300 - 1 . 1 5 6 0 - 1 . 0 4 0 0 - 0 . 4955 2 - 0 . 8 9 508 -0 .87632 - 0 . 77477E-01 - 0 . 2 6 0 9 2 -0 .16368 2 8 . 2 9 . 30 . - 0 . 8 3 8 0 0 1.1450 - 0 . 7 4 9 0 0 - 0 . 5 2 5 3 7 0'. 96566 - 0 . 22158 - 0 . 31263 0 . 179 34 -0 .52742 3 1 . 32 . - 0 . 4 3 6 0 0 - 0 . 8 5 1 0 0 - 0 . 12216 - 0 . 6 8 4 0 6 - 0 . 3 1 3 8 4 - 0 . 16694 CONTROL CARD NO. 3 * STPREG * ARRAY RESTORED FROM AREA 5 ARRAY WR TTT FN IN AREA 6 CONTROL CARD NO. 4 * PARCOR * ARRAY RESTORED FROM AREA 6 PARTIAL CORRELATIONS VARIABLE TRIPGN FACTOl FACTO 5 .XR.XPI..N i . . . a a o _ _ _ ______________ FACTOl 0 .9095 - 1 . 0 0 0 FACT05-0 .1399 0 .1714D-01 - 1 . 0 0 0 * END OF CONTROL SET * STOP 0 EXECUTION TERMINATED RFS N O . 0 1 9 8 0 8 U N I V E R S I T Y OF B C COMPUTING CENTRE MTSI AN059 ) JOB S T A R T : 16: 1 0 : 2 2 0 3 - 2 5 - 7 0 ,$SIGNON PLAK T I ME= 5M PAGES=50 C 0 P I E S = 3 6 PR10=V !**.LA.S_T. .5 IGNON WAS: 1 6 : 0 4 : 29 0 3 - 2 5 - 7 0 ! USER \" PL A K \" S I G N E D ON AT 1 6 : 1 0 : 2 7 ' ON 0 3 - 2 5 - 7 0 |$RUN * T R I P 4 = * S 0 U R C E * E X E C U T I O N B E G I NS T R I P / 3 6 0 I M P L E M E N T A T I O N 3 / 1 8 / 7 0 RFS NO. 019804 UNIVERSITY OF B C COMPUTING CENTRE MTS.AN059) JOB S T A R T : 16:12:31 03-25-70 APPENDIX H MULTIPLE REGRESSION OUTPUTS OF MODEL I I I . _ J $SLGNON PLAK TlME=5M PAGES-50 C0PIE8=7 PRIO=V * * L A S T SIGNCN WAS: 16 :10:27 03-25-70 USER \"PLAK' ' SIGNED ON AT 16:12:38 ON 03-25-70 $RUN STRIP 4=*S0URCE* EXECUTION BEGINS TRIP/360 IMPLEMENTATION 3/18/70 0 0 0 1 1 1 2 2 2 2 3 3 3 4 4 5 5 6 6 7 7 8 1 6 9, 2 5 8 1 4 6 8 C I 5 0 5 0 5 0 5 0 5 0 » • • _ • • • • • . . . • • * • . .* • * * * • . * • _ • • • _ • * • • • • • • • C O N T R O L C A R D S 1. I N M S D C 5 1 1 1 1 2 . S T P R E G 4 1 1 2 3 3 3 3 3 . E N D N O T E i O U T D A T E D * I N V R * OR * M U L R E G * R O U T I N E S H A V E B E E N R E P L A C E D B!Y T H E E Q U I V A L E N T * S T P R E G * CONTROL CARD NO. 1 * INMSDC * FORMAT CARDS ( F I D . 5 / 3 F 1 0 . 7 , 2OX, F 10. 7 ); INPUT DATA TRIPGN SI.ZE EMPLOY DENS I STUD - 1 . 1 2 7 - 1 . 9 4 8 4 .232 L.T192 0.1308 0 .4870 - 0 . 4 3 0 9 0 .4631 -4.1202 - 0 . 5 4 5 3 2 .5 84 1 .669 0 .2656 - 0 . 3 4 2 4 D - 0 1 4 . 9.07 1.221 0 .4077 0 .5215 - 2 . 8 2 1 0.9488D-01 1.782 2..2 41 C.9168D-01 0.:1800D-02 - 0 . 9 0 4 1 0 .3360 0 .3243 0 .3212 0 .15 84 - 0 . 3 8 3 3 0 .562 0 0 .4808 0 .11150-01 - 0 . 1 0 3 5 - 0 . 5 5 0 6 2 .026 2 . 9 0 6 0 .2779 l . :002 -0 .9188 - 0 . 