UBC Theses and Dissertations

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UBC Theses and Dissertations

The prediction of physics grades at the university level from previously recorded data Creelman, Arthur Graham 1964

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THE PREDICTION OF PHYSICS GRADES AT THE UNIVERSITY LEVEL FROM PREVIOUSLY RECORDED DATA by ARTHUR GRAHAM CREELMAN B.A., U n i v e r s i t y o f B r i t i s h Columbia, 1931 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the F a c u l t y of E d u c a t i o n We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1964 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of E d u c a t i o n The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada i i ABSTRACT The aim of t h i s study vas to p r e d i c t the P h y s i c s grades of North Vancouver Se n i o r Secondary P h y s i c s 91 students i n P h y s i c s 101 courses at the grade X I I I and the u n i v e r s i t y l e v e l , and i n P h y s i c s 200, and P h y s i c s 155 and 156 at the u n i v e r s i t y l e v e l . The p r e d i c t i o n v a r i a b l e s used were the i n t e l l i g e n c e q u o t i e n t r a t e d by O t i s S e l f - A d m i n i s t e r i n g T e s t s o f Mental A b i l i t y , Higher Examination: Form C, together with the grades i n P h y s i c s 91 and Mathematics 91. These v a r i a b l e s were used to p r e d i c t the grades f o r P h y s i c s 100, 200 and P h y s i c s 155 and 156. The i n t e l l i g e n c e q u o t i e n t and the grades i n P h y s i c s 101, and Mathematics 101 were used to p r e d i c t the grades f o r P h y s i c s 200 and P h y s i c s 155 and 156. The study was undertaken to determine whether the i n t e l l i g e n c e q u o t i e n t and the standard of achievement i n p r e r e q u i s i t e courses provide a b a s i s f o r p r e d i c t i o n o f success i n the advanced p h y s i c s c o u r s e s . Such a p r e d i c t i o n would be of value i n o f f e r i n g academic guidance. Because o f the m u l t i v a r i a t e nature of the p r e d i c t o r s , the p r e d i c t e d grade was equated to the p r e d i c t i o n v a r i a b l e s by a m u l t i p l e r e g r e s s i o n e q u a t i o n . When the c o e f f i c i e n t of c o r r e l a t i o n was s i g n i f i c a n t beyond the one per cent l e v e l , the n u l l h y p o thesis was r e j e c t e d and the p r e d i c t i o n equation which r e s u l t e d was assumed to be s i g n i f i c a n t l y p r e d i c t i v e w i t h i n the s t a t i s t i c a l l i m i t s s t a t e d . i i i The accuracy of these p r e d i c t i o n s was t e s t e d by c a l c u l a t i n g the c o r r e l a t i o n s between sets of a c t u a l grades i n P h y s i c s 101, P h y s i c s 200, and P h y s i c s 155 and 156 f o r students who graduated from 1957 to 1961 from North Vancouver S e n i o r Secondary S c h o o l , and the corresponding s e t s of p r e d i c t e d grades f o r students who graduated from 1947 to 1957. P h y s i c s 101 grades as given by the Department o f Ed u c a t i o n or the U n i v e r s i t y o f B r i t i s h Columbia showed c o r r e l a t i o n c o e f f i c i e n t s that were s i g n i f i c a n t w i t h both f i n a l course grade p r e d i c t o r s as given by the classroom teacher and u n i v e r s i t y entrance examination grade p r e d i c t o r s . P h y s i c s 101 grades y i e l d e d h i g h e r c o r r e l a t i o n c o e f f i c i e n t s w i t h u n i v e r s i t y entrance grade p r e d i c t o r s than w i t h l e t t e r grade p r e d i c t o r s . P h y s i c s 155 and 156 grades showed c o r r e l a t i o n c o e f f i c i e n t s t h a t were s i g n i f i c a n t w i t h both l e t t e r grade p r e d i c t o r s a s s i g n e d by the hi g h school t e a c h e r s , with the P h y s i c s 101 grades and Mathematics 101 grades assigned by the U n i v e r s i t y of B r i t i s h Columbia, and with the grades a s s i g n e d by the Department of E d u c a t i o n . P h y s i c s 200 grades showed c o r r e l a t i o n c o e f f i c i e n t s that were s i g n i f i c a n t w i t h both l e t t e r grade p r e d i c t o r s assigned by the hi g h s c h o o l teachers and with the P h y s i c s 101 grades and Mathematics 101 grades assigned by the U n i v e r s i t y o f B r i t i s h Columbia and the grades assigned by the Department of E d u c a t i o n . i v P h y s i c s 155 and 156 and P h y s i c s 200 grades had higher m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s w i t h U n i v e r s i t y grade p r e d i c t o r s than with l e t t e r grade p r e d i c t o r s . A c t u a l grades f o r Grade XIII P h y s i c s 101 and U n i v e r s i t y P h y s i c s 101 c o r r e l a t e d s i g n i f i c a n t l y with corresponding p r e d i c t e d grades* A c t u a l grades f o r P h y s i c s 155 and 156 and P h y s i c s 200 c o r r e l a t e d with p r e d i c t e d grades. The c o e f f i c i e n t s of c o r r e l a t i o n , u s i n g U n i v e r s i t y grade p r e d i c t o r s to p r e d i c t P h y s i c s 155 and 156 and P h y s i c s 200 grades, were both s i g n i f i c a n t . The c o e f f i c i e n t o f c o r r e l a t i o n , u s i n g l e t t e r grade p r e d i c t o r s to p r e d i c t P h y s i c s 155 and 156, was s i g n i f i c a n t * The r e s u l t s o f the study I n d i c a t e d that i t i s p o s s i b l e to p r e d i c t P h y s i c s 101 grades f o r North Vancouver Senior Secondary P h y s i c s 91 students* U n i v e r s i t y entrance grade p r e d i c t o r s give equations with higher c o e f f i c i e n t s of c o r r e l a t i o n than l e t t e r grade p r e d i c t o r s . The r e s u l t s a l s o i n d i c a t e d that i t i s p o s s i b l e to p r e d i c t the grades of P h y s i c s 155 and 156 and P h y s i c s 200 with l e t t e r grade p r e d i c t o r s and U n i v e r s i t y grade p r e d i c t o r s . These r e s u l t s , made a v a i l a b l e t o the c o u n s e l l o r , would enable him to advise students as to t h e i r p r o b a b i l i t y o f success, i f they were to e n r o l l i n P h y s i c s 101, P h y s i c s 155 and 156 and P h y s i c s 200. ACKNOWLEDGEMENT I wish to express my g r a t i t u d e to the f o l l o w i n g persons f o r a s s i s t a n c e r e c e i v e d i n completing t h i s study: Mr. Ben R. Whitinger, my t h e s i s a d v i s e r ; Dr. Harry R. S t e i n for a r r a n g i n g the use of the I.B.M. computer; Mr. Dan Dempsey, f o r h i s pe r m i s s i o n to use the record cards of North Vancouver Senior Secondary Schoo l ; and to Mr. Wallace R e g i s t r a r of the U n i v e r s i t y of B r i t i s h Columbia, f o r h i s per m i s s i o n to use the r e c o r d cards of the U n i v e r s i t y . V TABLE OF CONTENTS PAGE LIST OF TABLES. . . . . . . . v i i i LIST OF FIGURES . . x ACKNOWLEDGEMENTS x i CHAPTER I . THE PROBLEM AND DEFINITIONS OF TERMS USED . . . . 1 The Problem 3 Statement of the problem. 3 Statement of the n u l l h y p o t h e s i s . . . . . . . 3 D e f i n i t i o n s of Terms Used . . . . . . . . . . . 7 S u c c e s s f u l grade. . . . . . . . . . . . . . . 7 Independent v a r i a b l e . . . 7 U n i v e r s i t y P h y s i c s 101 7 Grade X I I I P h y s i c s 101 7 I I . REVIEW OF THE LITERATURE. 8 L i t e r a t u r e on p r e d i c t i o n . . . . . . . . . . . 8 L i t e r a t u r e on p r e d i c t i o n In B r i t i s h Columbia. 12 I I I . DESIGN 14 The Sample 14 Dependent and Independent V a r i a b l e s 15 Dependent v a r i a b l e s . . . . . . . . . . . . . 15 Independent v a r i a b l e s 15 Procedure 16 P r e d i c t i o n 19 Mathematical Procedure. . . . . . . 19 IV. THE RESULTS 20 R e s u l t s from Data Based on the 1947-57 P r e d i c t i o n V a r i a b l e s . . . . 21 P r e d i c t i o n e q u a t i o n s . . . . . . . . . . . . . 21 C o r r e l a t i o n s between p r e d i c t e d grades and a c t u a l grades 21 v i CHAPTER PAGE IV. R e g r e s s i o n equations f o r P h y s i c s 101 21 Reg r e s s i o n equations f o r P h y s i c s 155 and 156 25 Reg r e s s i o n equations f o r P h y s i c s 200 28 P r e d i c t i o n f o r P h y s i c s 200 30 R e s u l t s from Data based on 1947-1961 P r e d i c t i o n V a r i a b l e s . . 31 P r e d i c t i o n e q u a t i o n s . . 31 Reg r e s s i o n equations f o r P h y s i c s 101 32 Re g r e s s i o n equations f o r P h y s i c s 155 and 156 . 35 Reg r e s s i o n equations f o r P h y s i c s 200 38 Summary of r e s u l t s . . . . . . . . . . . . . . 41 C o r r e l a t i o n s of P r e d i c t e d Grades and P r e r e q u i s i t e s . . . . . . . . . . . 46 C o r r e l a t i o n s between P r e d i c t e d Grades and A c t u a l Grades. . . . . . . . . . . . . . . . 48 V. CONCLUSION . . . . , 52 C o n c l u s i o n s . . . . . . . . 52 Pl a n n i n g Academic S t u d i e s . . 56 P r e d i c t i o n of I n d i v i d u a l Grades . . . . . . . . 56 For P h y s i c s 101 56 For P h y s i c s 155 and 156 57 For P h y s i c s 200 58 A p p l i c a t i o n s of p r e d i c t i o n . . . . . . . . . . 58 Comparison between the Grades o f P h y s i c s 101 Courses. . . . . . . . . . . . . . . . . . . 59 C o u n s e l l i n g . . . . . . . . . . . . . . . . . . 61 C o u n s e l l i n g i n d i v i d u a l Grade XII s t u d e n t s . . . 61 C o u n s e l l i n g i n d i v i d u a l Grade X I I I students • . 64 Re l a t e d Problems f o r Research . . . . . . . . . 6 5 Summary. . . . . . . . . . . . . . . . . . . . 65 BIBLIOGRAPHY . . . . . . 67 APPENDIX PROGRAMMING OF MATHEMATICAL PROCEDURE 69 v i i i LIST OF TABLES TABLE PAGE 1. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 101 U.B.C. . . . . . . . . 21 2. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e o f Ryl23 f o r P h y s i c s 101 U.B.C 22 3. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r Physics 101 G.XIII 23 4. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 101 G.XIII 24 5. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 25 6. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 . 26 7. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 27 8. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200 . . . 28 9. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200 29 10. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200 . . . . . . . . . . . 30 11. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 101 .U. B.C. 32 12. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 101 U. B .C 33 13. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 101 G.XIII 34 14. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 101 G.XIII 34 15. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 35 16. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 36 i x TABLE PAGE 17. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 36 18. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 . . 37 19. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 155, 156 38 20. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200 38 21. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200. 39 22. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200 40 23. P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of Ryl23 f o r P h y s i c s 200 40 24. Summary of Re g r e s s i o n Equations . . . . . . 42 25. C o r r e l a t i o n between P r e d i c t e d Grades and A c t u a l Grades f o r C o l l e g e P h y s i c s Courses 49 26. H i s t o r y of P r e d i c t o r Scores and C r i t e r i a . . . . . . . 76 27. P r e d i c t i o n V a r i a b l e s and the P r e d i c t e d C r i t e r i a f o r the P h y s i c s 91 C l a s s of 1961-62 77 28. P r e d i c t i o n V a r i a b l e s and the P r e d i c t e d C r i t e r i a f o r the U n i v e r s i t y P h y s i c s 101 C l a s s of 1961-62 . . 81 29. P r e d i c t i o n V a r i a b l e s and the P r e d i c t e d C r i t e r i a f o r the U n i v e r s i t y P h y s i c s 101 C l a s s of 1961-62 . . 82 30. Comparison o f the P r e d i c t e d C r i t e r i a and the A c t u a l Grades f o r Completed P h y s i c s Courses . . . . 83 31. Comparison of the P r e d i c t e d C r i t e r i a and the A c t u a l Grades f o r Completed P h y s i c s Courses . . . . 86 LIST OF FIGURES FIGURES PAGE 1. P h y s i c s 101 Grades P r e d i c t e d by L e t t e r Grades. . 60 2. P h y s i c s 101 Grades P r e d i c t e d by U n i v e r s i t y Entrance Grades 62 CHAPTER I THE PROBLEM AND DEFINITIONS OF TERMS USED S o c i a l pressure leads many students to e n r o l l In u n i v e r s i t y entrance courses i n high school and l a t e r to attempt e d u c a t i o n at the u n i v e r s i t y l e v e l . Often i n s u f f i c i e n t c o n s i d e r a t i o n Is gi v e n to the chances of a t t a i n i n g a s a t i s f a c t o r y l e v e l o f achievement i n u n i v e r s i t y s u b j e c t matter. The r e s u l t s a t t a i n e d by some students i n elementary u n i v e r s i t y p h y s i c s and mathematics courses I n d i c a t e a background which g i v e s l i t t l e reasonable chance of success In advanced p h y s i c s . A knowledge of the v a r i a b l e s which p r e d i c t success at the U n i v e r s i t y l e v e l would be of value to the c o u n s e l l o r of se n i o r high school s t u d e n t s . Paul Horst* In speaking of d i f f e r e n t i a l p r e d i c t i o n s o f success i n v a r i o u s c o l l e g e s u b j e c t areas s t a t e d : These procedures, I am sure, w i l l p r o v i d e the b a s i s f o r more e f f e c t i v e student guidance In the high s c h o o l s , more e f f i c i e n t u t i l i z a t i o n of our highe r e d u c a t i o n a l r e s o u r c e s and a high e r c a l i b e r of w e l l t r a i n e d c o l l e g e graduates. Paul H o r s t , " D i f f e r e n t i a l P r e d i c t i o n of Success i n Various C o l l e g e Course Areas," C o l l e g e and U n i v e r s i t y , 31: Number 4, 456-7, 1956. 2 2 E l i z a b e t h and George Baker demonstrate that success i n s p e c i f i c s u b j e c t f i e l d s could be p r e d i c t e d more r e a d i l y 3 than general success i n u n i v e r s i t y * G a r r e t t and Adams were of the o p i n i o n that "high school r e c o r d s t e l l more about success i n c o l l e g e p h y s i c s than do c o l l e g e entrance t e s t r a n k s . " U n i v e r s i t y p h y s i c s i s a p r e r e q u i s i t e f o r c e r t a i n academic ch o i c e s at the u n i v e r s i t y l e v e l . I t i s important that a student a p p r a i s e h i s p r o s p e c t s of success In the study of p h y s i c s at the u n i v e r s i t y , l e v e l . I t i s a l s o Important f o r a student to decide whether he i s more l i k e l y to succeed i n P h y s i c s 101 i n grade X I I I or at u n i v e r s i t y . E l i z a b e t h Baker and George Baker, " F a c t o r A n a l y s i s o f High School V a r i a b l e s and Success In U n i v e r s i t y S u b j e c t s f o r the F i r s t Semester i n U n i v e r s i t y . " J o u r n a l of Experimental  E d u c a t i o n , 24:315-18, June 1956. H.L. G a r r e t t and Sam Adams, " S c h o l a s t i c Background as R e l a t e d to Success i n C o l l e g e P h y s i c s , " J o u r n a l of E d u c a t i o n a l  Research, 47:545-9, March 1954. 3 The Problem Statement of the problem. The purpose of the study was to p r e d i c t the p h y s i c s grades o f North Vancouver Se n i o r Secondary students who e n r o l l i n f u t u r e p h y s i c s courses at the grade XIII or u n i v e r s i t y l e v e l , and to give some i n d i c a t i o n o f the accuracy o f these p r e d i c t i o n s . P r e d i c t i o n s were made f o r the grades of P h y s i c s 101, P h y s i c s 200 and P h y s i c s 155 and 156, u s i n g as p r e d i c t i o n v a r i a b l e s the i n t e l l i g e n c e q u o t i e n t s o f the studen t s , and the f i n a l grades obtained by them i n P h y s i c s 91 and Mathematics 91. P r e d i c t i o n s were a l s o made f o r the grades o f P h y s i c s 200 and Ph y s i c s 155 and 156 us i n g as p r e d i c t i o n v a r i a b l e s the i n t e l l i g e n c e q u o t i e n t s o f the studen t s , and the f i n a l grades obtained by them i n P h y s i c s 101 and Mathematics 101. Si n c e t h i s was a problem of e s t i m a t i n g the grade In one su b j e c t from a knowledge of the pr e v i o u s grades i t was nece s s a r y to show that changes i n the recorded grades of a student were accompanied by a corresponding change i n the p r e d i c t e d grade. The m u l t i v a r i a t e nature o f the p r e d i c t o r s i n d i c a t e d t h at t h i s was a problem i n m u l t i p l e r e g r e s s i o n . I f the r e s u l t i n g equations are p r e d i c t i v e , they can be used to p r e d i c t f u t u r e grades i n p h y s i c s at the u n i v e r s i t y l e v e l . Statement of the n u l l h y p o t h e s i s . The f o l l o w i n g m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s are not s i g n i f i c a n t bases f o r p r e d i c t i n g success i n p h y s i c s courses at the u n i v e r s i t y l e v e l : j 4 (1) The f i n a l l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of U n i v e r s i t y P h y s i c s 101. (2) The Department o f E d u c a t i o n U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s are not s i g n i f i c a n t p r e d i c -t o r s f o r the grades of U n i v e r s i t y P h y s i c s 101. (3) The f i n a l l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of Grade XIII P h y s i c s 101. (4) The U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 and the I n t e l l i g e n c e q u o t i e n t s are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of Grade X I I I P h y s i c s 101. (5) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 given by classroom teacher and the I n t e l l i g e n c e q u o t i e n t s are not s i g n i f i c a n t p r e d i c -t o r s f o r the grades of P h y s i c s 155 plu s 156, (6) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 g i v e n by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t f o r the students who a c q u i r e d P h y s i c s 101 grades at the U n i v e r s i t y are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 155 p l u s 156. 5 (7) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 given by the classroom teacher and the I n t e l l i g e n c e q u o t i e n t f o r the students who a c q u i r e d P h y s i c s 101 grades at North Vancouver High School are not s i g n i f i c a n t p r e d i c t o r s f o r the grades o f P h y s i c s 155 p l u s 156. (8) The grades of U n i v e r s i t y P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t are not s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 155 p l u s 156. (9) The grades of Grade X I I I P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t are not s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 155 p l u s 156. (10) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 g i v e n by the classroom teacher and the I n t e l l i g e n c e q u o t i e n t are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 200. (11) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 given by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t f o r the students who a c q u i r e d P h y s i c s 101 grades at the U n i v e r s i t y are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 200. (12) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 g i v e n by the classroom teacher and the I n t e l l i g e n c e q u o t i e n t f o r the students who a c q u i r e d P h y s i c s 101 grades at North Vancouver High 6 School are not s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 200. (13) The grades of U n i v e r s i t y P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t are not s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 200. (14) The grades o f Grade X I I I P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t are not s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 200. I f the n u l l hypotheses are r e j e c t e d , the p r e d i c t e d grades f o r P h y s i c s 101, P h y s i c s 200 and P h y s i c s 155 and 156 f o r i n d i v i d u a l students can be c a l c u l a t e d , c o n s i d e r i n g the standard e r r o r . ° 0 7 D e f i n i t i o n of Terms Used S u c c e s s f u l grade. General P h y s i c s courses have two purposes. They are r e q u i r e d as p r e r e q u i s i t e s to f u r t h e r s t u d i e s and are a c o n t r i b u t i o n to the c u l t u r a l background of the s tudent. Those grades which are accepted as p r e r e q u i s i t e s to f u r t h e r p h y s i c s are d e f i n e d as s u c c e s s f u l grades. Independent v a r i a b l e . The independent v a r i a b l e s are the i n t e l l i g e n c e q u o t i e n t s and the recorded grades f o r v a r i o u s p h y s i c s and mathematics c o u r s e s . U n i v e r s i t y P h y s i c s 101 r e f e r s to the P h y s i c s 101 course o f f e r e d at the U n i v e r s i t y o f B r i t i s h Columbia. Grade X I I I P h y s i c s 101 r e f e r s to the P h y s i c s 101 course o f f e r e d by the Department of E d u c a t i o n to Grade X I I I s t u d e n t s . CHAPTER I I REVIEW OF THE LITERATURE There are many r e f e r e n c e s to m u l t i v a r i a t e p r e d i c t o r s and the p r e d i c t i o n of success at u n i v e r s i t y or i n u n i v e r s i t y s u b j e c t s * Of those surveyed, r e f e r e n c e s were made to the problem of p r e d i c t i o n i n the United S t a t e s o f America and to the s i m i l a r problem i n Canada. Few e n q u i r i e s have concerned themselves s p e c i f i c a l l y with P h y s i c s and none with the choice between grade X I I I and u n i v e r s i t y p h y s i c s . L i t e r a t u r e on P r e d i c t i o n . P r e d i c t i o n by the use of a n a l y s i s o f m u l t i p l e r e g r e s s i o n and m u l t i p l e a b s o l u t e p r e d i c t i o n b a t t e r y has been used by Paul H o r s t * at the U n i v e r s i t y of Washington. Research on the problem of p r e d i c t i n g c o l l e g e success r e s u l t e d i n p r e d i c t i o n formulas f o r t h i r t y - t w o c o l l e g e courses p r e d i c t e d from s i x high school grades and seven entrance examination measures. Paul H o r s t , ' ' D i f f e r e n t i a l P r e d i c t i o n o f Success i n Var i o u s C o l l e g e Course Areas," C o l l e g e and U n i v e r s i t y , 31: Number 4, 456-71, 1956. 9 Accuracy of p r e d i c t i o n was determined f o r over f i v e thousand cases. T h i s i n f o r m a t i o n , which i s s u p p l i e d to every student a p p l y i n g f o r admission to the U n i v e r s i t y o f Washington w i l l continue to be used i n the area of d i f f e r e n t i a l guidance f o r s p e c i a l i z e d areas of t r a i n i n g r a t h e r than as a b a s i s o f admission to the U n i v e r s i t y . The r e s u l t s of h i s study have convinced him that there was a d e f i n i t e r e l a t i o n s h i p between p r e d i c t e d and achieved grades i n c e r t a i n s u b j e c t f i e l d s . The D i v i s i o n of Counseling and T e s t i n g S e r v i c e s , 2 U n i v e r s i t y of Washington has a p r e - c o l l e g e d i f f e r e n t i a l guidance program, 1962 e d i t i o n , which uses p r e d i c t e d grade p o i n t averages as a guide f o r p l a n n i n g u n i v e r s i t y c o u r s e s . The Washington P r e - C o l l e g e D i f f e r e n t i a l Guidance Data Sheet l i s t s grade averages f o r h i g h school grades i n s i x s u b j e c t s f o r each semester, f o r a l l four years at high s c h o o l , and seven p r e - c o l l e g e d i f f e r e n t i a l guidance t e s t s c o r e s . From these a grade p o i n t average i s p r e d i c t e d . T h i s grade p o i n t average i s used to show what percentage of p u p i l s w i t h s i m i l a r achievement r e c e i v e d B or b e t t e r grade p o i n t averages, i n f o r t y - s i x s u b j e c t f i e l d s . The b u l l e t i n notes that the accuracy o f the grade p o i n t averages i s a f f e c t e d by h i g h school grades and c o l l e g e grades which are not a b s o l u t e l y a c c u r a t e . The b u l l e t i n s t a t e s t h a t the p r e d i c t e d grade p o i n t C h a r t i n g a C o l l e g e Career with Washington P r e - C o l l e g e  D i f f e r e n t i a l Guidance Data (1962 E d i t i o n ) , The D i v i s i o n of C o u n s e l i n g and T e s t i n g S e r v i c e s , U n i v e r s i t y of Washington, S e a t t l e , Washington, pp. 2-7. 10 averages have proven reasonably accurate f o r a number of c o l l e g e course a r e a s . I t a l s o s t a t e s that the choice o f a program o f study should be based on a number o f c o n s i d e r a t i o n s i n a d d i t i o n to the p r e d i c t e d grades. The p r e d i c t e d grades are computed through the use of a computer u s i n g the high school grade averages and the t e s t averages to c a l c u l a t e the p r e d i c t e d grade by e v a l u a t i n g m u l t i p l e r e g r e s s i o n e q u a t i o n s . 3 W.L. Wallace p r e d i c t e d grades i n s p e c i f i c c o l l e g e courses at the U n i v e r s i t y o f Michigan u s i n g three n a t i o n a l t e s t s and three l o c a l t e s t s as p r e d i c t i o n v a r i a b l e s , to o b t a i n a m u l t i p l e c o e f f i c i e n t of c o r r e l a t i o n with the f i r s t semester average. The o b t a i n e d c o r r e l a t i o n of .554 was low f o r p r a c t i c a l a p p l i c a t i o n of t e s t r e s u l t s . Wallace recommended that each I n s t i t u t i o n should e s t a b l i s h i t s own set of v a l i d 4 t e s t s , a recommendation a l s o made by Paul H o r s t . Horst s t a t e d t h a t a m u l t i p l e p r e d i c t i o n b a t t e r y was of more value than a g e n e r a l p r e d i c t i o n o f c o l l e g e s u c c e s s . E l i z a b e t h and 5 George Baker came to t h i s same c o n c l u s i o n i n a study at the U n i v e r s i t y of C a l i f o r n i a at D a v i s . They s t a t e d that In t h e i r W.L. Wallace, "The P r e d i c t i o n of Grades i n S p e c i f i c C o l l e g e Courses," J o u r n a l of E d u c a t i o n a l Research, Volume 44, A p r i l 1951. ^Paul H o r s t , "A Technique f o r the Development of a M u l t i p l e Absolute P r e d i c t i o n B a t t e r y , " P s y c h o l o g i c a l Monograph, 69 Number 5:390, 1955. 5 E l i z a b e t h Baker and George Baker, " F a c t o r A n a l y s i s of High School V a r i a b l e s and Success In U n i v e r s i t y S u b j e c t s f o r the F i r s t Semester i n U n i v e r s i t y , " J o u r n a l of Experimental  E d u c a t i o n , 24:315-8, June 1956. 11 o p i n i o n success i n s u b j e c t f i e l d s c ould be p r e d i c t e d , but success i n u n i v e r s i t y could not be p r e d i c t e d so r e a d i l y . D.L. A r n o l d and G. Schoepfle at Kent S t a t e U n i v e r s i t y s t u d i e d the c o r r e l a t i o n between high school and c o l l e g e grades* They showed from examination o f a s c a t t e r diagram comparing hi g h school s c i e n c e grades and grades i n f i r s t year c o l l e g e p h y s i c s that the c o r r e l a t i o n was h i g h . A s c a t t e r diagram comparing grades i n high school mathematics and f i r s t year c o l l e g e mathematics showed the c o r r e l a t i o n o f these grades was a l s o h i g h . No s t a t i s t i c a l a n a l y s i s was made. The authors s t a t e d that an attempt should be made to counsel the students without proven a b i l i t y i n s c i e n c e and mathematics out of the f i e l d o f p h y s i c s . J.P. M a l l o r y and o t h e r s ^ at Kansas S t a t e C o l l e g e s t a t e d that the c o r r e l a t i o n c o e f f i c i e n t between the grade p o i n t average of the f i r s t three t e s t s i n P h y s i c s and the f i n a l grade p o i n t averages i n e n g i n e e r i n g was 0.88. They s t a t e d that t h i s was a s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t between the grades i n P h y s i c s 1 and the rank order of the grade p o i n t averages f o r students graduating i n e n g i n e e r i n g . D.L. A r n o l d and G. S c h o e p f l e , " C o r r e l a t i o n o f High School and C o l l e g e Grades," American J o u r n a l of P h y s i c s , 26: 537-9, November 1958. 7 J . P . M a l l o r y et a l , " P r e d i c t i n g A t t r i t i o n -S u r v i v a l i n F i r s t Year E n g i n e e r i n g , " American J o u r n a l o f  P h y s i c s , 24:605-10, December 1956. 12 Sam Adams and H.L. G a r r e t t found that few s t u d i e s have been done on success i n c o l l e g e p h y s i c s p r e d i c t e d from the high school s c h o l a s t i c background. The s t u d i e s r e p o r t e d are r e p r e s e n t a t i v e of the r e s e a r c h i n the p r e d i c t i o n of success i n u n i v e r s i t y courses* From these s t u d i e s s e v e r a l i n f e r e n c e s were made by the authors* The s t u d i e s were most s u c c e s s f u l l f made from p r e d i c t o r s r e l a t e d to a s p e c i f i c s u b j e c t f i e l d to a c r i t e r i o n i n the same su b j e c t f i e l d . General success i n u n i v e r s i t y cannot be p r e d i c t e d r e a d i l y . Each u n i v e r s i t y should develop I t s own set of t e s t s . The c o r r e l a t i o n between high school grades and p r e d i c t e d c o l l e g e grades i n the same f i e l d seem to be h i g h . M u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s showed a much grea t e r degree of r e l i a b i l i t y and t h e r e f o r e m u l t i p l e r e g r e s s i o n equations were of more use i n p r e d i c t i o n . 9 L i t e r a t u r e on p r e d i c t i o n i n Canada. Harry W. Dosso, r e p o r t e d In h i s study the zero order c o r r e l a t i o n between examination r e s u l t s i n p h y s i c s and scores on c o l l e g e a p t i t u d e t e s t s . The c o r r e l a t i o n c o e f f i c i e n t s between f i r s t year c o l l e g e p h y s i c s marks and h i g h school p h y s i c s marks were Sam Adams and H.L. G a r r e t t , S c h o l a s t i c Background as r e l a t e d to Success i n C o l l e g e P h y s i c s , J o u r n a l of E d u c a t i o n a l Research, 47:545-9, March 1954. 9 I I Harry W. Dosso, A Study on the C o r r e l a t i o n Between Examination R e s u l t s In P h y s i c s and Scores on C o l l e g e Aptitude T e s t s , "The C a t a l y s t , J o u r n a l of the B r i t i s h Columbia Science Teacher'8 A s s o c i a t i o n of the B r i t i s h Columbia Teacher's F e d e r a t i o n , V o l . 2, No. 1, October 1962. 13 .74 f o r the group that wrote u n i v e r s i t y entrance examinations and .61 f o r the group that r e c e i v e d recommendation grades In P h y s i c s 91 and d i d not w r i t e departmental examinations. The V i c t o r i a .College study showed that f o r t h e i r own school the c o r r e l a t i o n between C o l l e g e A p t i t u d e t e s t grades and u n i v e r s i t y p h y s i c s grades was low as was a s i m i l a r c o r r e l a t i o n at the U n i v e r s i t y of B r i t i s h Columbia. T h i s c o r r o b o r a t e d the c o n c l u s i o n that success i n s u b j e c t f i e l d s c o u l d be p r e d i c t e d from p r e v i o u s grades i n the same su b j e c t f i e l d , hut that general examination scores were not very u s e f u l i n p r e d i c t i n g success i n s u b j e c t f i e l d s . Donald V. B l a c k 1 s t u d i e d the c o r r e l a t i o n between the f i n a l high s c h o o l grades i n E n g l i s h , s o c i a l s t u d i e s , mathematics, p h y s i c s , chemistry and a f o r e i g n language and the grades i n v a r i o u s freshman e n g i n e e r i n g s u b j e c t s o f f e r e d at the U n i v e r s i t y of A l b e r t a . The study was made with two hundred and f o r t y - f i v e e n g i n e e r i n g freshmen. For the grades of P h y s i c s 21 the c o r r e l a t i o n c o e f f i c i e n t from the p r e d i c t i o n equation was .654 with a standard e r r o r of 15.4. The c o r r e l a t i o n c o e f f i c i e n t between a c t u a l grades and p r e d i c t e d grades i n t h i s s u b j e c t was .611 with a standard e r r o r o f 14.5. Donald V. Black, " D i f f e r e n t i a l Grade P r e d i c t i o n s , " A l b e r t a J o u r n a l of E d u c a t i o n a l Research, 7:86-92, June 1961. CHAPTER I I I DESIGN The purpose of t h i s study was to d e v i s e a method to p r e d i c t grades i n f u t u r e p h y s i c s courses f o r the p h y s i c s students of North Vancouver Senior Secondary S c h o o l . The i n t e l l i g e n c e q u o t i e n t and the recorded achievement i n P h y s i c s 91 and Mathematics 91 were used as p r e d i c t i o n v a r i a b l e s to show that c o r r e l a t e d v a r i a t i o n s c o u l d p r e d i c t grades i n P h y s i c s 101, P h y s i c s 200 and P h y s i c s 155 and 156. T h e i r i n t e l l i g e n c e q u o t i e n t and t h e i r recorded achievement i n Grade XIII P h y s i c s 101 and Mathematics 101 were used as p r e d i c t i o n v a r i a b l e s to show that c o r r e l a t e d v a r i a t i o n s could p r e d i c t grades i n P h y s i c s 200 and P h y s i c s 155 and 156. The p r e d i c t e d grades would be s u b j e c t to the standard e r r o r . The Sample The sample used was made up of the students who wrote examinations i n P h y s i c s 101 e i t h e r as a u n i v e r s i t y s u b j e c t or as a Grade X I I I s u b j e c t , and who have p r e v i o u s l y r e c e i v e d grades i n P h y s i c s 91 and Mathematics 91 at North Vancouver High School (now North Vancouver Sen i o r Secondary School) duri n g the years from 1947 to 1962, as set out i n Table 30 i n the Appendix. Dependent and Independent V a r i a b l e s Dependent variables» In t h i s study the c r i t e r i a of success were d e f i n e d as the f i n a l grades g i v e n I n : (a) U n i v e r s i t y P h y s i c s 101 (b) Grade XIII P h y s i c s 101 (c) Second year U n i v e r s i t y courses (1) P h y s i c s 155 plus P h y s i c s 156 (a composite grade) (2) P h y s i c s 200 Independent v a r i a b l e s . The independent v a r i a b l e s were c l a s s i f i e d as: (a) The f i n a l course grades as estimated by the classroom t e a c h e r . (b) The f i n a l grades awarded by the Department of E d u c a t i o n f o r the U n i v e r s i t y Entrance Examina-t i o n s . (c) The i n t e l l i g e n c e q u o t i e n t r a t e d by O t i s S e l f -A d m i n i s t e r i n g T e s t s of Mental A b i l i t y , Higher Examinations: Form C. These v a r i a b l e s were recorded as q u o t i e n t s and f i n a l grades at North Vancouver Senior Secondary School and at the U n i v e r s i t y o f B r i t i s h Columbia. Some of the p r e d i c t i o n v a r i a b l e s are expressed by a seven p o i n t grading system from A through B, C&, C, C-, D, to E. For the purpose of computation, these grades were r e p l a c e d by A»7, B*»6, C«f**5, C«4, 0-^3, D C 32, E»l. The U n i v e r s i t y Entrance and Grade XIII 16 grades given by the Department of E d u c a t i o n were s t a t e d as percentages* When the grades of u n i v e r s i t y p h y s i c s courses such as P h y s i c s 101, Mathematics 101, P h y s i c s 200, were used as p r e d i c t i o n v a r i a b l e s or c r i t e r i a i n the c a l c u l a t i o n o f the r e g r e s s i o n e q u a t i o n , the t o t a l score was one hundred and f i f t y p o i n t s . When the grades of P h y s i c s 155 and P h y s i c s 156 were used as c r i t e r i a , the t o t a l score was i n d i c a t e d by two hundred which was the sum of the t o t a l score f o r these courses. O t i s S e l f - A d m i n i s t e r i n g T e s t s of Mental A b i l i t y , Higher Examination: Form C q u o t i e n t s were used. Procedure. S t a t i s t i c a l treatment to formulate m u l t i p l e r e g r e s s i o n equations equating the c r i t e r i o n o f success to the p r e d i c t i o n v a r i a b l e s was completed f o r the f o l l o w i n g r e l a t i o n -s hips : Dependent V a r i a b l e Grades i n : (a) U n i v e r s i t y P h y s i c s 101 (b) U n i v e r s i t y P h y s i c s 101 (c) Grade X I I I P h y s i c s 101 Independent V a r i a b l e s (a) P h y s i c s 91 and Mathematics 91 given by classroom teacher and I n t e l l i g e n c e Q u o t i e n t . (b) P h y s i c s 91 and Mathematics 91 awarded f o r U n i v e r s i t y Entrance Examinations and I n t e l l i g e n c e Q u o t i e n t . (c) P h y s i c s 91 and Mathematics 91 given by classroom teacher and I n t e l l i g e n c e 17 (d) Grade X I I I P h y s i c s 101 (e) P h y s i c s 155 plus P h y s i c s 156 (£) P h y s i c s 155 p l u s P h y s i c s 156 Q u o t i e n t . (d) P h y s i c s 91 and Mathematics 91 awarded f o r U n i v e r s i t y Entrance Examinations and I n t e l l i g e n c e Q u o t i e n t . (e) (1) P h y s i c s 91 and Math-ematics 91 given by classroom teacher and I n t e l l i g e n c e Q u o t i e n t . (2) P h y s i c s 91 and Math-ematics 91 given by the classroom teacher and I n t e l l i g e n c e Q u o t i e n t , but a c q u i r i n g P h y s i c s 101 standing at the U n i v e r s i t y . (3) P h y s i c s 91 and Math-ematics 91 given by classroom teacher and I n t e l l i g e n c e Q u o t i e n t , but a c q u i r i n g P h y s i c s 101 standing as a member of the Grade X I I I P h y s i c s 101 c l a s s . ( f ) (1) U n i v e r s i t y P h y s i c s 101, Mathematics 101 and I n t e l l i g e n c e Q u o t i e n t . 18 (2) Grade X I I I P h y s i c s 101, Mathematics 101 and I n t e l l i g e n c e Q u o t i e n t . (g) P h y s i c s 200 (g) (1) P h y s i c s 91 and Math-ematics 91 given by classroom teacher and I n t e l l i g e n c e Q u o t i e n t . ( 2 ) P h y s i c s 91 and Math-ematics 91 given by classroom teacher and I n t e l l i g e n c e Q u o t i e n t , but a c q u i r i n g P h y s i c s 101 st a n d i n g at the U n i v e r s i t y . (3) P h y s i c s 91 and Math-ematics 91 given by classroom teacher and I n t e l l i g e n c e Q u o t i e n t , but a c q u i r i n g P h y s i c s 101 as a member of the Grade X I I I P h y s i c s 101 c l a s s . (h) P h y s i c s 200 (h) (1) U n i v e r s i t y P h y s i c s 101, Mathematics 101 and I n t e l l i g e n c e Q u o t i e n t . (2) Grade X I I I P h y s i c s 101, Mathematics 101 and 19 I n t e l l i g e n c e Q u o t i e n t . P r e d i c t i o n . M u l t i p l e r e g r e s s i o n equations were d e r i v e d from the data f o r the sample from 1948 to 1958. M u l t i p l e r e g r e s s i o n equations were d e r i v e d from the data from 1948 to 1961. From the a n a l y s i s of each set of r e g r e s s i o n s , a c o e f f i c i e n t of c o r r e l a t i o n between the independent v a r i a b l e s and the dependent v a r i a b l e , and the s i g n i f i c a n c e of each c o e f f i c i e n t were e s t a b l i s h e d . I f the n u l l hypothesis i s r e j e c t e d , then the chances of success of each i n d i v i d u a l student should be p r e d i c t a b l e . The a ccuracy of these p r e d i c t i o n s was t e s t e d by c a l c u l a t i n g the c o r r e l a t i o n s between se t s of a c t u a l grades i n Grade X I I I P h y s i c s 101 and the U n i v e r s i t y P h y s i c s 101, P h y s i c s 200, and P h y s i c s 155 and 156, f o r 1959, 1960, and 1961, and c o r r e s -ponding s e t s of c r i t e r i a p r e d i c t e d by the a p p r o p r i a t e m u l t i p l e r e g r e s s i o n e q u a t i o n s . Mathematical Procedure. The d e v i a t i o n score method was used to c a l c u l a t e the p r e d i c t i o n equation f o r m u l t i p l e r e g r e s s i o n . The constant term which re p r e s e n t e d the c o n t r i b u t i o n of the nonexperlmental f a c t o r s then disappeared. The programming of the mathematical procedure Is d i s c u s s e d i n the appendix. Using the D o o l i t t l e method the c o e f f i c i e n t s a^ , a 2 , and a^ can be e v a l u a t e d * The c o e f f i c i e n t s then can be s u b s t i t u t e d i n the equation Y * a ^ ^ <¥ *2*2 * a 3 X 3 * C t o 8*ve the e q u a t i o n f o r the l i n e of m u l t i p l e r e g r e s s i o n . T h i s equation can be used f o r p r e d i c t i o n . CHAPTER IV THE RESULTS R e s u l t s from Data Based on the 1947-1957 P r e d i c t i o n V a r i a b l e s P r e d i c t i o n e q u a t i o n s . In order to compare p r e d i c t e d grades w i t h a c t u a l grades, the p o p u l a t i o n was d i v i d e d Into two groups. The grades of the students graduating from North Vancouver S e n i o r Secondary S c h o o l , from June 1947 to June 1957 at the Grade XII l e v e l , were the v a l u e s used to d e r i v e a set of p r e d i c t i o n e q u a t i o n s . P e r t i n e n t p r e d i c t i o n v a l u e s such as the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t and i t s s i g n i f i c a n c e and number o f degrees of freedom, the standard e r r o r , and the s i g n i f i c a n c e of the c o n t r i b u t i o n of the independent v a r i a b l e s to the r e g r e s s i o n were i n c l u d e d i n the study. The computations f o r these equations, with t a b u l a t i o n s of the p e r t i n e n t p r e d i c t i o n v a l u e s , are Included i n the appendix i n Tabular Summaries 1 to 10. C o r r e l a t i o n s between p r e d i c t e d grades and a c t u a l grades. The Grade X I I I and U n i v e r s i t y P h y s i c s grades of s t u d e n t s , who had graduated from North Vancouver Senior Secondary School from June 1958 to June 1961 at the Grade XII l e v e l , were compared with the p r e d i c t e d grades f o r these same s t u d e n t s . The l i n e a r r e g r e s s i o n equations used f o r p r e d i c t i o n are expressed by the general e q u a t i o n Y » a i x j ^ a 2 X 2 * a 3 X 3 * C * The p r e d i c t e d grades and a c t u a l grades were c o r r e l a t e d . 