2 790 - 0 . 2 4 8 9 0 .1530 0 .3810 - 0 . 2 3 4 6 - 0 . 3 2 9 0 0 .2783D-01 -0 .28 80 0 .37 20 - 0 . 2 3 4 7 - 0 . 9 9 1 0 - 0 . 8 4 9 8 0 .8012D-01 0 .12 76 0.5727D-O1 0 .5010 0 .4818 0 .2099 0. 2660 -0 .5072 1 . 196 0 .9055 0 .8030D-01 0 .4513 - 0 . 5 4 3 1 - 0 . 6 0 0 0 0 - 0 1 0 .2947 0 .2582 0 .2 233 - 0 . 3 0 9 4 - 0 . 8 5 1 0 - 0 . 7 1 4 8 0 .3285 0..8 8 56D-O1 -0 .4894D-01 0 .4630 - 0 . 2 1 0 7 0 .1003 - 0 . 5 5 2 3 - C . 3513 0 .8700 0 .7431 0 .47450-01 0 .2514 - 0 . 3 5 8 3 - 0 . 6 8 7 0 - 0 . 4 9 1 8 0 . 5 6 88D-01 0 .2037 - 0 . 29.45D-01 - 0 . 1 3 0 0 D - 0 1 0 .1208 0 .3892 0 .1431 - 0 . 3 2 6 0 -0.94-40 - 0 . 8 8 1 5 0 .1385 0 .3886 -0 .7629D-01 - 0 . 3 9 8 0 - 0 . 5 1 9 9 0 .3671 - 0 . 3 1 8 5 0.8628 - 0 . 5 0 2 0 - 0 . 3 9 0 2 0 .3231 0. 3332 -0 .1171 -0.411-0 - 0 . 2 9 3 5 0 .2155 6 .2510 - 0 . 2 0 8 1 - 0 . 9 3 9 0 - 0 . 8 4 6 0 0 .1775 0 .4251 -0 .6917D-01 -0.57,30 - 0 . 5 9 5 4 0 .2776 0. 1636 -0 .9198D-01 - 1 . 1 5 6 - 1 . 0 2 0 0 . 3 1 7 7 0 .3076 ,0. 1575D-01 - 1 . 0 4 0 - 0 . 9 9 6 7 0 .1933 0 .1448 1. 536 - 0 . 8 3 8 0 - 0 . 6 2 1 3 - 0. 31 62 0 .3030 -0 .8048D-01 1.145 1^161 0 .1106 0.4390 - 0 . 3 7 9 9 - 0 . 7 4 9 0 - 0 . 1 7 3 5 0 .4042D-01 - 0 . 8 5 3 9 D - 0 1 - 0 . 1399 - 0 . 4 3 6 0 0 .5366D-01 - 0 .1177 0.2330 - 0 . 1 4 3 5 - 0 . 8 5 1 0 - 0 . 5 8 3 4 0 . 1620 0. 2654 -0 .52510-01 32 OBSERVATIONS 31 DEGREES OF FREEDOM - - - - - - - - • © NAME MEAN S. 'D. TRIPGN-0 .3125D-04 0 .9999 SIZE - 0 . 3 1 2 5 D - 0 6 0 .9923 EMPLOY 0 . 3 1 2 5 0 - 0 6 0 .8005 DENS 1—0 .18750-05 0 .9888 STUD - 0 . 3 1 2 5 0 - 0 6 1.000 CORRELATION MATRIX VARIABLE TRLPGN SIZE EMPLOY DENS I STUD TRIPGN 1. 0000 SIZE 0 . 9078 l .OCOO EMPLOY - 0 . 1 5 6 2 - 0 . 3 2 5 1 1.0000 DBNSI - 0 . 2 0 7 8 0 .0218 0.18 26 1.0000 STUD 0 .1769 0 .0021 - 0 . 0 1 0 2 0 .0024 1.0000 J CONTROL CARD NO, * S T P R E G * DEPENDENT .VARIABLE IS TRIPGN RSQ 0 .9460 FPROB. = STD ERR Y = VAR CONST. SIZE 0 .0000 0 .2489 COBFF -0. 31480-04 0 .9904 STD ERR 0 .0440 0 .0478 F-RATIO 429 .0756 FPROB. 0.0000 EMPLOY DENSI STUD 0 .2675 -0.2718 0 .1776 0 .0603 0.046 2 0 .0447 19 .7063 3 4 . 6 8 09 15 .7943 0.0002 0 .0000 0.0005 "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0093346"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Planning"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Multicollinearity in transportation models"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/34904"@en .