21 These grades and c o r r e l a t i o n s are Included i n Table 27 i n the appendix. Reg r e s s i o n equations f o r P h y s i c s 101. The r e g r e s s i o n equation which r e l a t e d the grades of U n i v e r s i t y P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 1. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .695 (P<.01) The standard e r r o r was 19.3. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y t o the p r e d i c t i o n . To be s i g n i f i c a n t beyond the one per cent l e v e l the sample mean d i f f e r e n c e must be so great that i t would occur i n l e s s than one per cent of the p o p u l a t i o n s f o r which the n u l l h ypothesis i s t r u e . TABLE 1 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... fo r U n i v e r s i t y P h y s i c s 101 y C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 101 U.B.C. Phy s i c s 91 L.G. Mathematics I.Q. 91 L.G. Y » 4.10* Xx -.210* X 2 4-2.02* X 3 +27.5 S.E. = 19.3 or 12.9 % R y l 2 3 8 8 * 6 9 5 * • S i g n i f i c a n t beyond the one per cent l e v e l P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between t h i r t y 22 s i x cases of a c t u a l grades f o r U n i v e r s i t y P h y s i c s 101 and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of U n i v e r s i t y P h y s i c s 101 on the l e t t e r grades for P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s was .77. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 30 i n the appendix. The r e g r e s s i o n equation which r e l a t e d the grades of U n i v e r s i t y P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 i s given i n Table 2. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .863 ( P < . 0 1 ) . The standard e r r o r was 15.0. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 2 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... fo r U n i v e r s i t y P h y s i c s 101 y C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 101 U.B.C. Ph y s i c s 91" U.E . Mathematics 91 U.E. I.Q. Y » +.423* 4-1.04* X 2 +.920* X 3 S.E. « 15.0 or 10.0 % R y l 2 3 * .863* • S i g n i f i c a n t beyond the one per cent l e v e l 23 P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between eighteen cases of a c t u a l grades for U n i v e r s i t y P h y s i c s 101, and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of U n i v e r s i t y P h y s i c s 101 on the U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s was .83. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 30 i n the appendix. The r e g r e s s i o n equation which r e l a t e d the grades of Grade XIII P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 3. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .696 (P< .01). The standard e r r o r was 9.44. The P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 3 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e - o f R ... f o r Grade XIII P h y s i c s 101 y C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 101 G.XIII P h y s i c s 91 L.G. Mathematics 91 L.G. I.Q. Y <* 5.83* X L +2.42* X 2 +.148* X 3 +21.8 S.E. •» 9.44 or 9.44 % R y l 2 3 " - 6 9 6 * • S i g n i f i c a n t beyond the one per cent l e v e l 24 P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between t h i r t y -nine cases o f a c t u a l grades for Grade XIII P h y s i c s 101, and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of Grade XIII P h y s i c s 101 on the l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s was .48. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 31 i n the appendix. The r e g r e s s i o n equation which r e l a t e d the grades of Grade X I I I P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 i s given i n Tab l e 4. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .958. The standard e r r o r was 4.80. Ph y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 4 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R . f o r Grade X I I I P h y s i c s 1.01 7 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 101. G.XIII P h y s i c s 91 U .E . Mathematics I.Q. 91 U.E. Y - +.943* X x +.256** X 2 -.243 X 3 -10.5 S.E. •» 4.80 or 4.80 % R y l 2 3 m ' 9 5 8 * • S i g n i f i c a n t beyond the one per cent l e v e l 25 P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between e i g h t cases of a c t u a l grades f o r Grade X I I I P h y s i c s 101, and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of Grade X I I I P h y s i c s 101 on the U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s was .81. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 31 i n the appendix. R e g r e s s i o n equations f o r P h y s i c s 155 and 156. The r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 5. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .557 ( P < . 0 1 ) . The standard e r r o r was 22.2. The i n t e l l i g e n c e q u o t i e n t , and the Ph y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n beyond the 10 per cent l e v e l . TABLE 5 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e o f R ... f o r P h y s i c s 155 and 156 y i C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant .Physics 155,156 Ph y s i c s 91 Mathematics I.Q. 91 L.G. 91 L.G. Y m +2.76 X x +1.90 X 2 +1.74 X 3** +76.1 S.E. •» 22.2 or 11.1 % R =» .557** K y l 2 3 * * S l g n i f l e a n t beyond the f i v e per cent l e v e l 26 P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between seven cases of a c t u a l grades f o r P h y s i c s 155 and 156 on the l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s was .91. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 27 i n the appendix. The r e g r e s s i o n equation which r e l a t e d the grades of Phy s i c s 155 and 156 to the I n t e l l i g e n c e q u o t i e n t and the grades of U n i v e r s i t y P h y s i c s 101 and Mathematics 101 i s given i n Table 6. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .658 ( P < . 0 1 ) . The standard e r r o r was 20.1. The i n t e l l i g e n c e q u o t i e n t and the P h y s i c s 101 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 6 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... f o r P h y s i c s 155 and 156 y l * J C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 155, Ph y s i c s 101 Mathematics I.Q. 156 U.B.C. 101 U.B.C. Y • .835** X t +.00527 X 2 +1.42**X 3 -78.3 S.E. « 20.1 or 10.1 % R y l 2 3 • .658* • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n l f l e a n t beyond the f i v e per cent l e v e l P r e d i c t i o n s were made f o r grades from the sample f o r 27 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between seven cases of a c t u a l grades f o r P h y s i c s 155 and 156, and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of P h y s i c s 155 and 156 on the grades f o r U n i v e r s i t y P h y s i c s 101 and Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t s was .86. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 30 i n the appendix. The r e g r e s s i o n equation which r e l a t e d the grades of Ph y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and grades of Grade X I I I P h y s i c s 101 and Mathematics 101 i s given i n Table 7. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .550 not s i g n i f i c a n t f o r 3 and 5 degrees of freedom. TABLE 7 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e o f R ... f o r P h y s i c s 155 and 156 y l / C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 155, P h y s i c s 91 Mathematics I.Q. 156 L.G. 91 L.G. Y » .931 Xx -.931 X 2 +1.71 X 3 +94.8 R y l 2 3 " .550 not s i g n i f i c a n t No p r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961, because the m u l t i p l e c o r r e l a t i o n was not s i g n i f i c a n t . 28 R e g r e s s i o n equations f o r P h y s i c s 200. T h e - r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 200 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 8. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .910 ( P < . 0 1 ) . The standard e r r o r was 17.4. The i n t e l l i g e n c e q u o t i e n t and the P h y s i c s 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . The p r e r e q u i s i t e P h y s i c s 101 was taken at the U n i v e r s i t y . TABLE 8 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n Standard E r r o r and S i g n i f i c a n c e of f o r P h y s i c s 200 C o e f f i c i e n t , R y l 2 3 C r i t e r i o n . P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 200 P h y s i c s 91 Mathematics L.G. 91 L.G. I.Q. Y - 20.0* X 1 +2.15 X 2 +1.10**X 3 -51.8 S.E. - 17.4 or 11.6 % R y l 2 3 * .910* • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n l f l e a n t beyond the f i v e per cent l e v e l P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between seven cases of a c t u a l grades f o r P h y s i c s 200* and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of P h y s i c s 200 on the l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s was .13. These grades and 29 c o r r e l a t i o n s are Included i n Table 30 i n the appendix. The r e g r e s s i o n equation which r e l a t e d the grades of Phy s i c s 200 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s g i v e n i n Table 9. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n was .667 not s i g n i f i c a n t f o r 3 and 1 degrees of freedom. TABLE 9 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R 1 _ fo r P h ysics 200 y l Z J C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 200 Ph y s i c s 91 L.G. Mathematics 91 L.G. I.Q. Y » -5.681 X x +1.12 X 2 +8.56 X 3 +8.89 R y l 2 3 - 6 6 7 not s i g n i f i c a n t T h i s equation was not used to make p r e d i c t i o n s f o r grades from the sample f o r 1958, 1959, I960, and 1961. The r e g r e s s i o n equation which r e l a t e d - t h e grades of Ph y s i c s 200 to the i n t e l l i g e n c e q u o t i e n t and the grades of U n i v e r s i t y P h y s i c s 101 and Mathematics 101 i s given In Table 10. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .916 ( P < . 0 1 ) . The standard e r r o r was 16.8. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 101 and Mathematics 101 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . 30 TABLE 10 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R f o r P h y s i c s 200 y I Z J C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-57 Constant P h y s i c s 200 Ph y s i c s 101 Mathematics I.Q. U.B.C. 101 U.B.C. Y m .826* X t +1.98** X 2 +1.16**X 3 -3.71 S-.E... • 16.8 or 11.2 t R y l 2 3 - .916* • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n i f l e a n t beyond the f i v e per cent l e v e l P r e d i c t i o n s were made f o r grades from the sample f o r 1958, 1959, 1960, and 1961. The c o r r e l a t i o n between seven cases of a c t u a l grades f o r P h y s i c s 200, and grades p r e d i c t e d by the r e g r e s s i o n equation f o r the r e g r e s s i o n of the grades of Ph y s i c s 200 on the grades f o r U n i v e r s i t y P h y s i c s 101 and Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t s was .48. These grades and c o r r e l a t i o n s are i n c l u d e d i n Table 30 In the appendix. P r e d i c t i o n f o r P h y s i c s 200. P r e d i c t i o n s f o r the grades of P h y s i c s 200, made by the equation r e s u l t i n g from the r e j e c t i o n of the r e g r e s s i o n o f P h y s i c s 200 grades on the i n t e l l i g e n c e q u o t i e n t and P h y s i c s 91 and Mathematics 91 l e t t e r grades, showed a c o r r e l a t i o n of .13 with a c t u a l grades of students with U n i v e r s i t y P h y s i c s 101 p r e r e q u i s i t e . T h i s was not s i g n i f i c a n t f o r s i x degrees of freedom. S i n c e only one 31 student with Grade XIII p r e r e q u i s i t e completed P h y s i c s 200 du r i n g the years 1958, 1959, 1960, no f u r t h e r c o r r e l a t i o n s were attempted. P r e d i c t i o n s for the grades of P h y s i c s 200 were c a l c u l a t e d from the equation f o r the r e g r e s s i o n of P h y s i c s 200 grades on the i n t e l l i g e n c e q u o t i e n t and U n i v e r s i t y P h y s i c s 101 and Mathematics 101 grades. They c o r r e l a t e d with the a c t u a l grades of P h y s i c s 200 with a s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t . P r e d i c t i o n s were not made f o r the grades of P h y s i c s 200 from the equation f o r the r e g r e s s i o n of P h y s i c s 200 on the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades f o r Ph y s i c s 91 and Mathematics 91, with Grade X I I I P h y s i c s 101 as a p r e r e q u i s i t e . The m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was not s i g n i f i c a n t . R e s u l t s from Data Based on the 1947-1961 P r e d i c t i o n V a r i a b l e s P r e d i c t i o n E q u a t i o n s . Combining the groups, the grades of the students graduating from North Vancouver Senior Secondary School from June 1947 to June 1961 at the Grade XII l e v e l were t a b u l a t e d . These grades were used to formulate a set of p r e d i c t i o n equations to p r e d i c t grades f o r P h y s i c s 101, Ph y s i c s 155 and 156, and Ph y s i c s 200. P r e d i c t i o n values such as the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t and i t s s i g n i f i c a n c e and number of degrees of freedom, the standard e r r o r , and the s i g n i f i c a n c e of the c o n t r i b u t i o n of the Independent v a r i a b l e s to the r e g r e s s i o n were i n c l u d e d i n the study. The computations f o r these equations were t a b u l a t i o n s of the p e r t i n e n t p r e d i c t i o n 32 values are i n c l u d e d i n the appendix i n the Tabular Summaries 11 to 23. The second set of equations was formulated because of the e f f e c t of the l a r g e r degrees of freedom f o r the r e s i d u a l s on the s i g n i f i c a n c e of the c o r r e l a t i o n s and the c o n t r i b u t i o n of the p r e d i c t i o n v a r i a b l e s * R e g r e s s i o n equations f o r P h y s i c s 101 * The r e g r e s s i o n equation which r e l a t e d the grades of U n i v e r s i t y P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 11. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .668 ( P < . 0 1 ) . The standard e r r o r was 19.5. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 11 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R _ f o r U n i v e r s i t y P h y s i c s .101 7 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 101 P h y s i c s 91 Mathematics 91 I .Q. U.B.C. L.G. L.G. Y => 4-7.37* 4-0.52** X 2 4-1 .54* X 3 4-23.7 S.E. « 19.5 or 13.0 % R y l 2 3 » .668* • S i g n i f i c a n t beyond the one per cent l e v e l • • S i g n i f i c a n t beyond the f i v e per cent l e v e l ~—---T—---~——*—*~~——*———•' ' " - — — — • '• — — — — — — — — — — • " — 33 The r e g r e s s i o n equation which r e l a t e d the grades of U n i v e r s i t y P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 i s given i n Table 12. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .859 ( P < . 0 1 ) . The standard e r r o r was 14.2. P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 12 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R fo r U n i v e r s i t y P h y s i c s 101 y 1 " C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 101 Ph y s i c s 91 Mathematics I.Q. U.B.C. U.E . 91 U.E. Y • .582** X x +1.07* X 2 +.570 X„ -38.7 3 S .E. • 14.2 or 9.44 % Ry 1 2 3 " - 8 5 9 * • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n i f l e a n t beyond the f i v e per cent l e v e l The r e g r e s s i o n equation which r e l a t e d the grades of Grade X I I I P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 13. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .647 (P< .01). The standard e r r o r was 8.92. The i n t e l l i g e n c e q u o t i e n t , and the Ph y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . 34 TABLE 13 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R f o r Grade X I I I P h y s i c s 101 y l Z 3 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 101 G.XIII P h y s i c s 91 L.G. Mathematics 91 L.G. I.Q. 4.30* X± +2.79* X 2 +.156* X 3 +27.8 S.E. • 8.92 or 8.92 % R y l 2 3 ° * 6 4 7 * • S i g n i f i c a n t beyond the one * * S i g n i f l e a n t beyond the f i v e per cent l e v e l per cent l e v e l The r e g r e s s i o n equation which r e l a t e d the grades of Grade XIII P h y s i c s 101 to the i n t e l l i g e n c e q u o t i e n t and the U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 i s given i n Table 14. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .855 ( P < . 0 1 ) . The standard e r r o r was 6.77. P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 14 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... f o r Grade X I I I P h y s i c s 101 v l " C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947 -61 Constant P h y s i c s 101 G.XIII P h y s i c s 91 U.E. Mathematics 91 U.E. I.Q. Y « .910 X x +3.72 X 2 -.648 X 3 -6.48 S.E. - 6.77 or 6.77 % Ryl23 - .855* • S i g n i f i c a n t beyond the one per cent l e v e l 35 Regr e s s i o n equations f o r P h y s i c s 155 and 156. The r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 15. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .619 ( P < . 0 1 ) . The standard e r r o r was 22.3. The i n t e l l i g e n c e q u o t i e n t and the Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 15 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... f o r P h y s i c s 155 and 156 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947 -61 Constant P h y s i c s 155, Ph y s i c s 91 Mathematics I .Q. 156 L.G. 91 L.G. Y » 1.28 Kl +9.13** X 2 +1 .73**X3 +41.5 S.E. 22.3 or 11.2 % Ryl23 - .619* • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n i f l e a n t beyond the f i v e per cent l e v e l The r e g r e s s i o n e q u a t i o n which r e l a t e d the grades of P h y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 16. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .582 ( P < . 0 1 ) . The standard e r r o r was 22.1. The i n t e l l i g e n c e q u o t i e n t s and the Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . 36 TABLE 16 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R f o r P h y s i c s 155 and 156 y l Z 3 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 15 5, 156 P h y s i c s 91 L.G. Mathematics 91 L.G. I.Q. Y * 1.79 X t +7.12* X 2 +1.53* X 3 S.E. • 22.1 or 11.1 % R y l 2 3 ' ' 5 8 2 * • S i g n i f i c a n t beyond the one per cent l e v e l The r e g r e s s i o n equation which r e l a t e d the grades of Ph y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 Is given In Table 17. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .706 not s i g n i f i c a n t f o r 3 and 6 degrees of freedom. The standard e r r o r was 27.2. TABLE 17 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R, f o r P h y s i c s 155 and 156 yl23 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 155, 156 P h y s i c s 91 Mathematics I.Q. Y m 1.24 X x +11.1 x 2 +2.99 X 3 +2.69 S.E.> 27.2 . R y l 2 3 " ' 7 0 8 or 13.8 % not s i g n i f i c a n t 37 The r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and the grades of U n i v e r s i t y P h y s i c s 101 and Mathematics 101 i s given i n Table 18. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .709 ( P < . 0 1 ) . The standard e r r o r was 19.2. The I n t e l l i g e n c e q u o t i e n t and the P h y s i c s 101 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 18 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t . Standard E r r o r and S i g n i f i c a n c e of R ... for P h y s i c s 155 and 156 y l Z J C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 155, P h y s i c s 101 Mathematics I.Q. 156 U.B.C. 101 U.B.C. Y • .970* X j 4-.0881 X 2 4-1.33**X3-10.2 S.E. * 19.2 or 9.59 % R y l 2 3 * . 7 0 9 * • S i g n i f i c a n t beyond the one per cent l e v e l * * S l g n i f l e a n t beyond the f i v e per cent l e v e l The r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 155 and 156 to the i n t e l l i g e n c e q u o t i e n t and the grades of Grade X I I I P h y s i c s 101 and Mathematics 101 i s given i n Table 19. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .682 not s i g n i f i c a n t f o r 3 and 6 degrees of freedom. The standard e r r o r was 27.9. 38 TABLE 19 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... fo r P h y s i c s 155 and 156 y l Z 3 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 155, 156 P h y s i c s 101 U.B.C. Mathematics 101 U.B.C. I.Q. Y » .447 X x +.557 X 2 +2.31 X 3 +7.01 S.E. » 27.9 < R y l 2 3 - .682 or 14.0 % not s i g n i f i c a n t R e g r e s s i o n equations f o r P h y s i c s 200. The r e g r e s s i o n e q u a t i o n which r e l a t e d the grades o f P h y s i c s 200 to the i n t e l l i g e n c e q u o t i e n t and the l e t t e r grades of P h y s i c s 91 and Mathematics 91 i s given i n Table 20. For t h i s r e g r e s s i o n e quation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .785 ( P ^ . 0 1 ) The standard e r r o r was 19.5. The P h y s i c s 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 20 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R . .« f o r P h y s i c s 200 y*<" C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 200 Ph y s i c s 91 Mathematics I.Q. L.G. 91 L.G. Y * 3.53 X x .871 X 2 +2.87**X 3 +1.77 S . E . 0 19.5 or 13.0 % R y l 2 3 m «785* • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n i f l e a n t beyond the f i v e per cent l e v e l 39 The r e g r e s s i o n equation which r e l a t e d the grades of Ph y s i c s 200 to the i n t e l l i g e n c e q u o t i e n t i s given i n Table 21. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .796 (P< .01). The standard e r r o r was 19.7. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . TABLE 21 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R ... f o r P h y s i c s 200 y A Z J C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947 -61 Constant P h y s i c s 200 P h y s i c s 91 Mathematics I . Q . L.G. 91 L.G. Y • 4.49* Xj^ -.296** X 2 4/2.94**X3 4-15.7 S.E. - 19.7 or 9.87 % R ' «* . 796* yl23 • S i g n i f i c a n t beyond the one per cent l e v e l * * S i g n i f l e a n t beyond the f i v e per cent l e v e l The r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 200 to the I n t e l l i g e n c e q u o t i e n t and the grades of U n i v e r s i t y P h y s i c s 101 and Mathematics 101 i s given i n Table 22. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .870 ( P < . 0 1 ) . The standard e r r o r was 17.1. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 101 grades c o n t r i b u t e d s i g n i f i c a n t l y to the p r e d i c t i o n . 40 TABLE 22 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R_ f o r P h y s i c s 200 yl23 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 200 Phy s i c s 101 Mathematics I.Q. U.B.C. 101 U.B.C. Y <=• .760 X x +.0724 X 2 +1.51 X 3 -22.8 S.E. 17.1 or 11.4 % R y l 2 3 m - 8 7 0 * • S i g n i f i c a n t beyond the one per cent l e v e l The r e g r e s s i o n equation which r e l a t e d the grades of P h y s i c s 200 to the i n t e l l i g e n c e q u o t i e n t and the grades of Grade X I I I P h y s i c s 101 and Mathematics 101 i s given i n Table 23. For t h i s r e g r e s s i o n equation the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t was .987 (P <',01). The standard e r r o r was 7.34. The i n t e l l i g e n c e q u o t i e n t , and the P h y s i c s 91 and Mathematics 91 grades c o n t r i b u t e d s i g n i f i c a n t l y . TABLE 23 P r e d i c t i o n E q u a t i o n , M u l t i p l e C o r r e l a t i o n C o e f f i c i e n t , Standard E r r o r and S i g n i f i c a n c e of R f o r P h y s i c s 200 yl23 C r i t e r i o n P r e d i c t i o n V a r i a b l e s 1947-61 Constant P h y s i c s 200 P h y s i c s 101 G.XIII Mathematics I.Q 101 G.XIII Y =* 3.74** X, -2.60 X, +2.20 X 3 -2.32 S.E. «« 7.34 or 4.88 % R y l 2 3 .987* * S i g n i f l e a n t beyond the one per cent l e v e l * * S l g n i f l e a n t beyond the f i v e per cent l e v e l 41 Summary of R e s u l t s . In order to p r e d i c t grades i n fu t u r e p h y s i c s courses t h i s study formulated an e m p i r i c a l r e l a t i o n s h i p which would a i d i n p r e d i c t i n g success i n P h y s i c s 101, P h y s i c s 155 and 156 and P h y s i c s 200 from a v a i l a b l e f i n a l r ecorded grades of students who had entered these h i g h e r p h y s i c s c o u r s e s . P h y s i c s 101 grades were obtained at the Grade X I I I or U n i v e r s i t y l e v e l f o r courses which had been made as n e a r l y a l i k e as p o s s i b l e by the Ph y s i c s C u r r i c u l u m R e v i s i o n Committee of the Department of E d u c a t i o n . The recorded f i n a l h i g h s c h o o l grades were used as the p r e d i c t i o n v a r i a b l e s f o r P h y s i c s 101 students e n r o l l e d at the U n i v e r s i t y of B r i t i s h Columbia or at North Vancouver Se n i o r Secondary S c h o o l . The f i n a l grades In P h y s i c s 101 were used as a measure of the c r i t e r i a of success i n t h i s course. M u l t i p l e r e g r e s s i o n equations were formulated to p r e d i c t the grades f o r P h y s i c s 101 from the grades o f P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t . These grades were f i n a l l e t t e r grades or u n i v e r s i t y entrance grades g i v e n by the Department of E d u c a t i o n . There were four s e t s of these equations n e c e s s a r y . Each equation was formulated t w i c e . The m u l t i v a r i a t e r e l a t i o n s h i p s were obtained f o r the student p o p u l a t i o n s from 1947 to 1957 so that p r e d i c t i o n s could be made f o r the years 1958 to 1961. The p r e d i c t e d grades were then compared to the a c t u a l grades obtained d u r i n g these three y e a r s . These equations are r e f e r r e d to as equations A. These equations and an a n a l y s i s of the r e g r e s s i o n are shown In Table 24. 42 TABLE 24 SUMMARY OF REGRESSION EQUATIONS Summary of the c h a r a c t e r i s t i c s of the p r e d i c t i o n v a r i a b l e s , c r i t e r i a , m u l t i p l e r e g r e s s i o n e quations, and c o e f f i c i e n t s of m u l t i p l e c o r r e l a t i o n used f o r the p r e d i c t i o n of c o l l e g e p h y s i c s grades Equations A were from sample f o r 1947 to 1957 Equations B were from sample f o r 1947 to 1961 C r i t e r i a P r e d i c t i o n v a r i a b l e s Constant Y Xx X 2 x 3 c P h y s i c s 101 P h y s i c s 91 Mathematics I.Q. U.B.C. L • G • 91 L.G. * A. Y * 4-4.10* X x - .210* X 2 4-2.02* X 3 4-27.5 S.E. » 19.31 or 9% Ryl23 * .695* B. Y • 4-7.37* X x -0.501** X 2 4-1.54* X 3 4-23.7 S.E. - 19.5 or 13.0% Ryl23 « .668* Ph y s i c s 101 P h y s i c s 91 Mathematics I.Q. U.B.C. U.E. 91 U.E. A. Y * 4- .424** X t 4-1.04 X 2 4- .920**X 3-32.3 S .E . .- 15.0 or 10.0% Ryl23 m .863* B. Y - 4- .581** Xx 4-1.07* X 2 4- .565 X 3 -38.7 S.E. .- 14.2 or 9.47% Ryl23 » .859* 43 TABLE 24 (continued) C r i t e r i a P r e d i c t i o n V a r i a b l e s Constant Y V X 2 X 3 C Ph y s i c s 101 P h y s i c s 91 G.XIII L.G. Mathematics 91 L.G. I.Q. A. Y «* 4-5.83* X t S.E. m 9.44 or 9.44% Ryl23•» .696* 4-2.42* X 2 + .148 X 3 +21.8 B. Y - +4.30* X x S.E. 8.92 or 8.92% Ryl23 - .647* 4-2.79* X 2 + .157* X 3 +27.8 Ph y s i c s 101 P h y s i c s 91 G.XIII U.E. Mathematics 91 U.E. I.Q. A. Y » + .943* Kx S.E. .» 4.80 or 4.80% Ryl23 '» .958* 4- .225** X 2 - .243 X 3 -10.5 B. Y - 4- .910** Kx S.E. » 6.77 or 6.77% Ryl23.- .855* + .372** X 2 - .647 X 3 - 6.49 Phy s i c s 155, P h y s i c s 91 156 L.G. Mathematics 91 L.G. I.Q. A l l students A. Y - 2.76 Xx S.E. » 22.2 or 11.1% Ryl23 * .557** +1.90 X 2 +1.74** X 3 +76.1 B. Y « -1.28 S.E. * 22.4 or 11.2% Ryl23 * .619* +9.13** X 2 +1.73** X 3 +41.5 Ph y s i c s 101 p r . U.B.C. A. Y » 1.79 X t S.E. " 22.1 or 11.1% Ryl23 » .582* +7.12* X 2 +1.53* X 3 +55.4 44 TABLE 24 (continued) C r i t e r i a Y P r e d i c t i o n V a r i a b l e s X l X 2 X 3 Constant C B. Y -s •& • ** Ryl23 * 1.24 X x +1.11 X 2 27.2 or 13.67. .708 not s i g n i f i c a n t +2.99 ; S3 +2.68 Phy s i c s 155, 156 Ph y s i c s 101 Mathematics 101 I.Q. U n i v e r s i t y students A. Y -S.E. " Ryl23 -.835**^ + .00527 X 2 20.1 or 10.1% .658* +1.42** X 3 -78.3 B. Y » S •£ • Ryl23 »' .970 X x + .00881 X 2 19.2 or 9.59% .709* +1.33 X 3 -101.7 Grade XIII students A. Y » S .E . •» Ryl23 • .931 X x - .931 X 2 .550 not s i g n i f i c a n t +1.71 X 3 +94.8 B. Y » S .E . -Ryl23 » .447 X x + .557 X 2 2 7.91 or 13.96% .682 not s i g n i f i c a n t +2.31 X 3 +7 . 01 Ph y s i c s 200 Phy s i c s 91 Mathematics L.G. 91 L.G. I.Q. A l l students Y » 4.49* Xj^ - .296** X 2 +2.94** X 3 +15.7 S.E. « Ryl23 -19.73 or 9.87% .796* U.B.C. Physics i 101 p r . A. Y m S.E. • Ryl23 -+20.0* X t +2.15 X 2 17.4 or 11.6% .910* +1.10** X 3 -51.8 45 TABLE 24 (continued) C r i t e r i a Y P r e d i c t i o n V a r i a b l e s X l X 2 Constant X 3 C G.XIII P h y s i c s 101 p r . A. Y » S •£ • Ryl23 •» -5.68 X x +11.2 X 2 .667 not s i g n i f i c a n t + .0856 X 3 +88.9 B. Y » 3.74** X x -2.60** X 2 -2.20 X 3 -2.32 S . E . w Ryl23 * 7.34 or 4.88% .987* P h y s i c s 200 Ph y s i c s 101 Mathematics 101 I.Q. U.B.C. P h y s i c s 101 p r . A. Y " S.E. » Ryl23 « .826* X t + .198** X 2 16.8 ror 11.2% .916* +1.16** X 3 -37.1 B. Y » S.E. -Ryl23 -* .760 Xj + .00724 X 2 17.1 or 11.4% .870* +1.51 X 3 -22.8 G. X I I I P h y s i c s 101 p r . Y • 3.74 % x -2.60 X 2 +2.20 X 3 -23.2 S •& • 888 Ryl23 » 7.34 or 4.88% .987* Ry 123 m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t S.E. standard e r r o r A equations f o r experience from 1947 to 1957 B equations f o r experience from 1947 to 1961 * s i g n i f i c a n t beyond 1% ** s i g n i f i c a n t beyond 5% p r . p r e r e q u i s i t e 46 The i n t e l l i g e n c e q u o t i e n t and the f i n a l high school grades were used as p r e d i c t i o n v a r i a b l e s to p r e d i c t the grades for P h y s i c s 155 and 156 and P h y s i c s 200. Each equation was formulated t w i c e . The c o r r e l a t i o n c o e f f i c i e n t between a c t u a l grades and p r e d i c t e d grades f o r P h y s i c s 155 and 156 and P h y s i c s 200 were s i g n i f i c a n t f o r l e t t e r grade p r e d i c t o r s . The recorded f i n a l grades o f the Ph y s i c s 101 students were used as p r e d i c t i o n v a r i a b l e s , and f i n a l grades i n P h y s i c s 155 and 156 or i n P h y s i c s 200 were used as a .measure of the c r i t e r i a of success i n f u t u r e p h y s i c s c o u r s e s . M u l t i p l e r e g r e s s i o n equations were formulated f o r the r e g r e s s i o n o f the grades f o r P h y s i c s 155 and 156 on the grades of P h y s i c s 101 and Mathematics 101 and the I n t e l l i g e n c e q u o t i e n t . There were two sets of these equations necessary, s i n c e the P h y s i c s 101 grades were recorded at the U n i v e r s i t y or at North Vancouver Seni o r Secondary S c h o o l . M u l t i p l e r e g r e s s i o n equations were formulated f o r r e g r e s s i o n o f the grades f o r P h y s i c s 200 on the grades of P h y s i c s 101 and Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t . These equations and an a n a l y s i s of the r e g r e s s i o n are shown i n Table 24. C o r r e l a t i o n s of P r e d i c t e d Grades and P r e r e q u i s i t e s From the summary s e v e r a l trends appear. Using high school f i n a l l e t t e r grade r a t i n g s the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s f o r the p r e d i c t i o n s of U n i v e r s i t y P h y s i c s 101 47 were .668 and .695 and f o r Grade XIII P h y s i c s 101 were .647 and . 6 9 6 , a l l s i g n i f i c a n t beyond one per cent. Using u n i v e r s i t y entrance grades the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s f o r the p r e d i c t i o n s of U n i v e r s i t y P h y s i c s 101 were .859 and .863 and f o r Grade XIII P h y s i c s 101 were .855 and .958 a l l s i g n i f i c a n t beyond one per cen t . A comparison of these c o r r e l a t i o n c o e f f i c i e n t s i n d i c a t e d t h at grades granted by the Department of E d u c a t i o n as the r e s u l t s of the U n i v e r s i t y Entrance Examinations p r e d i c t e d success i n c o l l e g e p h y s i c s with g r e a t e r c o r r e l a t i o n than d i d l e t t e r grades recorded by North Vancouver Se n i o r Secondary S c h o o l . Using h i g h school f i n a l l e t t e r grade r a t i n g s the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s f o r the p r e d i c t i o n s o f P h y s i c s 155 and 156 were-.619, .582, and .708 a l l s i g n i f i c a n t beyond one per cent and .557 s i g n i f i c a n t beyond f i v e per c e n t . Using high school f i n a l l e t t e r grade r a t i n g s the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s f o r the p r e d i c t i o n s of P h y s i c s 200 were .785, .796, .987, and .910 a l l s i g n i f i c a n t beyond one per c e n t . High School f i n a l l e t t e r grades made s i g n i f i c a n t p r e d i c t i o n equations f o r P h y s i c s 155 and 156 and P h y s i c s 200. Using U n i v e r s i t y or Grade XIII grade p r e d i c t o r s , the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s f o r ' t h e p r e d i c t i o n s of the grades of P h y s i c s 155 and 156 were .658, .709, and .682 a l l s i g n i f i c a n t beyond one per cent and f o r P h y s i c s 200 were .916 and .870, both s i g n i f i c a n t beyond one per c e n t . U n i v e r s i t y or Grade X I I I grade p r e d i c t o r s made s i g n i f i c a n t p r e d i c t i o n 48 equations f o r P h y s i c s 155 and 156 and P h y s i c s 200. C o r r e l a t i o n s between P r e d i c t e d Grades and A c t u a l Grades The r e l i a b i l i t y of the p r e d i c t i o n grades f o r P h y s i c s 101, P h y s i c s 155 and 156 and P h y s i c s 200 was t e s t e d . P r e d i c t i o n equations formulated with the grades o f the students graduating from North Vancouver Senior Secondary School from June 1947 to June 1957 at the Grade XII l e v e l were used to p r e d i c t f o r students who graduated from June 1958 to June 1961. The p r e d i c t e d grades were c o r r e l a t e d with the a c t u a l grades recorded f o r these same p u p i l s over the same p e r i o d o f time. See Tables 30 and 31 i n the appendix. The c o r r e l a t i o n c o e f f i c i e n t s are l i s t e d i n Table 25 which f o l l o w s . The r e l a t i o n s h i p s between the p r e d i c t e d grades and the p r e d i c t i o n v a r i a b l e s were rep r e s e n t e d by the m u l t i p l e c o e f f i c i e n t of c o r r e l a t i o n . The r e l a t i o n s h i p between p r e d i c t e d grades and a c t u a l grades f o r the same p h y s i c s course were given by a zero order c o r r e l a t i o n between these grades. T h i r t y - s i x U n i v e r s i t y P h y s i c s 101 grades p r e d i c t e d by l e t t e r grade p r e d i c t o r s and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d w i t h the t h i r t y - s i x a c t u a l grades with a c o r r e l a t i o n c o e f f i c i e n t of .77. T h i r t y nine Grade XIII P h y s i c s 101 grades p r e d i c t e d by l e t t e r grade p r e d i c t o r s and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d with t h i r t y - n i n e a c t u a l grades with a c o r r e l a t i o n c o e f f i c i e n t of .48. E i g h t e e n U n i v e r s i t y P h y s i c s 101 grades p r e d i c t e d by u n i v e r s i t y entrance grades and the i n t e l l i g e n c e 49 TABLE 25 CORRELATION COEFFICIENTS BETWEEN PREDICTED GRADES AND ACTUAL GRADES FOR COLLEGE PHYSICS COURSES For students who graduated from June 1958 to June 1961 from North Vancouver Sen i o r Secondary School C o r r e l a t i o n C o e f f i c i e n t s Between the Course V e r t i c a l P a i r s 1. 2. 3. 4. Ph y s i c s 101 U.B.C. X X P h y s i c s 101 Grade X I I I X X Ph y s i c s 101 p r . p r e d i c t o r s L.G. X X Ph y s i c s 101 p r . p r e d i c t o r s U.E. X X C o r r e l a t i o n c o e f f i c i e n t s .77* .48* .83* .81* Number of cases 36 39 18 8 Ry 123 f o r p r e d i c t e d c r i t e r i a .668* .647 .863 .855* P h y s i c s 200 X X Ph y s i c s 200 p r . p r e d i c t o r s L.G. X Ph y s i c s 200 p r . p r e d i c t o r s P h y s i c s 101 etc. X C o r r e l a t i o n c o e f f i c i e n t s .13 .48 Number of cases 7 7 Ry 123 f o r p r e d i c t e d • c r i t e r i a .910* .916* P h y s i c s 155 and 156 X X Ph y s i c s 155 and 156 p r . p r e d i c t o r s L.G. X Ph y s i c s 155 and 156 p r e d i c t o r s P h y s i c s 101 etc. X C o r r e l a t i o n c o e f f i c i e n t s Number of cases 7 7 • S i g n i f i c a n t Ry 123 f o r p r e d i c t e d beyond one per c r i t e r i a .557** .658* cent * * S i g n i f l e a n t beyond f i v e per cent 50 q u o t i e n t c o r r e l a t e d with the eighteen a c t u a l grades with a c o r r e l a t i o n c o e f f i c i e n t of .83. E i g h t Grade XIII P h y s i c s 101 grades p r e d i c t e d by u n i v e r s i t y entrance grades and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d with e i g h t a c t u a l grades with a c o r r e l a t i o n of .81. A c t u a l grades had a high e r c o r r e l a t i o n w i t h P h y s i c s 101 grades p r e d i c t e d by u n i v e r s i t y entrance grades than with P h y s i c s 101 grades p r e d i c t e d by l e t t e r grades. The m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s between U n i v e r s i t y P h y s i c s 101 and i t s p r e d i c t o r s and between Grade XIII P h y s i c s 101 and i t s p r e d i c t o r s were s i m i l a r when l e t t e r grades were used as p r e d i c t o r s . A s i m i l a r i t y was a l s o noted between the p a i r of c o r r e l a t i o n c o e f f i c i e n t s that r e s u l t when u n i v e r s i t y entrance grades were used as p r e d i c t o r s . These c o e f f i c i e n t s are i n c l u d e d i n Table 25. A s i m i l a r comparison f o r p r e d i c t e d and a c t u a l grades f o r P h y s i c s 200 and P h y s i c s 155 and 156 was made. Seven P h y s i c s 200 grades p r e d i c t e d by Grade XII l e t t e r grade p r e d i c t o r s and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d with seven a c t u a l grades with a c o r r e l a t i o n o f .13. Seven P h y s i c s 200 grades p r e d i c t e d by P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d with seven a c t u a l grades with a c o r r e l a t i o n c o e f f i c i e n t of .48, n e i t h e r o f which were s i g n i f i c a n t . S i x P h y s i c s 155 and 156 grades p r e d i c t e d by Grade XII l e t t e r grade and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d w i t h s i x a c t u a l grades with a c o r r e l a t i o n c o e f f i c i e n t of .91. S i x 51 P h y s i c s 155 and 156 p r e d i c t e d by P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t c o r r e l a t e d with s i x a c t u a l grades w i t h a c o r r e l a t i o n c o e f f i c i e n t of .86. A c t u a l grades had a h i g h e r c o r r e l a t i o n with p r e d i c t e d P h y s i c s 155 and 156 grades than with p r e d i c t e d P h y s i c s 200 grades. CHAPTER V CONCLUSION AND IMPLICATIONS The r e s e a r c h d e s c r i b e d i n the p r e v i o u s chapters was planned to I n v e s t i g a t e the problem of p r e d i c t i o n o f success i n P h y s i c s 101, P h y s i c s 155 and 156 and Ph y s i c s 200 f o r Grade XII P h y s i c s students at North Vancouver Senior Secondary S c h o o l . Grades were p r e d i c t e d s t a t i s t i c a l l y and the r e l i a b i l i t y of these p r e d i c t i o n s was examined. Con c l u s i o n s From the s t a t i s t i c a l evidence presented i n the r e s u l t s the f o l l o w i n g c o n c l u s i o n s were i n f e r r e d . (1) The f i n a l l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s were s i g n i f i c a n t p r e d i c t o r s f o r the grades of U n i v e r s i t y P h y s i c s 101. Ther e f o r e the experimental h y p o t h e s i s (1) was r e j e c t e d . (2) The Department of E d u c a t i o n U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s were s i g n i f i c a n t p r e d i c t o r s f o r the grades of U n i v e r s i t y P h y s i c s 101. T h e r e f o r e the experimental h y p o t h e s i s (2) was r e j e c t e d . (3) The f i n a l l e t t e r grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s were s i g n i f i c a n t p r e d i c t o r s f o r the grades of Grade XIII P h y s i c s 101. Ther e f o r e the experimental hypothesis (3) was r e j e c t e d . The U n i v e r s i t y Entrance grades f o r P h y s i c s 91 and Mathematics 91 and the i n t e l l i g e n c e q u o t i e n t s were s i g n i f i c a n t p r e d i c t o r s f o r the grades of Grade X I I I P h y s i c s 101. Ther e f o r e the experimental h y p o t h e s i s (4) was r e j e c t e d . The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 given by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t s were s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 155 p l u s 156. T h e r e f o r e the experimental hypothesis (5) was r e j e c t e d . The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 given by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t f o r the students who ac q u i r e d P h y s i c s 101 grades at the U n i v e r s i t y were s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 155 plus 156. T h e r e f o r e the experimental hypothesis (6) was r e j e c t e d . The f i n a l l e t t e r grades of P h y s i c s 91 and Mathematics 91 given by the classroom teacher and i n t e l l i g e n c e q u o t i e n t f o r the students who ac q u i r e d P h y s i c s 101 grades at North Vancouver High School were not proved s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 155 plus 156 Therefore the experimental hypothesis (7) was not 54 r e j e c t e d . (8.) The grades of U n i v e r s i t y P h y s i c s 101, Mathematics 101 and the I n t e l l i g e n c e q u o t i e n t were s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 155 plus 156. Th e r e f o r e the experimental hypothesis (8) was r e j e c t e d . (9) The grades of Grade X I I I P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t were not proved s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 155 p l u s 156. Th e r e f o r e the experimental h y p o t h e s i s (9) was not r e j e c t e d . (10) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathe-matics 91 given by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t were s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 200. Ther e f o r e the experimental hypothesis (10) was r e j e c t e d . (11) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathe-matics 91 gi v e n by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t f o r the students who a c q u i r e d P h y s i c s 101 grades at the U n i v e r s i t y were s i g n i f i c a n t p r e d i c t o r s f o r the grades of P h y s i c s 200. Th e r e f o r e the experimental hypothesis (11) was r e j e c t e d . (12) The f i n a l l e t t e r grades of P h y s i c s 91 and Mathe-matics 91 given by the classroom teacher and the i n t e l l i g e n c e q u o t i e n t f o r the students who a c q u i r e d P h y s i c s 101 grades at North Vancouver High School were not proved s i g n i f i c a n t p r e d i c t o r s 55 f o r the grades of P h y s i c s 200. T h e r e f o r e the experimental hypothesis (12) was not r e j e c t e d . (13) The grades of U n i v e r s i t y P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t were s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 200. T h e r e f o r e the experimental hypothesis (13) was r e j e c t e d . (14) The grades of Grade XIII P h y s i c s 101, Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t were s i g n i f i c a n t p r e d i c t o r s f o r P h y s i c s 200. T h e r e f o r e the experimental hypothesis (14) was r e j e c t e d . The s t a t i s t i c a l p r e d i c t i o n of P h y s i c s 101, P h y s i c s 155 and 156, and P h y s i c s 200 f o r a sample was expedient. P h y s i c s 101 grades were p r e d i c t e d from r e g r e s s i o n equations with i n t e l l i g e n c e q u o t i e n t s combined with recorded l e t t e r grades or w i t h u n i v e r s i t y entrance grades i n P h y s i c s 91 and Mathe-matics 91. P h y s i c s 200 and P h y s i c s 155 and 156 grades were p r e d i c t e d from i n t e l l i g e n c e q u o t i e n t s combined with P h y s i c s 91 and Mathematics 91 grades as (a) recorded l e t t e r grades at the Grade XII l e v e l (b) u n i v e r s i t y entrance grades. The m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s were s i g n i f i c a n t beyond one per c e n t . P h y s i c s 200 and P h y s i c s 155 and 156 grades were p r e d i c t e d from i n t e l l i g e n c e q u o t i e n t s combined with P h y s i c s 101 and Mathematics 101 grades. C o r r e l a t i o n s between s e t s of a c t u a l grades i n P h y s i c s 101, P h y s i c s 155 and 156, P h y s i c s 200, and corresponding s e t s of p r e d i c t e d grades showed p r e d i c t i v e accuracy. 56 P l a n n i n g Academic S t u d i e s The c o u n s e l l o r s of North Vancouver Senior Secondary School used t h i s p r e d i c t i o n study when p l a n n i n g f u r t h e r academic courses i n P h y s i c s with students i n t e r e s t e d i n t h i s d i s c i p l i n e . The grades f o r P h y s i c s 101, P h y s i c s 155 and 156, and P h y s i c s 200 were p r e d i c t e d w i t h i n l i m i t s s e t by the a p p r o p r i a t e standard e r r o r s . These p r e d i c t i o n s helped i n making a choice between the F a c u l t y of Science or A p p l i e d S c i e n c e and other F a c u l t i e s at the U n i v e r s i t y of B r i t i s h Columbia. I f a student chose a programme f o r which h i s p r e d i c t e d grades i n d i c a t e l i t t l e l i k e l i h o o d of success, at l e a s t he d i d so conscious of the c h a l l e n g e . P r e d i c t i o n of I n d i v i d u a l Grades For P h y s i c s 101. P h y s i c s 101 grades were p r e d i c t e d f o r the f i f t y - f i v e s u c c e s s f u l P h y s i c s 91 students of the year 1961 to 1962. T h e i r recorded l e t t e r grades and i n t e l l i g e n c e q u o t i e n t s were used to make these p r e d i c t i o n s . The p r e d i c t e d P h y s i c s 101 grades were made assuming that a l l of these students had entered U n i v e r s i t y P h y s i c s 101. The p r e d i c t e d P h y s i c s 101 grades were then made assuming that the same students had entered Grade XIII P h y s i c s 101. Twenty-four of these P h y s i c s 91 students of the year 1961 to 1962 a l s o wrote the Department o f E d u c a t i o n u n i v e r s i t y entrance examinations. T h e i r recorded Mathematics 91 and P h y s i c s 91 grades and t h e i r i n t e l l i g e n c e q u o t i e n t s were used 57 to make p r e d i c t i o n s . P r e d i c t e d P h y s i c s 101 grades were made assuming t h a t a l l o f these students had entered U n i v e r s i t y P h y s i c s 101. P r e d i c t e d P h y s i c s 101 grades were then made assuming that these students had entered Grade XIII P h y s i c s 101. These r e c o r d s and p r e d i c t i o n s are t a b u l a t e d i n Table 27 i n the appendix. For P h y s i c s 155 and 156. P h y s i c s 155 and 156 grades were p r e d i c t e d f o r the tw e n t y - f i v e s u c c e s s f u l P h y s i c s 91 students of 1961 to 1962. I n t e l l i g e n c e q u o t i e n t s and the recorded l e t t e r grades f o r the term ending June 1962, were used to make these p r e d i c t i o n s . P r e d i c t i o n s were made f o r each student who had r e c e i v e d a p r e d i c t e d p r e r e q u i s i t e grade f o r P h y s i c s 101. One p r e d i c t i o n was made from an equation which assumed Grade XIII P h y s i c s 101 as a p r e r e q u i s i t e . Another p r e d i c t i o n was made from an equation which assumed U n i v e r s i t y P h y s i c s 101 as a p r e r e q u i s i t e . These r e c o r d s and r e s u l t s are contained i n Table 27, i n the appendix. The recorded grades f o r U n i v e r s i t y P h y s i c s 101 and Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t s given to the s u c c e s s f u l U n i v e r s i t y P h y s i c s 101 studen t s , f o r the term ending June 1962, were used to p r e d i c t grades i n P h y s i c s 155 and 156 f o r each of twelve s t u d e n t s . These records and r e s u l t s are t a b u l a t e d i n Table 28, i n the appendix. The recorded grades f o r Grade X I I I P h y s i c s 101 and Mathematics 101 and the I n t e l l i g e n c e q u o t i e n t s given to the s u c c e s s f u l Grade XIII P h y s i c s 101 studen t s , f o r the term 58 ending June 1962, were used to p r e d i c t grades i n P h y s i c s 155 and 156 f o r each o f seventeen s t u d e n t s . These records and r e s u l t s are t a b u l a t e d i n Table 29, i n the appendix. For P h y s i c s 200. To p r e d i c t P h y s i c s 200 grades, the recorded grades f o r U n i v e r s i t y P h y s i c s 101 and Mathematics 101 and the i n t e l l i g e n c e q u o t i e n t s given to the s u c c e s s f u l U n i v e r s i t y Physics-101 students f o r the term ending June 1962, were used to p r e d i c t grades i n P h y s i c s 200 f o r each of twelve s t u d e n t s . These r e c o r d s and r e s u l t s are t a b u l a t e d i n T a b l e 28, i n the appendix. The recorded grades and i n t e l l i g e n c e q u o t i e n t s given to the s u c c e s s f u l Grade X I I I P h y s i c s 101 s t u d e n t s , f o r the term ending June 1962, were used to e v a l u a t e the r e l e v a n t m u l t i p l e r e g r e s s i o n formulas. These c r i t e r i a were used as the p r e d i c t e d grades i n P h y s i c s 200 f o r each of seventeen s t u d e n t s . These r e c o r d s and r e s u l t s are t a b u l a t e d i n Table 29, i n the appendix• A p p l i c a t i o n of p r e d i c t i o n . The school c o u n s e l l o r f o r North Vancouver Se n i o r Secondary School obtained the f o l l o w i n g i n f o r m a t i o n from Table 27 In the appendix. Student number 19 had a p r e d i c t e d grade of s i x t y - f o u r per cent In Grade XIII P h y s i c s 101. The standard e r r o r was seven per c e n t . The same student had a p r e d i c t e d grade of f i f t y - e i g h t per cent i n U n i v e r s i t y P h y s i c s 101. The standard e r r o r was nine per c e n t . By r e f e r r i n g to the normal d i s t r i b u t i o n of standard s c o r e s , the student was t o l d of h i s chances of o b t a i n i n g grades w i t h i n one or two standard e r r o r s o f h i s p r e d i c t e d grades i n t h i s s u b j e c t . Comparison between the Grades of P h y s i c s 101 Courses C o n s i d e r a t i o n was now given to the g e n e r a l comparison between the grades p r e d i c t e d f o r U n i v e r s i t y P h y s i c s 101 and Grade XIII P h y s i c s 101 by l e t t e r -grade p r e d i c t o r s . As can be seen from Table 27 i n almost every i n s t a n c e the grade p r e d i c t e d f o r a student was h i g h e r f o r Grade XIII P h y s i c s 101 than f o r U n i v e r s i t y P h y s i c s 101. However, the d i f f e r e n t i a l was more s i g n i f i c a n t f o r the lower r a n k i n g student. A graph showing the r e l a t i o n s h i p between the rank order and the grades f o r each of these p r e d i c t i o n s i s shown on page (60 . The graph shows that ten students would score below s i x t y per cent and none would score below f i f t y per cent i n Grade XIII P h y s i c s 101. The f a c t that there was no f a i l u r e s p r e d i c t e d i n Grade XIII P h y s i c s was c o n s i s t e n t w i t h experience which recorded two f a i l u r e s i n the past three y e a r s . Furthermore these s t u d e n t s , f o r whom the f o r e c a s t was made, had a mean i n t e l l i g e n c e q u o t i e n t r a t i n g of 122 which i s higher than 188, the mean of the i n t e l l i g e n c e q u o t i e n t from the recorded achievement. T h i s can be seen i n Table 27 i n the appendix. P r e d i c t i o n s e v a l u a t e d by u n i v e r s i t y entrance grades showed the p r e d i c t e d grades hi g h e r f o r Grade XIII P h y s i c s 101 than f o r U n i v e r s i t y P h y s i c s 101. These independently assigned u n i v e r s i t y entrance grades, used as p r e d i c t i o n v a r i a b l e s , ON OO N 3 3 Z X 3 I Q 3 N 3 O 0 3 61 p r e d i c t e d a p a t t e r n of p r e d i c t e d P h y s i c s 101 grades almost i d e n t i c a l t o the one p r e d i c t e d by f i n a l l e t t e r grades. Again the d i f f e r e n t i a l s were more pronounced f o r the lower r a n k i n g s t u d e n t s . These p r e d i c t i o n s are contained i n Table 27 i n the appendix. A graph showing the r e l a t i o n s h i p between the rank order and grades f o r each of Grade X I I I and U n i v e r s i t y P h y s i c s 101 Is shown on page £2. xhe graph shows that f i v e students scored below f i f t y per cent and seven scored below s i x t y per cent f o r U n i v e r s i t y P h y s i c s 101 whereas one student scores below f i f t y per cent and four below s i x t y per cent f o r Grade XIII P h y s i c s 101. C o u n s e l l i n g C o u n s e l l i n g the i n d i v i d u a l Grade XII s t u d e n t . The problem of adjustment to the more mature academic method o f i n s t r u c t i o n at a u n i v e r s i t y i s a d i f f i c u l t one f o r many st u d e n t s . T h i s adjustment was made one year l a t e r f o r those students who remained i n Grade X I I I . The e f f e c t of t h i s d e lay was i m p l i e d by some of the r e s u l t s of t h i s study. A boy, student f i f t y - f o u r , with an A high s c h o o l academic r a t i n g , an i n t e l l i g e n c e q u o t i e n t of one hundred f o r t y , and a p r e d i c t e d grade of eight-two per cent f o r U n i v e r s i t y P h y s i c s 101 was b e t t e r advised to take i n s t r u c t i o n at the U n i v e r s i t y where b e t t e r l i b r a r y f a c i l i t i e s were a v a i l a b l e and s u b j e c t f i e l d a u t h o r i t i e s would give more depth to h i s e d u c a t i o n . 62 E U G E N E D I E T Z G E N C O . N O . 3 7 5 63 Other students who i n d i c a t e d an a b i l i t y to make f i r s t or second c l a s s marks i n U n i v e r s i t y P h y s i c s 101 were s i m i l a r l y a dvised to attempt to do so, other f a c t o r s being p r o p i t u o u s . The grades are t a b u l a t e d i n Table 27 i n the appendix. I t was po i n t e d out to student e i g h t e e n t h a t , of p u p i l s with h i s experi e n c e , s i x t y - e i g h t per cent would score l e s s than s i x t y - f i v e per cent i n U n i v e r s i t y P h y s i c s 101 and that f i f t y per cent o f such students would score l e s s than f i f t y -two per cen t . I n the case of p u p i l s with the same experience i n Grade X I I I P h y s i c s 101, s i x t y - e i g h t per cent would score more than f i f t y - f o u r per cent and f i f t y per cent would score more than sixty-two per c e n t . H i s chances of success were b e t t e r i n Grade X I I I . The c h o i c e of student 10 was not so c l e a r l y d e f i n e d . I t was p o i n t e d out that s i n c e a standard d e v i a t i o n was gre a t e r i n the U n i v e r s i t y sample than i n the Grade X I I I by 12.9 to 8.3, that f a i l u r e would be more probable In U n i v e r s i t y P h y s i c s 101. The p r e d i c t e d grades f o r student 54 were made from l e t t e r grade or u n i v e r s i t y entrance p r e d i c t o r s , f o r U n i v e r s i t y P h y s i c s 101 and Grade XIII P h y s i c s 101. From u n i v e r s i t y entrance grades h i s p r e d i c t e d U n i v e r s i t y P h y s i c s 101 grade was eighty-two per cent w i t h nine per cent standard e r r o r and h i s Grade X I I I P h y s i c s grade was e i g h t - f o u r per cent with seven per cent standard e r r o r . From l e t t e r grades h i s p r e d i c t e d U n i v e r s i t y P h y s i c s 101 grade was e i g h t y - n i n e per 64 cent with t h i r t e e n per cent standard e r r o r and eight-one per cent w i t h nine per cent standard e r r o r . There was a drop i n the standard e r r o r i n the grades p r e d i c t e d from the u n i v e r s i t y entrance grades. The p r e d i c t e d grades were i n r e a s o n a b l y c l o s e agreement although they r e s u l t e d from four independent p r e d i c t i o n s . For other comparisons r e f e r to Table 27. C o u n s e l l i n g i n d i v i d u a l Grade X I I I s t u d e n t s . Before c o u n s e l l i n g i n d i v i d u a l students from Grade X I I I P h y s i c s 101 c l a s s of 1961 - 1962. they were compared with the sample. The mean i n t e l l i g e n c e q u o t i e n t was 116.18 f o r the c l a s s of 1961 - 1962. The mean i n t e l l i g e n c e q u o t i e n t from the sample was 122.67 f o r P h y s i c s 200 students with U n i v e r s i t y P h y s i c s 101 p r e r e q u i s i t e * I n a l i k e manner the means o f the other p r e d i c t o r s were reduced below the means of the grades from the sample. T h i s was not a b r i l l i a n t c l a s s . Only seven of the seventeen were p r e d i c t e d as being able to make a second c l a s s mark i n P h y s i c s 200. None of the p u p i l s had f i r s t c l a s s marks p r e d i c t e d i n t h i s s u b j e c t . I t was decided to p r e d i c t reasonable success i n the s u b j e c t f o r f i v e students and to i n d i c a t e to two of these that P h y s i c s 200 would prove to be a very d i f f i c u l t s u b j e c t . Only two o f the f i v e students i n d i c a t e d t h e i r i n t e n t i o n of e n r o l l i n g i n P h y s i c s 200. Table 29 shows two p r e d i c t e d second c l a s s grades, ten pass grades, and f i v e f a i l u r e s In the p r e d i c t e d P h y s i c s 65 155 and 156 grades. Three students have decided to e n r o l l In P h y s i c s 155 and 156. Many o f the other students were persuaded to f o l l o w other l i n e s of endeavor. R e l a t e d Problems f o r Research Some u n i v e r s i t y f a c u l t i e s r e q u i r e P h y s i c s 101 as a p r e r e q u i s i t e f o r entrance i n t o t h e i r f a c u l t y . A study should be made to see i f success i n P h y s i c s 101 i s r e l a t e d to success i n these f a c u l t i e s * A f u r t h e r study to compare the grades f o r s i m i l a r achievement i n U n i v e r s i t y P h y s i c s 101 and Grade X I I I P h y s i c s 101 would be u s e f u l . Then f o r each o f these courses a minimum grade which would i n s u r e a reasonable chance o f success i n P h y s i c s 155 and 156 and i n P h y s i c s 200 could be set • Summary The purpose of t h i s study was to p r e d i c t the p h y s i c s grades f o r North Vancouver S e n i o r Secondary P h y s i c s 91 students i n P h y s i c s 101 at the Grade X I I I or U n i v e r s i t y l e v e l , or i n P h y s i c s 155 and 156, or P h y s i c s 200. I t was e s t a b l i s h e d t h a t P h y s i c s 101 grades could be p r e d i c t e d from the i n t e l l i g e n c e q u o t i e n t s and the f i n a l h i g h s c h o o l grades i n P h y s i c s 91 and Mathematics 91. P r e d i c t e d P h y s i c s 101 grades were made from f i n a l h i g h school l e t t e r grades or u n i v e r s i t y entrance grades g i v e n by the Department o f E d u c a t i o n . I n each case the c o r r e l a t i o n c o e f f i c i e n t between 66 a c t u a l grades obtained f o r the sample from 1948 to 1961 and p r e d i c t e d grades f o r the same p e r i o d was s i g n i f i c a n t . However, the standard e r r o r s were lower when u n i v e r s i t y entrance grades r a t h e r than l e t t e r grades were used as p r e d i c t o r s . The grades for Ph y s i c s 155 and 156 and f o r Ph y s i c s 200 were p r e d i c t e d . The p r e d i c t i o n v a r i a b l e s were the i n t e l l i g e n c e q u o t i e n t s and the f i n a l l e t t e r grades f o r Ph y s i c s 91 and Mathematics 91 or the U n i v e r s i t y grades or Grade XIII grades f o r P h y s i c s 101 and Mathematics 101. The p r e d i c t e d grades f o r P h y s i c s 155 and 156 and f o r P h y s i c s 200 c o r r e l a t e d with a c t u a l grades which were obtained In these s u b j e c t s by the sample from 1948 to 1961. P r e d i c t i o n s were made f o r the North Vancouver Senior Secondary Physics 91 and P h y s i c s 101 students f o r the school year 1961 to 1962. The p r e d i c t i o n s were used to counsel these students i n t h e i r choice of f u r t h e r academic s t u d i e s . 67 BIBLIOGRAPHY A. Books Barr, A r v i l S., Robert A. David and Palmer 0. Johnson. E d u c a t i o n a l Research and A p p r a i s a l . Chicago, J.B. L i p p i n c o t t Co., 1953. Walker, Helen M. Elementary S t a t i s t i c a l Methods. New York, Henry H o l t and Company, 1948. '\p Wert, Jamese., Ch a r l e s 0. Ne i d t , J . St a n l e y Ahmann. S t a t i s t i c a l ix Methods i n E d u c a t i o n and P s y c h o l o g i c a l Research. New York, A p p l e t o n - C e n t u r y - C r o f t s , I n c o r p o r a t e d , 1954. Johnson, Palmer 0. S t a t i s t i c a l Methods In Research. New York, P r e n t i c e - H a l l , I n c o r p o r a t e d , 1949. General S t a t i s t l c s . Orange, New J e r s e y , Monroe C a l c u l a t i n g Machine Company, I n c o r p o r a t e d , 1961. Campbell, W i l l i a m G i l e s . Form and S t y l e i n T h e s i s W r i t i n g . Boston, Houghton M i f f l i n Company. B. P e r i o d i c a l s Adams, Sam and H.L. G a r r e t t . " S c h o l a s t i c Background as Re l a t e d t o Success i n C o l l e g e P h y s i c s , " J o u r n a l of E d u c a t i o n a l Research, 47:545-9, March, 1954. Ar n o l d , D.L. and G. S c h o e p f l e . " C o r r e l a t i o n of High School and C o l l e g e Grades," American J o u r n a l of .Physics, 26:537-9, November, 1958. Baker, E l i z a b e t h C , and George A. "Factor A n a l y s i s o f High School V a r i a b l e s and Success i n U n i v e r s i t y S u b j e c t s f o r the F i r s t Semester i n U n i v e r s i t y , " J o u r n a l of Experimental  E d u c a t i o n , 24:315-18, June, 1956. Ho r s t , P a u l . "A Technique f o r the Development of a D i f f e r e n t i a l P r e d i c t i o n B a t t e r y , " P s y c h o l o g i c a l Monograph, 68 Number 9, Whole Number 380, 1954. H o r s t , P a u l . "A Technique f o r the Development of a M u l t i p l e Absolute P r e d i c t i o n B a t t e r y , " P s y c h o l o g i c a l Monograph, 69 Number 5, Whole Number 390, 1955. 68 H o r s t , P a u l . " D i f f e r e n t i a l P r e d i c t i o n of Success i n V a r i o u s C o l l e g e Course Areas," C o l l e g e and U n i v e r s i t y , 31 Number 4, 456-71, 1956. Jackson, R.A. " P r e d i c t i o n of the Academic Success of C o l l e g e Freshmen," J o u r n a l of E d u c a t i o n a l Psychology," 46:296-301 May, 1955. " M a l l o r y , J.P., and o t h e r s . " P r e d i c t i n g A t t r i t i o n - s u r v i v a l i n F i r s t Year E n g i n e e r i n g , " American J o u r n a l of P h y s i c s , 24: 605-10, December, 1956. McQuarry, J.P., and o t h e r s . "What F a c t o r s Determine Student Achievement i n F i r s t Year C o l l e g e Chemistry?" J o u r n a l of  Chemical E d u c a t i o n , 29:460-464, September, 1952. P i e r s o n , L.R. "High School Teacher P r e d i c t i o n of C o l l e g e Success," Personnel and Guidance J o u r n a l , J37:142-5, October, 19TcT V e r n i e r , CM., and o t h e r s . " D i f f e r e n t i a l P r e d i c t i o n of a S p e c i f i c Behavior from Three P r o j e c t i v e Techniques," J o u r n a l of C o n s u l t i n g Psychology, 19:175-82, June, 1955. Wallace, W.L. "The P r e d i c t i o n of Grades i n S p e c i f i c C o l l e g e Courses," J o u r n a l of E d u c a t i o n a l Research, Volume 44, A p r i l , 1951. APPENDIX PROGRAMMING OP MATHEMATICAL PROCEDURE The problem o f p r e d i c t i o n of success i n phy s i c s was now concerned w i t h s e t t i n g up the m u l t i p l e r e g r e s s i o n equations which would p r e d i c t success i n Physics 101 from the knowledge of p r e d i c t i o n scores already mentioned. Values and operations which were necessary t o programme~ mathematical procedure f o r m u l t i p l e r e g r e s s i o n t a b l e s and to c a l c u l a t e c o e f f i c i e n t s of c o r r e l a t i o n s and the F and t t e s t s of s i g n i f i c a n c e and r e l a t i v e c o n t r i b u t i o n s to r e g r e s s i o n , f o l l o w i n the order of t h e i r use and development. Raw Scores. The raw scores which were p e r t i n e n t were c o l l e c t e d and arranged i n v e r t i c a l columns so that sums and sums of squares could be e a s i l y d erived. The c a l c u l a t i n g was done on a Monromatic c a l c u l a t o r . The cross products were checked against the sums of squares as they were c a l c u l a t e d . Student Physics 91 Mathematics 91 Physics 101 1 ^ X 3 Y Derived values t o determine r e g r e s s i o n c o e f f i c i e n t s . Prom the sums and sums of squares and cross products of the raw scores, the sums and sums of squares and cross products of the d e v i a t i o n scores were c a l c u l a t e d . The systematic procedure '110 i s illustrated i n the following set of symbols and systems of equations, N = SX-L = SX 3 = 2Y = SX2 = SX 3Y SJ^Y :SX2Y 3X^ 3 SX-^ Xg 2X2X3 Derived covariances Symbol (Raw Score) Symbol (Deviation Deviation-Raw Score Score) Equivalents 2 Y 2 2 2 s 2 &x 2 2 ^ 3 2 s x i 2 2 X 2 2 =2X2 - i l ^ l ^ Y 2x xy 2X2Y Bx 2y= 2 X 2Y- E§_I 2X3Y SX3y=aC3Y- H l l % X 2 2x-^x2 2^ X 3 2 x l x 3 2X2X3 2 x 2 x 3 ^ 3=2X2X3- ( 2 * 8 ) P * 3 i Normal Equations. The method of least squares i s used and the expression ( y^- a l x l ~ a 2 x 2 ~ a 3 x 3 ) ^ s differentiated with respect t o al» a2» and a3» arid each of the derivatives i s set 71 equal t o zero. The normal equations r e s u l t i n g from s e t t i n g the d e r i v a t i v e s of the d i f f e r e n t i a t e d r e g r e s s i o n equation equal t o zero r e s u l t e d i n the f o l l o w i n g e q u a l i t i e s . Sx-jy = a x s x 2 + a^s x-_x2 + a^ s x - j X ^ 2 s x 2 y = a-_ 2 x 1 x 2 + a 2 S x 2 + a^ 2 x 2 x ^ s x ^ y = a-L + ag.sxye^ + S u b s t i t u t e i n the above equations from the t a b l e of deri v e d covariances and solve f o r a-^ , a 2, a^ u s i n g the D o o l i t t l e method. These w i l l evaluate the equation f o r the l i n e of m u l t i p l e r e g r e s s i o n . Y * a - ^ + agXg + £3X3 + C The m u l t i p l e r e g r e s s i o n c o e f f i c i e n t . The r e g r e s s i o n c o e f f i c i e n t s enable us to p r e d i c t the values of the c r i t e r i o n v a r i a b l e . The accuracy w i t h which t h i s was accomplished was determined by the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t . This was done by the a n a l y s i s of variance which d i v i d e s the sum o f squares of the d e v i a t i o n s of the c r i t e r i o n i n t o two p a r t s , one a s s o c i a t e d w i t h r e g r e s s i o n and the other a r e s i d u a l . These values were d e r i v e d as i n d i c a t e d and Included i n an a n a l y s i s o f m u l t i p l e r e g r e s s i o n . Derived values t o determine m u l t i p l e r e g r e s s i o n t a b l e S.S. of Regression = a^ 2 x-jy + a 2 2 x 2 y + a^Sx^y S.S. of Residuals = s y 2 - a ^ x ^ - a 2 2 x 2 y - a 3 2 x^y 7-2 • 2 , „ . a i 2 x , y + aoSXpy + a^sxoy Ry(l,2,3) = 1 _T S T 2 A n a l y s i s o f M u l t i p l e R e g r e s s i o n Table Source o f Degrees o f 'Sum o f Mean V a r i a t i o n Freedom Squares Square R e g r e s s i o n m R 22y 2 R R e s i d u a l s N - ra - 1 (1 - R 2 )sy 2 ( 1 - R 2 ) y j 2 N - m - 1 T o t a l N - 1 s y 2 Fm,N-m-l = ' » " V m ( l - R 2 ) The r e l a t i v e Importance o f the v a r i a b l e s i n the p r e d i c t i o n o f the c r i t e r i a were o f i n t e r e s t i n t h i s s t u d y . The r e l a t i v e c o n t r i b u t i o n of each p r e d i c t i o n v a r i a b l e s t o t h e r e g r e s s i o n was c a l c u l a t e d by comparing the c o n t r i b u t i o n of each v a r i a b l e t o t h e sum of squares o f r e g r e s s i o n . T h i s r a t i o was expressed as a percentage , p r o v i d i n g a l l terms i n the above r a t i o s are p o s i t i v e . R e l a t i v e c o n t r i b u t i o n of p r e d i c t i o n v a r i a b l e s t o r e g r e s s i o n S . S . o f r e g r e s s i o n a-^  sx^y + a 2 S x 2 y + a3 F o r f i r s t v a r i a b l e i * 1 j * - 7 ^ "' '•• ( a l S X j y + a 2 s x 2 y :+ a^ Sx^y Por second variable Por third variable v - — — — , ( a i 2 x i y + a 2 2 X 2 y + a 3 s x 3y Por computing various coefficients of correlation relative to the problem. 2 S. S. of X1 regression r = : * ' . i r y l S. S. of total r 2 S. S. of Xg regression y 2 S. S. of total o S. S. of Xo regression y J • S. S. of total . _ r (N - 2) 1 - r 2 GAIN DUE TO THE ADDITION OP A PREDICTION VARIABLE A method of testing whether a significant gain i n the a b i l i t y to predict occurs when a variable is added to the prediction scheme is to test whether the difference between the respective coefficients of correlation is significant. The following table i s used to summarize the results of the correlation. 74 C o e f f i c i e n t s of C o r r e l a t i o n and Test of S i g n i f i c a n c e f o r A d d i t i o n of the V a r i a b l e Gain due t o a d d i t i o n of a p r e d i c t i o n v a r i a b l e Source of Degrees Sum of squares , Mean Square V a r i a t i o n of Freedom m-Variable Regression m 2 2 R (l,2...m)2y (m - 1) V a r i a b l e Regression m - 1 2 2 R y(l,2...m-n)2y Gain Due to 1 R 2(l,2.*.m) - R 2 R 2 ( l , 2 . • .m)..- R A d d i t i o n of * • x Jp 7 „ * y p V a r i a b l e (1,2...m-n) 2 y & (l,2...m-n) s y * 2, ' x 2 1 - R y ( l » 2 . . . m ) 2 y 2 i n v a r i a b l e H - m - 1 1-R y(l,2...m) S y * ^ _ 1 R e s i d u a l s T o t a l N - 1 2y« R 2(l,2...m)-R_(l,2...ra-n) H - m - 1 P l f H,a-1 = — 2—g n 1 - R y(l,2...m) Necessary Systems of Equatlons f o r Complete Computations R^2 3 = 1 - U-4 2 ) ( l-4 3 > 2) R y l 3 = 1 " ( 1 - r y l » ( 1 - r y 3 . 1 » ( l - r ^ X l - r f a ) 75 r. y 3 . l 2 (1 - r y ) ( l - r f 3 ) INTERPRETATION OP RESULTS AS APPLIED TO PROBLEM Prom the above r e s u l t s and the P and t t a b l e s o f s i g n i f i c a n c e , the s i g n i f i c a n c e o f the means can be determined, at the $% and 1% l e v e l . The standard e r r o r of estimate can be determined and the e r r o r f o r one standard d e v i a t i o n and two standard d e v i a t i o n s can be shown and p r e d i c t a b i l i t y of scores can be i n d i c a t e d . TABLE 26 HISTORY OP PREDICTOR SCORES AND CRITERIA Stu d e n t 1 s High School G r a d u a t i o n P h y s i c s 91 Teachers' grade P h y s i c s 91 U.E. Ph y s i c s 101 U.B.C. P h y s i c s 101 Gr. X I I I P h y s i c s App. Sc, U.B.C. P h y s i c s A r t s & Sc. U.B.C. G13 Year G13 I9k6-i|.7 13 k 2 5 1 2 I 9 U 7 - P 22 5 9 3 7 - m. I9ii8-ij .9 23 6 5 5 CD «n 2 19^9-50 29 5- 3 l l 1 1 1950-51 16 6 3 3 - 2 2 1951-52 21 6 10 3 ll. 1 1 1952-53 27 10 9 3 2 • a - M 1953-55- 38 7 % K - 1 1954-55 51 $ 15 2 7 3 m> 1955-56 62 15 9 5 - mt 1956-57 ,63 15 13 10 3 3 1 2 1957-58 k9 6 12 8 5 - 1 I 1958-59 62 6 12 "9 3 3 1 1959-60 ¥ 23 7 10 - 2 8 2 1960-61 63 17 12 17 - - - -1961-62 66 30 — — — — T o t a l No* of Students 652 165 135 9k k.0 17 19 8 The number o f students i n c l u d e d i n any one year Is determined by the s t u d e n t s 1 h i g h s c h o o l g r a d u a t i o n y e a r . - s i . TABLE 27 PREDICTION VARIABLES AND THE PREDICTED CRITERIA POR THE PHYSICS 91 CLASS OP 1961-62 © P* -P co 1 2 3 I 6 7 8 9 1 0 I I 12 1 15 16 17 r-i O PH 5 6 6 7 5 $ 6 2 3 1 1 7 1* H O 81+ 76 ©If. 6 ? 67 33 90 H • • H O • Xi •P 1 • • H • X3 •P * 0 0 rH 1 a? • H 8 5 14 7 6 30 1 1 5 20 6 7k 18 7 96 27 4 2 2 z 78 21 3 11 6 76 25 3 1+7 ' 18 3 39 17 3 07 2 12 2 3k 06 7 81 20 1* 2 2 H H O H O H O • • • • XJ Xl Xl d Pi PH g • • ct • a? • • • • • • H H H O • • c y • : <vy H *g) H • O •W • • Ci5 • to «i4 • 0 • (—1 t=> H rH H H H H O H O O H O O H O H O H O H O • • , q • • »x! • r»»>»-P l» l»-p Xl Xi erj Xl Xi d XI Xi ci P H P H S Pi PH S PH PH S 08 H • H Cl3 W I A r-i t=> Ci) U N O • H H 1-3 • O •P © PH PH X? PH O PH rH rH O Pn rH U O PH o 79 6k Qk 6k 82 79 87 67 8 1 5 9 75 : • -P O © H P • l ^ H ^ 1AO H H H O x?i?i? PH PH PH rH U O PH 6 5 59 81 82 83 63 60 71 65 66 7 3 68 68 82 81 80 6k 61 63 69 70 7 0 6% k? 70 7k 73 65 & 57 7k —3 TABLE 27 (continued) 1 -a 3 •p to *4 PM 0 s o J? PM H -H fl H 0 s •P at * o o H I • H ' r • • H O tt » W • ftj a , t> • !=> H H O H 0 s H O - • • • fl >»>»+> flfld P H P-. S • • • O PM t I af c£ a? • M H H U • • • : c y H • W H »C3 • C3 • • pq • • c5 • rjj »t=> H H H H 1—) H H O H O O H O O H 0 s r l O " H O H O • • • • « f l • • fl •: «fl !»>»+> fl fl d fl fl flfl C M P M S C M P M S C M P H g k u O P H O P H c3 H vO • H rjj 1 A H 1 A O H H O •P o PQrH" P H flfl CM PM^ - • • C4 O PL, fl PM O • P O <D v O W • IA • O H £> • IA H X A O H H H 0 s fl fl fl PM PM PM • • • U It O PM 18 19 20 21 22 23 25 26 27 28 29 30 31 32 33 3§ 35 36 37 It 3 6 3 6 I 7 3 5 6 6 5 18 52 62 62 73 7 82 25 71 69 Ik 77 78 77 58 3 52 19 k9 53 52 k$ 59 5- 03 55 65 2 to 13 33 53 90 7 88 30 ^ 83 89 78 8 3 " " " 81 1* 16, 63 56 5 10 61 55 5 17 51 62 61 3 11 60 k8 68 1+8 63 56 3 56 26 i+e 56 53 3 00 39 58 38 7 81 18 67 61 77 72 72 6 4t 68 7 f 73 73 61 2 59 18 kl 59 53 57 5 12 51 65 69 5 66 19 55 53 69 62 63 8k 7 8k 25> 76 73 85 81 79 82 6 79 20 70 68 85 78 69 7 ? -6 26 70 7k 7k Ik T A B L E 21 ( c o n t i n u e d ) CD •a p -p co * • • • • • • • • • tl ti H •»» rH O H rH o o O O O • H • J • • XI XI • b b -p - P a? xi X! cr} P H AH £ H H a? o • w • H H O H O H O • • • XI > » > > - P XI Xl aj P H P H S O P H • • • a? a? a? • • • • • 08 o o • H H H 43 i • 40 O r<-\ CD O © • • : f V • c y • H • «C|J H H • CiJ i vO • • • « . • ! vO ffl • . rjj • • pq • • O • IA o C!J. t A • O :tt . ^ CiJ •£=> tU HCiJ • • H fc> • Nl ,£> t-^l •» CQ ^ * t l H H H H H H XA H • "LA H O H O O H O O H O t A O f c D H IA O H H O H O H O H H O H H O • • • • »£} • »Si • * xi ••• • ••>•• t?>?^ b b 4 3 bb* 3 r * » > > : > » r > » X l X l r f ! ? X l d X l X l c j XIX3 X! X l X i X i P H P H S ^ P H P H P H P H S PH P H P H P H P H ' • • • • • a - < o • < » « rH £ < rH SH rH ti U U rH fn O P H O P H O P H O P H O P H 63 63 70 70 l|.p 57 54 68 61|. •failed -- • 39 59 50 76 85 79 75 76 62 73 68 68 62 82+. 83 68 63 5% 75 72 61 62 75 77 71 71 k2 . 51*. 51 6k 52 67 7k 72 72 38 62 5% 61 70 62 6k 55 60 51 89 81 8k 92 89 61 66 6k 65 38 9 0 k l 47 48 & 51 52 1 55 3 3 7 6 6 6 i 3 6 It $ 7 5 28 06 ij.6 3 k$ 01 59 3 60 09 86 6 83 27 6 18 86 . 6 63 18 73 6 76 10 67 6 76 23 3 07 63 3 71 21 6 ... 23 6 ok 5 17 3 15 79 7 86 40 5 20 1+3 77 60 61 63 58 82 TABLE 27 (continued) • • • • 0 8 • » • • • o • H • H H H O O • o"N • • o © • • • - » • » CN CV • H O o; • cq • 53 H • p q H • C!J . N O • • • • 4»:! vo cq . • m * • • « » .(3 • • O • U N p C Q © U N «CiJ P » P P W>q ci> » p O • h3 H ci> • H p • P P tl % p r-i r-i H r l H r-i r-i H H U N H U N H O H O O O O O H O O H O u\o • U N O H H O H H O H O H H h H H H O • » ^ • > > X i • • • Xi • » X i • • • - • • • • * •1>»>»-P > s X l - P t>» > > - P •>» l>> X i X i & xixiM X i X l r t X I X I X ! X I X I X I P H P H § £j p ^ ! l P H P H S P H P H S P H P H P H P H P H P H ^ >•— - — * - — * ^—- *•—-* ^—" • • • • • • • • • • . U U r H U tt ti ti O P H O P H O P H O P H O P H O P H PREDICTED CRITERIA N 2k 52 2k 52 Y 62 58 72 67 S.E. 09 13 07 08 s 34 11 09 09 122 118 122 118 EMPIRICAL CRITERIA, N 39 123 18 72 f 68 60 61J. 64 S.E. 09 13 07 08 s 18 17 12 11 I.Q,. 121 119 116 117 Cr. Phy. 101 U.B.C. r e f e r s to the p r e d i c t e d grade f o r U n i v e r s i t y P h y s i c 0 7 11 05 i l 14 120 25 72 ©4 31 68 11 13 120 c r i t e r i o n of success. P r . Phy. 91 U.E. r e f e r s t o the recorded grade f o r the Physics 91 U n i v e r s i t y Entrance Examination used as a p r e d i c t i o n v a r i a b l e . •» Recorded on record card. TABLE 28 PREDICTION VARIABLES AND PREDICTED CRITERIA FOR THE UNIVERSITY PHYSICS 101 CLASS OP 1961-62 13 <D XS 3 •P CO 1 2 6 7 8 9 10 11 12 Average * 1-} r H O CO o •H 01 PH 6 4 i 1 7 6 m r-i O 01 o •H ra t>> fl PH 83 86 78 61}. 82 r-i O 01 O •H P 'I <D fl 6 2 7 6 •5 6 15 7 6 5.33 78.60 JL i H O 01 o •H s <o fl +> 89 69 96 85 68 68 * o o H I • H 5.17 79.17 26 13 15 15 16 20 15 26 18 20 20 l £ • • r-i o r H 03 O Ti 01 l» fl PH 18.25 68 50 95 50 55 81 52 92 50 73 68 i H O 01 O . •H - P I co fl - P £ o o CM 01 O •H 03 *>» fl < PH I fl fl -a 0 CD •H + 3 SH O O Ti •P Xf •H CD JH JH O PH o . r H fc> « r H O O "*' * "LfMAO H H • oq 01 o •ri m t» fl PH 01 o 01 e S P H H C O Ti >n <D •P •H r H eq o . ^ O I H o o •H H - P crj 01 > e o <D Ti fl 01 • M fl .• S PH H O •P O PH 85 50 94 62 67-45 76 51 76 50 62 67 67.78 69 35 79 ¥• kl 72 % 61 62 72 5p 51 88 48 70 66 30. 58.95 62.83 a Recorded, on r e c o r d c a r d . 00 I H TABLE 29 PREDICTION VARIABLES AND PREDICTED CRITERIA POR THE GRADE X I I I PHYSICS 101 CLASS OP 1961-62 © -P CO CU rl H O 01 o •H W PH H O ra o © P H CU tl r-i ra o •H •P a © Xi -p I t> H O 01 O Ti § © Xi 43 ai a-* o o r-i I • cf o H H s O iH ra o •H ra PH 15 18 07 10 25 31 17 13 20 06 § 17 15 17 10 22 TOE 1 2 6 7 8 9 10 I I 12 13 5 6 $ 3 i 3 3 5 59 72 59 50 61 72 59 73 56 57 75 55 58 62 .62.38- . 1|>65 62.29 78 7p 61+ 63 81 78 57 63 60 Tk 69 69 69 53 63 67.6I+, # Recorded on r e c o r d card. TABLE 30 COMPARISON OP PREDICTED CRITERIA AND ACTUAL GRADES POR COMPLETED PHYSICS COURSES-STUDENTS AND GRADE X I I GRADUATES WHO HAVE RECEIVED GRADES INDICATED I N FUTURE UNIVERSITY PHYSICS COURSES CD T J 3 P C O tt r-i O CQ O • r i ra fl PM o ra o •ri ra fl PM CiJ o ra o •H P ai S CD fl P • r l O ra o •H -P a) S CD fl -P a) O o H I • a? • o '• pq • r-i O H a o •rl ra PM CQ • O H O r l ra o •ri P aJ B o fl p 2 O ro " r l fn a} O •H ra -P ?H o o © «ri "H +3 CO T J • r i |>» © JH fl Pl OPm PM O ro "•• H JH a i o •H 01 43 f) O O © .H «H P 01 T > •ri |>>© ti fl fH O PM PM O pq • P o o C M a o •H ra t>> fl PM tt O •• O oi C M U o ra 43 o o • r i «ri 03 T > l>s © JH fl O PM PM Oi • r i JH © P r l O r-i H • O H 01 • O pq ra • r i • 0 01 • •ri tt ra fl sO vO • vO |>» P M U \ "LAM" t A f l H rH r l PH O «t *• O I A I A C M ra I A ro I A ra ai U <r-il • • r l h •• r l U •ri 01 O at o crj O JH O P ra •ri ra +5 •ri 01 43 © •ri O o JH O O JH O O 43 •ri 03 T\ •ri ra © TH t - j 43 ro TJ © «ri «ri 43 ra TJ fl © >> •ri t>» © •ri >> © P M JH fl J n f l ti JH fl U P M PM O P M PH O PH PH 1 2 3 6 . 7 8 9 10 I I 12 % 15 16 17 7 7 7 6 1 I 6 6 7 6 7 5 7 72 73 88 75 15 10k 108 86 76 20 10(5 120 96 97 80 23 102 85 101 106 15 75 75 81 20 83 106 83 21 77 90 85 97 32 13k 140 120 136 60 15 75 75 73 70 84 25 115 127 101 109 21 71 81 93 76 16 105 98 83 92 79 18 100 82 9 ? - „98 21 92 100 94 96 25 110 125 106 128 86 33 126 140 123 120 12 85 102 72 23 83 126 101 86 113 88 125 140 140 140 138 139 100 100 130 132 165 148 116 154 120 89 101 125 83 103 168 174 173 TABLE 30 (continued) 18 19 20 21 22 23 25 26 27 28 29 30 31 32 35 36 H to o 3 © ra 3 b • P X ! 00 P H 7 6 7 7 6 4 7 7 4 7 5 3.3 5> 7 7 7 r-i O m o •H ra X ! PH tl H o ra o •H - p a © cd S . H ra o •H +» a ) S © X I • p KV O O H I • a? H • • EJ r-i * .'. ra • • • o • • O • •H • & •• CiJ ra pq H 9 • cq • l » • O tl • tl X I PH H ra " H H o o O O o O ra O oi o O ra o ra H •H > - H U •• H CM • • C M fn ••CM -P . a -> o cd o cd O aJ O ra • S •H ra + 3 •H ra 4 3 ra •H ro + 3 •H ra + 3 o . S >PH O O fcO O o l l O O f-> o o •H © !© - H - H © «H «H •H © - H «H © Ti iH ra X ! 4 3 ra T J + 3 ra t J ra 4 3 CO ' O 4 3 ra »d b >H if>» © •H >> © l>» •H {>» © •H r » s © X I I H ^ ( H X I rn X ! PH I H X I rH PH S O PH PH O PH PH PH O PH PH O PH PH I 5 6 !> 76 79 83 67 83 86 78 64 77 83 6 2 7 6 5 6 5 7 6 4 7 7 6 69 92 80 70 89 96 85 68 88 87 Average Standard Deviation Correlation 22 122 108 100 1 1 1 1 25 113 107 101 96 20 109 III 96 107 86 18 108 111 91 96 20 104 98 88 109 20 lob 4 "'91 92 26 102 103 119 13 "75 P 70 15 15 143 141 85 120 75 93 73 16 82 92 79 28 121 114 112 15 78 77 73 28 138 l l 4 112 82 18 75 75 83 20 102 101 85 30 116 10:2 115 120 20 100 123 95 112 123 20 112 102 95 101 93 108 18 13 20 cq sO IA r-i •\ I A X A H ra o Ti ra & P H 120 60 97 91 106 .77 .13 125 112 24 93 133 128 26 CiJ ! vO • X A M " •» X A *• X A ra • • H U at O Ti 0 1 4 3 U O O © Ti Ti 4 3 ra ,o •rl S O U X ! U O PH PH 61 r H ra o Ti ro ! vO t» X A X ! r - l PH •» X A •• X A ra cr] 0 ra 43 o o ra $ Ti *>» © •s 4 3 139 138 144 141 144 14 .86 w CD O O' p . CP o J> H» O ct H» P i O 0 O: to 0 s P a> Qi O CD O r-t, P i O 4 o: p ta c+ p i P-CD a to P* . o i P % p cr- : CD P O 3 c1 CD H NP vn CO et o p -CD H sO O b-> O CO > O c r < ! P o p . p P i 4 CD H P cr H» O P CD < P e+ H« O 3 H H O VJT.CO CO H H O 0 0 s H ro o o co CD - O v O H ro ro oco vO H H H4=r C O O Physics 101 U.B.C. Criteria: Physics 101 Predictors: U.E. •Physics 200 U.B.C. Criteria: Physics 200 Predictors: Physics 101 Physics 155,156 U.B.C* Criteria: Physics 155,156 Predictors: L.G-. T A B L E 31 C O M P A R I S O N O P P R E D I C T E D C R I T E R I A A N D A C T U A L G R A D E S P O R C O M P L E T E D P H Y S I C S C O U R S E S -S T U D E N T S A R B G R A D E X I I G R A D U A T E S W H O H A V E R E C E I V E D G R A D E S I N D I C A T E D I N G R A D E X I I I P H Y S I C S © XS 3 43 co e & 1-3 H O CO o • r i CQ tr PH M H O ra O •rt 01 t>» fl PH C!3 o hH H O m o •ri 43 1 © fl 43 OJ !=> H O 43 aj S © fl 43 s O O r-l a? H rH 0 (*\ r-i H 01 <D O XS •rt aj s.. K3 S O to ••H U <a o • H 01 43 •fH'O O ©•ri iH 43 01 XS > » © f n f l H O oi H JH O ;oi 43 0 O •ri T-t 01 T J ;t>> © fl U «• a] •ri SH © + » •ri ti . . . O PH PH 1 2 6 7 8 9 10 I I 12 15 16 17 18 19 57 76 i 2 ft 2 I 2 !s ft 2 5 58 57 68 68 81 64 61 57 52 55 56 65 69 75 73 56 62 54 77 54 69 66 58 75 57 59 58 70 62 62 52 62 62 79 62 70 52 72 54 75 TABLE 3.1 (continued) 1 -d 53 •P CQ C& H O ra o •H ra I? PH h H H O Physics 91 Mathematics Mathematics o o rH t • • H Physics 101^ Grade 13 71 5 73 18 73 3 15 61 16 65 67 5 73 18 78 59 3 56 10 70 2 5? 10 64 4 18 67 5 25 74 72 4 20 63 7 17 81 59 7 18 78 5 75 20 57 50 2 55 8 63 .._ 4 20 60 61 4 58 15 74 72 3 17 69 59 6 62 12 69 6 15 67 18 53 6 22 63 65 8 C!J & H !« o ra " r H cd O •H ra -P U O o -P ra T J ;«H © cd •H © -P •H rH O PH to rH « O ra rH rH o W-P o o ra-d l>»© X! PHPH 20 21 22 23 . 24 25 26 27 28 29 30 31 32 34 35 36 37 38 39 Average Standard Deviation Correlation 71 68 58 60 50 69 •48 TABLE 3.1 (continued) U.E K» H O <^ H rH CQ <D O "tf •H Cd ra Jn 1>»C!J X! Pw Criteria:** Physics 101 Predictors: Average" 67 63 Standard Deviation 8 8 Correlation .81 # Recorded on record card. Predictions made for students who graduated from June 1958 to June 1961. Predicted. 89 TABULAR SUMMARY 1 PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 101 U.B.C. ON PHYSICS 91 MATHEMATICS 91 L . G . AND I.Q,. L . G., C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 101 U.B.C. Number of cases 90 P r e d i c t i o n v a r i a b l e s X - L Physics 91 L . G . X 2 Mathematics 91 L . G . X 3 I.Q.-100 Mean values of v a r i a b l e s Y 85.56 x x 5.25 x 3 5.07 x 3 18.54 Standard d e v i a t i o n of v a r i a b l e s y 26.37 x x 1.37 x 2 I . 3 6 . X3 7.14 C o e f f i c i e n t o f c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y i * 5 5 r y 2 • ¥ r y 3 # 68 S i g n i f i c a n t beyond 1.0$ 1.0$ 1.0$ A n a l y s i s " o f m u l t i p l e r e g r e s s i o n Source of Degrees of Sum of v a r i a t i o n freedom squares Mean square Regression 3 29 * 81+7 •I4J4. R e s i d u a l s 86 32,030.7.0 9,949.15 372.45 T o t a l 89 61,878.14 P 3 , 8 6 26.72 s i g n i f i c a n t beyond l£0$ R y l23_ .6947 S.E. = 19.30 or 12.87$ Regression equation  Y = i4,.10X1 - ,210X 2 + 2.02X 3 + 27.5 R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X ] [ Physics 91 L.G. X 2 Mathematics 91 X, I.Q. L.G. Percent 24. 1. 75. Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due t o the S i g n i f i c a n c e s of these a d d i t i o n of a d d i t i o n s X x P h y s i c s 91 L.G. s i g n i f i c a n t beyond 1% X 2 Mathematics 91 L.G. s i g n i f i c a n t beyond 1% X3 I.Q. s i g n i f i c a n t beyond 1% :90; TABULAR SUMMARY 1 (continued) RUN ON 90 ROWS OP DATA MEAN VALUES OP VARIABLES 5.255555E-00 5 .066666E-00 PHYSICS 91 L.G. MATH. 91 L.G. COVARIANCES ROW 1 1.877777E-00 ROW 2 1.364791+E-OO ROW 3 6.196129E-00 ROW Ij. 1.991+631E+01 1.36479i+E-00 1.838202E-00 5.971535E-00 1.728838E+01 STANDARD DEVIATIONS 1.370320E-00 1.355803E-00 CORRELATION COEFFICIENTS ROW 1 1 . 0 0 0 0 0 0 1 0 ROW 2 . 73459575 ROW 3 . 6 3 3 5 2 3 6 0 ROW 4 .55203515 .73459575 1.00000010 .6170971+4 •48359745 REGRESSION COEFFICIENTS 4.102433E-00 -2 .O9747O-OI CONSTANT TERM = 2 .746933E+01 RESIDUAL VARIANCE = 3.724547E+02 R.SQUARED = 4.823525E-01 1.858888E+01 I.Q>-100 6.196129E-00 5.971535E-00 5.0914,144^ +01 1.2717l4,7E+02 7.137327E-00 .63352360 .6170971*4 1.00000000 .67575841 2.022087E-00 8.555555E+01 PHYSICS 101 U.B.C. 1.994631E+01 1.728838E+01 1.271747E+02 6.952609E+02 2.63678OE+OI .55203515 .4835971+5 .67575841 1.00000000 91 TABULAR SUMMARY 2 PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 101 U.B.C. ON PHYSICS 91 U.E.., : MATHEMATICS 91 U.E. AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s • C r i t e r i o n Y Physics 101 U.B.C. Number of cases 2"3T P r e d i c t i o n v a r i a b l e s . ' " " • '  X-_ Physics 9 1 U.E. X 2 Mathematics 91 U.E. X ^ I.Q.-100 Mean values of v a r i a b l e s - - - .  Y 100.12 X X 77.21L . X 2 77.20 X 3 21.00 Standard d e v i a t i o n of v a r i a b l e s y 27.0*2 x_- 12.61+ xa,. 13.35' ' * 3 7.1+6 C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y l >72- W~~*y~. P X 3 . -77 S i g n i f i c a n t beyond 1.0$ 1.0$ 1.0$ A n a l y s i s " o f ' m u l t i p l e r e g r e s s i o n \ Source of Degrees of Sum of Mean square v a r i a t i o n freedom "squares ".. ! . . . Regression 3 13,825.92 1+,608.61+ Residuals 21 l+,752.72 226.1+2 T o t a l 21+ 18,578.61+ P 3,21 8.72 s i g n i f i c a n t beyond 1$ E y i 2 3 .8625 S.E. - 15.0I+: or 10.03$ Regression equation Y = .1+23X1 + 1.0l+X 2 + .92OX3 - 32.3 R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X X Physics. 91 X 2 Mathematics 9 1 X 3 I.Q. Percent 19. 56. 25. Advantage Of addip i n d i c a t e d v a r i a b l e s Advantage"due t o the a d d i t i o n of. S i g n i f i c a n c e s of these a d d i t i o n s X-L P h y s i c s 91 s i g n i f i c a n t beyond 1$, X 2 Mathematics 91 s i g n i f i c a n t beyond 1$ X 3 I.Q. s i g n i f i c a n t beyond 1$ 92 TABULAR SUMMARY 2 (continued) RUN ON 25 ROSS OP DATA MEAN VALUES OP VARIABLES 7.72ij.000E+01 7.720000E+01 PHYSICS 91 U.E. MATH. 91 U.g. COVARIANCES ROW 1 1.597733E+02 ROW 2 1.20i|.9l6E+02 ROW 3 6.654166E+01 ROW k 2.543866E+02 1 . 2 0 4 9 1 6 E + 0 2 1.782i|.99E+02 7.766666E+01 3.080999E+02 STANDARD DEVIATIONS 1.26l|Ol4E+01 1 . 3 3 5 1 O 2 E + 0 1 CORRELATION COEPPICIENTS ROW 1 1.00000000 ROW 2 .71398669 ROW 3 ' .706lOl|.9i| ROW % .72335735 .71398669 1.00000000 .78027^88 2.100000E+01 1.001200E+02 I.Q,.-100 PHYSICS 101 U.B.C, 6.654166E+01 7.766666E+01 5.558333E+01 1.602083E+02 .82942215 REGRESSION COEPPICIENTS 4.238284E-01 1.04O926E-00 CONSTANT TERM = -3.2305l5E+01 RESIDUAL VARIANCE = 2.264202E+02 R SQUARED = 7.440636E-OI . 7 0 6 1 0 4 9 4 . 7 8 0 2 7 4 8 8 1 . 0 0 0 0 0 0 0 0 . 7 7 2 3 4 5 2 7 9 . 2 0 4 3 3 6.E - 0 1 2 . 5 4 3 8 6 6 E + 0 2 3.080999E+02 1.602083E+02 7 . 7 4 1 0 9 9 E + 0 2 7 . 4 5 5 4 2 2 E»00 2.782283E+01 . 7 2 3 3 3 7 3 5 . 8 2 9 4 2 2 1 5 . 7 7 2 3 4 5 2 7 1 . 0 0 0 0 0 0 0 0 •93 TABULAR SUMMARY 3 PERTINENT VALUES PGR ANALYSIS OF LINEAR REGRESSION OP PHYSIOS 101 G. 13 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q,. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 101 G. 13 P r e d i c t i o n v a r i a b l e s Number of cases O^" X x Physics 91 L.G. X 2 Mathematics 91 L.G, Mean values of v a r i a b l e s •• - • X 3 I.Q.-100 Y 63.60 ^ I+.72 Tz I+..80 Standard d e v i a t i o n of v a r i a b l e s X3 18.02 y 12.73 x x 1.07 x 2 1.29 '.. X3 . 5,88 C o e f f i c i e n t of c o r r e l a t i o n - - f o r s i n g l e independent v a r i a b l e s 755" S i g n i f i c a n t beyond 1.0$ A n a l y s i s of m u l t i p l e r e g r e s s i o n T2 i.< r y 3 -39 1.0$ Source o f v a r i a t i o n Degrees of freedom Sura of squares Mean square Regression Re s i d u a l s 3 1+6 3,814.5.71]. tj.,098.ll+ 1,281.91 89.09 T o t a l 49 7,91+3.88 it}..70 s i g n i f i c a n t beyorid 1. .6958 ; S.E. = 9. P3,l+6 R y l 2 3 Regression equation  Y = 5.83X X + 2.1+2X2 + .1I+8X3 + 21.8 . """"" R e l a t i v e importance of v a r i a b l e s i f p r e d i c t i o n of c r i t e r i o n V a r i a b l e X^^ Physics 91 X 2 Mathematics 91 29. X^.I.Q. Percent 70. 1. Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due t o the a d d i t i o n of X-L Physics 91 X 2 Mathematics 91 X3 I.Q. S i g n i f i c a n c e s of these a d d i t i o n s s i g n i f i c a n t beyond 1$ s i g n i f i c a n t beyond 1$ not s i g n i f i c a n t 94 TABULAR SUMMARY 3 (continued) RUN ON 50 ROWS OP DATA MEAN VALUES OP VARIABLES 4.720000E-00 4.8OOOOOE-OO PHYSICS 91 L.G. MATH. 91 L.G. COVARIANCES ROW 1 1.144489E-00 ROW 2 7.795918E-01 ROW 3 2.515918E-00 ROW • k 8 . 9 2 6 5 3 0 E - 0 0 7 . 7 9 5 9 1 8 E - 0 1 1 . 6 7 3 4 6 9 E - 0 0 3 . 8 6 l 2 2 i}E - 0 0 9.163265E-00 STANDARD DEVIATIONS 1.069808E-00 1.293626E-00 CORRELATION COEPPICIENTS R O W 1 1.00000000 R O W 2 .56331644 R O W 3 .3998581^ 9 R O W 4 .65532264 .56331644 1.00000000 .50749519 1.802000E+01 6 .360000E+01 I.%.-100 PHYSICS lOr'G.13 .55631378 R E G R E S S I O N C O E P P I C I E N T S 5.826047E-00 2.421075E-00 C O N S T A N T T E R M = 2.182101E+01 R E S I D U A L V A R I A N C E = 8.909036E+01 R S Q U A R E D = 4.841I93E-01 2.515918E-00 3.861224E-00 3.459142E+01 2.911020E+01 5 .881447E -00 .39985849 .50749519 1.00000000 .38872229 1.475519E-01 8.926530E-00 9.163265E-00 2.9H020E+01 1.621224E+02 1.273273E+01 .65532264 .55631378 .38872229 1.00000000 95 TABULAR SUMMARY II. P E R T I N E N T V A L U E S POR A N A L Y S I S OP L I N E A R R EGRESSION OP P H Y S I C S 101 G. 13 ON P H Y S I C S 9 1 U.E., MATHEMATICS 91 U.E. AND I.Q.-100 C r i t e r i o n and pr e d i c t i o n variables  C r i t e r i o n Y Physics.101 G. 13 Number of cases 11 P r e d i c t i o n variables " •. X-L Physics 91 U.E. X 2 Mathematics 91 U.E. X3 I.Q . -10D Mean values of variables - . . - •- • • - Y 62.00 X i 63.6IL X 2 64.73 X3 17.^ Standard deviation of variables y 13.96 12.37 x 2 12.1^ .8 x 3 0T21 C o e f f i c i e n t of c o r r e l a t i o n f o r single independent variables S i g n i f i c a n t beyond 1.0$ 1,0% 1,0% Analysis of multiple regression ] Source of Degrees of Sum of Mean square v a r i a t i o n freedom squares  Regression 3 1,786.79 595.60 Residuals 7 161.21 23.03 T o t a l 10 1,948.00 " 2 5 . 8 4 s i g n i f i c a n t beyond 1.0$ R y l 2 3 .9577 S.E. = 4.80$ Regression Equation ; Y = .943X1 + .256X 2 - .243X3 - 10.5 ., Relative importance of variables i f pr e d i c t i o n of c r i t e r i o n Variable X1 Physics 91 X 2 Mathematics 91 X3 I.Q. Percent 72. 27. 1. Advantage of addip indicated variables Advantage due to the Significances of these additi o n of . additions X X Physics 91 S i g n i f i c a n t beyond 1% X 2 Mathematics 91 s i g n i f i c a n t beyond 5$ X3 I.Q,. not s i g n i f i c a n t 96 TABULAR SUMMARY 4 (continued) RUN ON 11 ROWS OP DATA MEAN VALUES OP VARIABLES 6.363636E+01 0.14.72727E+01 PHYSICS 91 U.E. MATH. 91 U.E. COVARIANCES ROW 1 1.5305ll,5E+02 ROW 2 1.352909E+02 ROW 3 5.959999E+01 ROW 4 1.645000E+02 1.352909E+02 1 . 5 5 8 l 8 l E+02 6.819999E+01 1.509000E+02 STANDARD DEVIATIONS 1.237152E+01 1.248271E+01 CORRELATION COEFFICIENTS ROW 1 1.OOOOOOOO ROW 2 .87606527 ROW 3 .69826I+OI4. ROW k .95268282 .87606527 1.00000000 .79190272 1.700000E+01 6.199999E+01 I.Q,;.-100 PHYSICS 101 G.13 .86613526 REGRESSION COEFFICIENTS 9.i+3l4,078E-01 2.555970E-01 CONSTANT TERM = -1.01+5099E+01 RESIDUAL VARIANCE = 2.302815E+01 R SQUARED. = 9 .172500E-01 5.959999E+01 6.819999E+01 1+.760000E+01 6.209999E+01 6.899275E-00 .69826404 .79190272 1.00000000 .64^90187 -2.I+28324E-01 1.645000E+02 1.509000E+02 6.209999E+01 1.9480Q0E+02 1.395707E+01 .95268282 .86613526 .64490187 1.00000000 TABULAR SUMMARY 5 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 155 AND 156 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q.-100 C r i t e r i o n and p r e d i c t i o n v a r i a b l e s - • - • •  C r i t e r i o n Y Physics 155 and 156 Number o f cases H]i P r e d i c t i o n v a r i a b l e s • • • ' ' X L P h y s i c s 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q.-100 Mean values of v a r i a b l e s  Y 139,29 Z i 5.6? X 2 5.62 I 3 21.17 Standard d e v i a t i o n of v a r i a b l e s y 24.91 x x 1.63 x i 1.01 x j ~ 6.28 C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s S i g n i f i c a n t beyond 10.0$ 10.0$ .1$ A n a l y s i s of m u l t i p l e r e g r e s s i o n ; ' Source of Degrees of Sum of Mean square v a r i a t i o n freedom squares  Regression 3 1L,!L21L*97 11+7.50 Residuals 20 9,81L1L.00 1+92.20 T o t a l 23 lii,268.97 p 3 , 2 3 3.13 s i g n i f i c a n t beyond 5$ R y l 2 3 .5569 S.E. = 2 2 . 2 1 or 11.11$ Regression equation  Y = 2.76X-L + 1.90X2 + I.74X3 + 76.1 R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X x P h y s i c s 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q. Percent 18. 10. 72. Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due to the S i g n i f i c a n c e s o f these a d d i t i o n of a d d i t i o n s P h ysics 91 S i g n i f i c a n t beyond 10$ X 2 Mathematics 91 S i g n i f i c a n t beyond 10$ X3 I.Q. S i g n i f i c a n t beyond 5$ 98 TABULAR SUMMARY 5 (continued) RUN ON 2lj. ROWS OP DATA MEAN VALUES OP VARIABLES 5.666666E-00 5.6214.999E-00 PHYSICS 91 L.G. MATH. 91 L.G. COVARIANCES ROW 1 2.666666E-00 ROW 2 8.695652E-01 ROH 3 2.1011+49E-00 ROW k 1.266666E-r01 8.695652E-01 1.027173E-00 2.934782E-0O 9.461956E-00 STANDARD BEVIATIONS 1.632993E-00 1.013i|.95E-00 CORRELATION C OEPPICIENTS R O W 1 1.00000000 R O * f 2 .52514.0701 R O W ,3 .201+88731 R O W 4 .31141949 .52540701 1.00000010 .1+6103561 .371+8231+7 REGRESSION COEFFICIENTS 2.757601E-00 1.901127E-00 CONSTANT TERM = 7.610730E+01 RESIDUAL VARIANCE = 1+.92201+2E+02 R SQUARED = 3.10101+9E-01 2.116666E+01 1.392916E+02 I.Q.,,-100 PHYSICS 155,156 2.1011+1+9E-00 2.931+782E-00 3.91+4927E+01 8.007971E+01 .20488731 .1+6103561 1.00000000 .51188307 1.741612E-00 1.266666E+01 9.461956E-00 8.007971E+01 6.203891+E+02 6.280865E-00 2.49076IE+OI . 3H4l9i+9 .371+82347 .51188307 1.00000000 99 TABULAR SUMMARY 6 . PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 155 AND 156 ON PHYSICS 101 U.B.C., MATHEMATICS 101 U.B.C. AND I.Q. P r e d i c t i o n v a r i a b l e s X 1 Physics 101 U.B.C. X 2 Mathematics 101 U.B.C. X3 I.Q.-100 Mean values of v a r i a b l e s X3 21.25 . Y 139.29 X x 1 0 4 . 0 8 . . I 2 H 3 . 7 1 Standard d e v i a t i o n of v a r i a b l e s y 24.91 ~"xj 13.39 x 2 18.84 x 3 6.29 C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s T l 756 S i g n i f i c a n t beyond 1.0$ A n a l y s i s of m u l t i p l e r e g r e s s i o n •72 .26 20.0$ •73 . 5 0 1 .0$ Source o f v a r i a t i o n Degrees of freedom Sum of squares. Mean square Regression Residuals 3 20 6,178*17 8,090.80 2,059.39 4 0 4 . 5 4 T o t a l 23 ;14,268.97 5.09 s i g n i f i c a n t beyond 1.$ .6579 S.E. = 20.11 or 10.05$ F3,20 Ryl23 Regression equation '  Y = .535X1 + .00527X2 + I.42X3 - 78.3 ' _ ~ ~ ~ R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X - , Physics 101 U.B.C. X 2 Mathematics 101 X - I.Q. U.B.C. •* Percent 58 . 0 . 4 2 . Advantage of addip i n d i c a t e d v a r i a b l e s  Advantage due to the S i g n i f i c a n c e s o f these a d d i t i o n of a d d i t i o n s X-L P h y sics 101 U.B.C. X 2 Mathematics 101 U.B.C. X3 I.Q. s i g n i f i c a n t beyond 5$ not s i g n i f i c a n t s i g n i f i c a n t beyond 5$ 100 T A B U L A R S U M M A R Y 6 (continued) R U N O N 2l\. R O W S O P D A T A M E A N V A L U E S O F V A R I A B L E S 1.01L0833E+02 1.13708 3E+02 P H Y S I C S 101 C O V A R I A N C E S R O W 1 I . 786881+E+02 R O W 2 I I . 09381LOE+01 R O W 3 2.676087E+01 R O W I I 1.87322liE+02 MATH. 101 iL.0938i|.OE+01 3.5IL821+2E+02 5.9551+3^+01 1.201+365E+02 S T A N D A R D D E V I A T I O N S 1.33671+3E+01 1. 883677E+01 C O R R E L A T I O N C O E F F I C I E N T S R O W 1 1.00000000 R O W 2 .16258336 R O W 3 .31818228 R O W I I .56261261 .16258336 1.00000000 .5021+9387 2.1250O0E+O1 3.929166E+01 I .Q, . - 1 0 0 P H Y S I C S 155,156 2.676087E+01 5.955431+E+Ol 3.958695E+01 7.8750OOE+O1 .25669629 R E G R E S S I O N C O E P P I C I E N T S 8.31+9027E-01 5.271969E-03 C O N S T A N T T E R M = -7.83177I+E+OI R E S I D U A L V A R I A N C E = I+.01+5381+E+02 R S Q U A R E D = I+.329811E-01 .31818228 .5021+9387 1.00000000 .50250720 1.I+16961+E-00 1.873221+E+02 1.201+365E+02 7.875000E+01 6.203891+E+02 6.291816E-00 2.1+90761E+01 .56261261 .25669629 .50250720 1.00000000 101 TABULAR SUMMARY 7 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 155 AND 156 AND GRADE 13 PHYSICS 101, MATHEMATICS 101 AND I.Q. Criterion and prediction variables ' Criterion Y Physics 155 and 156 Number of cases ST Prediction variables ' " v " " •• • • - - -X X Gr. 13 Physics 101 X 2 Gr. 13 Mathematics 101 X ^ I.Q.-100 Mean values of variables . • • - -Y 130.44 X X 74.11 X 2 73.kk % 20.44 Standard deviation of variables .. 7 23.12 x j 6.I4.3 x_T 8.96 X3 ij..72 Coefficient of correlation for single independent variables — ~ r J J 7% r ^ 1^7 r ~ riffi Significant beyond - •» Analysis of multiple regression Source of Degrees of Sum of Mean square variation freedom squares Regression 3 Residuals 5 592.34 Total 8 P'', 1.12 not significant R y l 2 3 Regression equation Y = .931XX - .931X2 + I.7IX3 + 94.8 Relative importance of variables i n prediction of criterion Variable X± Physics 101 X £ Mathematics 101 X ^ I.Q. Percent . -Advantage of addip indicated variables Advantage due to the Significances of these addition of additions X-L Physics 101 not significant X 2 Mathematics 101 not significant x 3 not significant 102 TABULAR SUMMARY 7 (continued) RUN ON 9 ROWS OP DATA MEAN VALUES OP VARIABLES 7.1+11111E+01 7.31|1}WLE+01 PHYSICS 101 COVARIANCES ROW 1 II. 13611OE+01 MATH. 101 2.1L19)|)|)|E4-Q1 ROW 3 2.056944E +01 2.iLl9lji|lLE+01 8.027777E+01 9.ii02777E-00 ROW 11 5.119444E+01 - 3 . 6 0 9 7 2 2 E + 0 1 STANDARD DEVIATIONS 6.1L31260E - 0 0 8.959786E - 0 0 CORRELATION COEPPICIENTS ROW 1 1.00000000 ROW 2 .I+I98768O ROW 3 .67762676 ROW 4 .34430365 .41987680 1.00000000 .22234254 -.17425730 REGRESSION COEPPICIENTS 9.310114E-OI -9.307119E-01 CONSTANT TERM = 9.481088E+01 RESIDUAL VARIANCE = 5.923411E+02 R SQUARED = 3.074014E-01 2.044444E+01 1.304444E+02 I.Q,-100 PHYSICS 155,156 2.056944E+01 9.402777E-0O 2.227777E+01 4.852777E+01 .67762676 .22234254 1.00000000 .44470226 1.711511E-00 5.119444E+01 -3 .609722E+01 4.852777E+01 5.345277E+02 4.719933E-00 2.311.985E+0I .34430365 -.17425730 .44470226 1.00000000 TABULAR SUMMARY 8 PERTINENT VALUES PGR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 200 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q. Criterion and prediction variables Criterion Y. Physics 200 Number of cases 13 Prediction variables " ' • ' " •• • X x Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q.-100 Mean values of variables ,• ,. .. • . Y 110.76 X-_ 6.15 X 2 6.23 X3 23.85 Standard deviation of variables •_ _ - • y 36.41 ~~x_ 1.114. x 2 1.17 x 3 5 2.59 Coefficient of correlation for single independent variables r y l . ' 8 * r y 2 . * 7 7 . 8 3 Significant beyond 1.00$ 1.00$ 1.00$ Source of Degrees of Sum of Mean square variation freedom - squares Regression 3 13,181.28 4,393*76 Residuals ,9 2,727.00 303.00 Total 12 15,908.28 P 3 > 9 li}..90 significant beyond 1$ Ryl23. .9103 S.E. = 17.40 or 11.60$ Regression equation Y = 20 . 0 0 X ! + 2 . 1 5 X 2 + 1 . 1 0 X 3 - 51.8 Relative importance of variables i n prediction of criterion Variable X__ Physics 91 L.G. X P Mathematics 91 X, I.Q> L.G. "* ••• Percent 6 8 . 6. 26. Advantage of addip indicated variables Advantage due to the Significances of these addition of additions X_ Physics 91 L.G. significant beyond 1$ X 2 Mathematics 91 L.G. not significant'. X 3 I.Q. significant beyond 5$ 1 0 4 T A B U L A R S U M M A R Y 8 (continued) R U N O N 13 R O W S O P D A T A M E A N V A L U E S O P V A R I A B L E S 6 . 1 5 3 8 L L 6 E - 0 0 6 . 2 3 0 7 6 9 E - 0 O P H Y S I C S 9 1 L . G . M A T H . 9 1 L . G . C O V A R I A N C E S R O W 1 1 . 3 0 7 6 9 2 E - 0 O R O W 2 1 . 0 L J I L 8 7 1 E - 0 0 R O W 3 8 . O 2 5 6 5 .1E-O0 R O W I I 3.720512E+01 1 . 0 I L I L 8 7 1 E - 0 O 1 . 3 5 8 9 7 1 + E - O O 7.-955128E-00 3.255769E+01 S T A N D A R D D E V I A T I O N S 1. II4.35I4,3E-00 1.165750E-00 C O R R E L A T I O N C O E P P I C I E N T S R O W 1 1.00000000 R O W 2 .78379889 R O W 3 .81599287 R O W 4 .89357020 .78379889 1 . 0 0 0 0 0 0 1 0 . 7 9 3 ^ 1 6 0 5 2.38IL615E+01 I . Q . - 1 0 0 8.0256LL1E-00 7 . 9 5 5 1 2 8 E - 00 .76705524 R E G R E S S I O N C O E P P I C I E N T S 1 .995382E+01 2.148163E-00 C O N S T A N T T E R M = - 5 . 1 7 5 4 6 O E + 0 1 R E S I D U A L V A R I A N C E = 3 . 0 3 0 0 7 3 E + 0 2 R S Q U A R E D = 8 . 2 8 5 7 6 0 E - 0 1 2.589615E+02 8 . 6 0 0 8 3 4 2 - 0 0 . 8 1 5 9 9 2 8 7 . 7 9 3 4 1 6 0 5 1 . 0 0 0 0 0 0 0 0 . 8 2 6 9 3 8 6 8 1 . 1 0 4 8 4 7 E - 0 0 1 . 1 0 7 6 9 2 E + 0 2 P H Y S I C S 2 0 0 3.720512E+01 3 . 2 5 5 7 6 9 E+01 7.397435E+01 2.589615E+02 1.325692E+03 3.641005E+O1 .89357020 .76705524 .82693868 1.00000000 105 TABULAR SUMMARY 9 PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 200 ON PHYSICS 91 L.G..,. MATHEMATICS 91 L.G. AND I.Q. Criterion and prediction variables Criterion Y Physics 200 Number of cases 5 Prediction variables X x Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q.-100 Mean values of variables Y 123.20 X X 5.1+0 X 2 5.60 X3 23.31 Standard deviation of variables y 15.16 x x 1.3ii X 2 1*P- x 3 5.1|.l Coefficient of correlation for single independent variables r y l -* 8 r y 2 Significant beyond .65 r y 3 -39 Analysis of multiple regression -Source of Degrees of Sum of variation freedom squares Mean square Regression 3 Residuals 1 1+99.54 Total 1+ ^1,3 1 , 0 0 n o t significant R y l 2 3 .667 Regression equation Y = - 5.65X! + 1.12X2 + 8.56X3 + 88.9 Relative importance of variables i n prediction of criterion Variable X-j^  Physics 91 L.G. X 2 Mathematics 91 L.G. Percent - -X 3 I.Q. Advantage of addip indicated variables Advantage due to the Significances of these addition of additions X x Physics 91 L.G. not significant X 2 Mathematics 91 L.G. not significant X3 I.Q. not significant 106 TABULAR SUMMARY 9 (continued) RUN O N 5 R O W S O P DATA MEAN VALUES O P VARIABLES 5.LL00000E-O0 5.6O0OOOE-O0 PHYSICS 91 L.G. MATH. 91 L.G. COVARIANCES ROW 1 1.800000E-00 ROW 2 1.950000E-00 ROW 3 2.550000E-00 ROW II. 1.190000E+01 1.950000E-00 2.300000E-00 3.950000E-00 1.510000E+01 STANDARD DEVIATIONS I.3I4.I6I4.OE-OO 1.516575E-00 CORRELATION GOEPPICIENTS ROW 1 1.00000010 ROW 2 .95837285 ROiaf 3 .35113179 ROW II .58523497 .95837285 1.00000010 •48117094 * 65695OILI . REGRESSION COEFFICIENTS -5 ..681952E-00 1.123547E+01 CONSTANT TERM = 8.887461E+01 RESIDUAL VARIANCE = 4«9954L2E+02 R. SQUARED = 4.563112E-01 2.iL)40000E+01 I.Q,,.-100 2.550000E-00 3.950000E-00 2.930000E+01 3. 2[LO0OOE+01 .35113179 48117094 1.00000000 .39493964 8.562702E-02 1.232000E+02 PHYSICS 200 1.190000E+01 1.510000E+01 3.240000E+01 2.297000E+02 5.t|.i2947E-oo 1.515585E+01 .58523497 .65695041 * 39494-964 1.00000010 1Q7 TABULAR SUMMARY 10 PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 200 ON PHYSICS 101 U.B.C, MATHEMATICS 101 U.B.C AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 200 Number of cases 13 P r e d i c t i o n v a r i a b l e s X1 Physics 101 U.B.C X 2 Mathematics 101 U.B.C. I.Q,,.-100 Mean values of v a r i a b l e s •• • .  Y 110.77 ^ i 117.31 X 2 118.31 X3 2 3 . 6 2 Standard d e v i a t i o n of v a r i a b l e s ; .. y 36.41 * i 24.38 x 2 28.58 ~~x^ oTii C o e f f i c i e n t o f c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y l .88 r y 2 .85 r y 3 .81 S i g n i f i c a n t beyond 1.0$ 1.0$ 1. 'a A n a l y s i s of m u l t i p l e r e g r e s s i o n Source of Degrees of Sura of Mean square v a r i a t i o n f r e e dom squares . Regression 3. 13,359.14 4>452.38 Residuals 9. 2,551.14 283.46 T o t a l 12. 15,908.28 F 3 j g 14.50 s i g n i f i c a n t beyond 1 . 0 $ R y l 2 3 .9163 S.E. = 1 6 . 8 4 or 1 1 . 2 3 $ Regression equation  Y = . 8 2 6 X ! + . 1 9 8 X 2 + 1 . 1 6 X 3 - 3.71 ' ' ~~~ ' R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X N Physics 1 0 1 U.B.C. X 2 Mathematics 1 0 1 X , I.Q. U.B.C Percent 69» 7» 24. Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due t o the S i g n i f i c a n c e s of these a d d i t i o n of a d d i t i o n s X - L Physics 101 U . B . C . s i g n i f i c a n t beyond 1$ X 2 Mathematics 101 U . B . C . s i g n i f i c a n t beyond 5$ X3 I.Q. s i g n i f i c a n t beyond 5$ 108 TABULAR SUMMARY 10 (continued) RUN ON 13 ROWS OP DATA MEAN VALUES OP VARIABLES 1.173076E+02 1.183076E+02 PHYSICS 101 G O V A R I A N C E S R O W 1 5.9LL2307E+02 R O W 2 5.8531IL1E+02-R O W 3 1.501282E+02 R O W k 7.818269E+02 MATH. 101 5.853114-1E+02 8.1706i|.lE+02 2.081L6I£E+02 8.883269E+02 S T A N D A R D D E V I A T I O N S 2.li,3768iLE+01 2.85814-33E+01 C O R R E L A T I O N C O E P P I C I E N T S ROW 1 1.00000000 ROW 2 .84000787 ROW 3 .72285.817 ROW k .88086974 .8IL®0Q787 1.00000000 .85597338 2.361538E+01 I.Q.-100 1.501282E+02 2.08IL6I5E+02 7.25897i|E+01 2.14.99038E+02 REGRESSION COEPPICIENTS 8.262424E-01 I.98IIIIE-OI . CONSTANT TERM = -3.710403E+01 RESIDUAL VARIANCE = ( 2.834695E+02 R SQUARED = 8.396294E-01 = .7228IL817 .85597338 1.00000000 ,80558980) l.l6)+9i|.4E-00 1.107692E+02 PHYSICS 200 7.818269E+02 8.883269E+02 2.499038E+02 1.325692E+03 8.519961E-00 3.641005E+01 .88086974 .85454905 .80558980 1.00000000 109 TABULAR SUMMARY 11 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 101 U.B.C. ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 101 U.B.C. P r e d i c t i o n v a r i a b l e s _____ Number of cases 123 X x Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q.-100 Mean values of v a r i a b l e s In 540 X. 5.12 '3 18.67 , Y 89.63^ (59.75$) Standard d e v i a t i o n of v a r i a b l e s _ ______ (17.22$) C o e f f i c i e n t o f c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s * l 1.35 x 2 1.37 x- 6.67 S i g n i f i c a n t 0.1$ A n a l y s i s of m u l t i p l e r e g r e s s i o n r y 2 .TIJS! 0.1$ •73 .588 0.1$ Source of v a r i a t i o n Degrees of freedom Sum of squares Mean square Regression Residuals 3 119 36,297.68 45,086.72 12,099.23 378.88 T o t a l 122 8l,384.1i0 P R 3,119 y l 2 3 31.94 which i s s i g n i f i c a n t beyond 1$ .668 S.E. 19.46 or 12.95$ Regression equation " • • • •• •• "- •• •  Y = 7.3701X-L - ..5012X2 + I.541OX3 + 23.6490 R e l a t i v e Importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X x Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q. Percent 47.62$ 2.62$ 49.76$ Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due t o the S i g n i f i c a n c e s of these a d d i t i o n of a d d i t i o n s X x Physics 91 L.G. 16.82 s i g n i f i c a n t beyond 1$ X 2 Mathematics 91 L.G. 3.35 s i g n i f i c a n t beyond 5$ X3 I.Q,. 21.25 s i g n i f i c a n t beyond 1$ 110 TABULAR SUMMARY 11 (Continued) RUN ON 123 ROWS OP DATA MEAN VALUES OP VARIABLES 5.39837^-00 5.121951E-00 PHYSICS 91 L.G. MATH. 91 L.G. CO-VARIANCES R O W 1 1 . 8 3 1 8 0 0 E - 0 0 R O W 2 1 . 2 3 7 9 0 1 L E - 0 O R O W 3 4.806OIOE-OO R O W I I 2 . 0 2 8 6 2 8 E + 0 1 1 .23790ILE-00 1 .878IL1L8E -00 5.352IL59E-00 1.6IL3022E+01 S T A N D A R D D E V I A T I O N S lo353liij.OE-.00 1.370565E-00 C O R R E L A T I O N C O E P P I C I E N T S ROW 1 1.00000010 ROW 2 .66731+211 ROW 3 .53200107 ROW I I ~ .58032676 .66734211 1 . 0 0 0 0 0 0 1 O .58508712 .46414439 REGRESSION COEPPICIENTS 7.370126E-00 -5.012247E-01 CONSTANT TERM = 2.364901E+01 RESIDUAL VARIANCE = 3.78876OE+O2 R SQUARED = 4 . 4 6 0 0 -2E - 0 1 1.866666E+01 8.963414E+OI I.Q.-100 PHYSICS 101 U.B.C. 4 . 8 0 6 0 1 0 E - 0 0 5.352459E-00 4.455191E+01 1.013934E+02 .53200107 .58508712 1.00000000 .58814694 1.541018E-00 2 . 0 2 8 6 2 8 E + 0 1 1 . 6 4 3 0 2 2 E +01 1 . 0 1 3 9 3 4 E+02 6 . 6 7 0 8 5 8 E + 0 2 6.674721E-00 2.582800E+01 .58032676 .46414439 .58814694 1.00000000 I l l TABULAR SUMMARY 12 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 101 U.B.C. ON PHYSICS 91 U.E., MATHEMATICS 91 U.E. AND I.Q-. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y 'Physics 101 U.B.C. Number of cases 39 P r e d i c t i o n v a r i a b l e s X x Physics 91 U.E. X 2 Mathematics 91 U.E. X3 I.Q.-100 Mean values of v a r i a b l e s " Y 102.08 X-, 76.23 (68.05$) Standard d e v i a t i o n o f v a r i a b l e s x 2 78.87 E3 20.56 y 26.20 x-, 13.21 x? 12.63 x , 7.07 (17.71$) * C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent^variables r y l S i g n i f i c a n t beyond 0.1$ r y 2 .811+ 0.1$ r y 3 .707 0.1$ A n a l y s i s of m u l t i p l e r e g r e s s i o n Source of D e g r e e s o f v a r i a t i o n freedom. Sum of squares Mean square Regression 3 Residuals 35 19,796.10 7,00l+.20 6,598.7 200.12 T o t a l - 38 26,800.30 P 3 , 3 5 = s i g n i f i c a n t beyond 1$ R y l 2 3 * 8 5 9 S.E. + l l | . . l 5 or ± 9.1+1+$ Regression equation Y = .5822X! + 1.071+0X2 + .5659X3 - 38.6631 * R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e , X-_ Physics 91 U.E. Percent 29.28$ X2 Mathematics 56.31$ 91 U.E. X 3 I#Q,. ll+.l+l$ Advantage of addip i n d i c a t e d v a r i a b l e s Advantage"due t o the a d d i t i o n of S i g n i f i c a n c e s a d d i t i o n s of these X]_ Physics 91 U.E. P value 6.29 s i g n i f i c a n t beyond 5$ X 2 Mathematics 91 U.E. P value 8.88' s i g n i f i c a n t beyond 1$ X^ I,Q,. P value .71+ not s i g n i f i c a n t 112 TABULAR SUMMARY 12 (continued) RUN ON 39 ROWS OP DATA MEAN VALUES OP VARIABLES 7 . 623076E+01 . 7 . 887179E+01 PHYSICS 91- U.E. MATH. 91 U.E. COVARIANCES ROW 1 1.7ii3927E+02 ROW 2 l.lii8l98E+02 ROW 3 6 . 5 6 2 9 & E + 0 1 ROW k 2 . 6 2 0 0 8 1 E + 0 2 l.lli8l98E+02 1.595357E+02 6 . 162685E+01 2 . 7 3 0 8 9 0 E + 0 2 STANDARD DEVIATIONS I.320578E+OI 1 .26307lrE+01 CORRELATION" COEPPICIENTS ROW 1 1 . 0 0 0 0 0 0 0 0 ROW 2 . 6 8 8 3 7 2 9 2 ROW 3 . 7 0 3 2 7 6 2 2 ROW k .7l|.708279 .68837292 1 . 0 0 0 0 0 0 1 0 .690L|1L906 2 . 0 5 6IL1 0E+ 0 1 1 .020769E+02: I.Q.-100 PHYSICS 101 U.B.C, .811L12950 REGRESSION COEPPICIENTS 5.822276E-01 I.O7ILI37E-OO CONSTANT TERM = -3.86630£E+01 RESIDUAL VARIANCE = 2.001238E+02 R SQUARED = 7.38 6518E-01 6.562955E+91 6.162685E-T-01 1+.993657E+01 1.326659E+02 7.066581E-00 .70327622 .690I44906 1.00000000 .70691696 5.658965E-01 2.62OO8IE+02 2.730890E+02 1.326659E+02 7.05283LLE+02 2.655717E+01 .74708279 .8ILL12950 .70691696 1.00000000 113 TABULAR SUMMARY 13' PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 101 G. 13 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q, C r i t e r i o n and p r e d i c t i o n v a r i a b l e s ""' t C r i t e r i o n Y „Physics 101 G. 13 .. Number of cases 72 P r e d i c t i o n v a r i a b l e s " ' • - -• • X! Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q.-100 Mean values of v a r i a b l e s . . . ' • Y 63.62 X^ IL.79 .. X 2 IL.[L7 X3 17.39 Standard d e v i a t i o n of v a r i a b l e s ~ 117113 x][ 1.05 xg" T7W " x j ~ 57P C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y l .554 P y 2 .525 r y 3 .373 S i g n i f i c a n t beyond 0.1$ 0.1$ 1.0$ A n a l y s i s of m u l t i p l e r e g r e s s i o n 1 Source o f Degrees of Sum of Mean square v a r i a t i o n freedom squares -Regression 3 3,900i22 1,300.07 Residuals 68 5,414.84 79.63 T o t a l 71 9,315.06 P 3 > 6 Q = 16.32 s i g n i f i c a n t beyond 1$ .' R y 123 .647 S.E. 8.92$ Regression equation ' - • ., " •  Y = LL.2977X! + 2.7913X2.+ .15589X3.+ 2.7.8044 ' _ R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X1 Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q, Percent . - " 52.05$ 4l.35$ - 6.60$ Advantage of addip i n d i c a t e d v a r i a b l e s  Advantage due t o the S i g n i f i c a n c e s of these a d d i t i o n o f a d d i t i o n s . X1 Physics 91 L.G. P value 14.38 s i g n i f i c a n t beyond 1$ X 2 Mathematics 91 L.G. P value 10.12 s i g n i f i c a n t , beyond 1$ X 3 I.Q. F value 11.58 s i g n i f i c a n t beyond 1$ .114 TABULAR SUMMARY 13 (continued) RUN ON 72 ROWS OP DATA MEAN VALUES OP VARIABLES 1L.791666E-00 -L-._L72221E-00 PHYSICS 91 L.G. MATH. 91 L.G. C O V A R I A N C E S R O W 1 1.096831E-00 R O W -2 5 .786381LE-01 R O W 3 2.053990E-00 R O W k 6.653168E-00 5.786381LE-01 1.830203E-00 3.1+3 348 9E-00 8.137323E-00 STANDARD DEVIATIONS 1. Oii.729 6E-00 1.352850E-00 CORRELATION COEPPICIENTS ROW 1 l.OOOOOOlO ROW 2 -.40840196 ROW ' 3 .3.6453578 ROW 4 .55462499 .40840196 1.00000000 .•47173447 .52513699 REGRESSION COEPPICIENTS 4.297736E-00 2.791333E-00 CONSTANT TERM ' = 2.780437E*01 RESIDUAL VARIANCE = 7.962647E+01 R SQUARED • •• • = 4.187147E-01 1.738888E+01 6.362499E+OI I.Q. PHYSICS 101 G.13 2.053990E-00 3.433489E-00 2.894522E+01 2.297887E+01 .36453578 .47173447 1.00000000 .37289018 1.577928E-01 6.653168E-00 8.137323E-00 2.297887E+01 1.311954E+02 5;380076E-00 1.145405E+01 .55462499 .52513699 .37289018 1.00000010 115 TABULAR SUMMARY ILL PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 101 G. 13 ON PHYSICS 91 MATHEMATICS 91 U.E. AND I.Q. U.E., C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 101 G. 13 Number P r e d i c t i o n v a r i a b l e s of cases 18 X x Physics 91 U.E. X 2 Mathematics 91 U.E. Mean val u e s of v a r i a b l e s X^ I.Q.-100 Y 6IL.22 X x 62.61 S 2 6ii.06 Standard d e v i a t i o n o f v a r i a b l e s X3 15.61 y 11.85 x x 10.ii3 x 2 10.70 x 3 6.20 C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y l .825 r y 2 .687 S i g n i f i c a n t beyond 0.1$ 1.0$ A n a l y s i s of m u l t i p l e r e g r e s s i o n r y 3 .IL71 I 10.$ Source of Degrees of Sum of v a r i a t i o n freedom squares Mean square Regression 3 1,71+6*07 Residuals l i t ,6LL1.13 ... 582.02 45.795 T o t a l 17 2,387.20 f3>11L = 12.1L0 s i g n i f i c a n t beyond 1$ R y i 2 3 .855 S.E. 6.77$ Regression equation Y = .9102Xi + ,3720X 2 - .6I175X3 - 6.1L883 R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X x Physics 91 U.E. X 2 Mathematics 91 Percent 62.81$ 21.92$ Advantage of addip i n d i c a t e d v a r i a b l e s . U.E. X3> I.Q. 15.27$ Advantage due t o the S i g n i f i c a n c e s a d d i t i o n of a d d i t i o n s of these Physics 91 U.E. F value 6.78 s i g n i f i c a n t beyond 5$ X 2 Mathematics 91 U.E. F value 6.16 s i g n i f i c a n t beyond 5$ X 3 I.Q,. F value not s i g n i f i c a n t '116 T A B U L A R S U M M A R Y lit (continued) R U N O N 1 8 R O W S O P D A T A M E A N V A L U E S O P V A R I A B L E S 6 . 2 6 1 1 1 1 E + 0 1 6 . L L O £ 5 5 5 E + 0 _ P H Y S I C S 9 1 U . E . M A T H . 9 1 U . E . C O V A R I A N C E S R O W 1 1.088398E+02 R O W 2 8.561111E+01 R O W 3 i|..iL60ii57E+01 R O W 4 1 . 0 2 0 3 2 6 E + 0 2 8.561111E+01 l.l44o84E+02 5.155228E+01 8.71Oli£7E+01 S T A N D A R D D E V I A T I O N S 1.0i+3263E+01 le0696l9E+01 C O R R E L A T I O N C O E P P I C I E N T S M O W 1 1.00000010 R O W ' 2 .76719723 R O M 3 .68917387 R O W I I .82534111 .76719723 1 . 0 0 0 0 0 0 0 0 .77689479 1.561111E+01 6.422222E+01 I . Q . - 1 0 0 P H Y S I C S 101 G . 1 3 4.460457E+01 5.155228E+01 3.84869E+OI 3485620E+01 .68722668 R E G R E S S I O N C O E P P I C I E N T S 9 . I O I 9 8 3 E - O I 3.72031L9E-01 C O N S T A N T T E R M = - 6 . 4 8 8 3 O I E -OO R E S I D U A L V A R I A N C E = 4.579481E+01 R S Q U A R E D = 7.314213E-01 .68917387 .77689479 1.00000000 .)47IL14558 -6.475458E-01 1.020326E+02 8.710457E+01 3-485620E+01 1.404183E+02 6 . 2 0 3 7 8 3 E ^ 0 0 1 . 1 8 4 9 8 2 E+01 .82534111 .68722668 .47414558 1.00000010 117 TABULAR SUMMARY 1$ PERTINENT VALUES POR ANALYSIS OF LINEAR REGRESSION OP PHYSICS 155 AND 156 ON PHYSICS 9 1 L.G.., MATHEMATICS .91 L.G; AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y P h y s i c s 155 and 1 5 6 Number P r e d i c t i o n v a r i a b l e s o f cases I L I X X P h y s i c s 9 1 L.G. X 2 Mathematics 9 1 L.G. Mean v a l u e s o f v a r i a b l e s X3 I . Q . - 1 0 0 Standard d e v i a t i o n o f v a r i a b l e s x"3 20.39 C o e f f i c i e n t o f c o r r e l a t i o n - f o r s i n g l e independent v a r i a b l e s r y l . 2 I L 6 r y 2 .526 S i g n i f i c a n t beyond 1 0 . $ 0 . 1 $ A n a l y s i s o f m u l t i p l e r e g r e s s i o n r y 3 •£°6 0 . 1 $ Source o f Degrees o f Sura o f Mean square v a r i a t i o n freedom squares R e g r e s s i o n 3 11* 5 4 6 - 4 0 R e s i d u a l s ' 37 18,545-88 3 , 8 4 8 . 8 0 T o t a l l+O 3 0 , 0 9 2 . 2 8 5*3,37 = 23.03 s i g n i f i c a n t beyond 1 $ R y l 2 3 .619 S.E. 2 2 . 3 2 or 1 1 . 1 6 $ R e g r e s s i o n e q u a t i o n Y = 1 . 2 8 1 3 X - L + 9.1250X2 + I . 7 3 0 3 X 3 + 4 1 . 5 3 7 5 R e l a t i v e importance o f v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X - _ P h y s i c s 91 L.G. X £ Mathematics 9 1 Percent 4.35$ ' 47-87$ Advantage o f addip i n d i c a t e d v a r i a b l e s . L.G. X3 I.Q. 47.78$ Advantage due to the S i g n i f i c a n c e s a d d i t i o n o f a d d i t i o n s o f these X _ i P h y s i c s 9 1 L.G. P va l u e not s i g n i f i c a n t X 2 Mathematics 9 1 L.G. P va l u e 4*784 s i g n i f i c a n t beyond 5$ X3 I.Q. P value 4*645 s i g n i f i c a n t beyond 5$ 118 TABULAR SUMMARY 15 (continued) RUN ON lp. ROWS OP DATA MEAN VALUES OP VARIABLES 5.. 512194^ -00 5439021LE-00 PHYSICS 91 L.G. MATH. 91 L.G. C O V A R I A N C E S R O W 1 2.106097E-0O R O W 2 6.945121E-01 R O W 3 II.LL51219E-01 R O W I4. 9.806097E-00 6.91L5121E-01 l.I02li39E-00 2.ii2lj.390E-00 1.5ll|if5lE+01 STANDARD DEVIATIONS 1.1451239E-00 1.0li9970E-0O CORRELATION COEPPICIENTS ROW; 1 1.00000010 ROW 2 •45578852 ROW . 3 .05343825 ROW 4 .24635405 .45578852 1.00000000 .40228861 2.039024E+01 1.335121E+02 I.Q.-100 PHYSICS 155,156 4.451219E-01 2.424390E-00 3.29439QE+01 7.969512E+01 .52587283 R E G R E S S I O N C O E P P I C I E N T S 1.281265E-00 9.125025E-0O C O N S T A N T T E R M ' ' = 4.l53754E+°l R E S I D U A L V A R I A N C E = 5. 012461LE+02 R S Q U A R E D ' = 3.8369IIE-OI .05343825 .40228861 1.00000000 .5062289O 1.73O280E-00 9.806097E-00 1.514451E+01 7.969512E+01 7.523060E+02 5.739677E-00 2.742819E+01 .24635405 .52587283 .50622890 1.00000000 119 TABULAR SUMMARY 16 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 155 AND 156 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 155 and 156 Number of cases 31 P r e d i c t i o n v a r i a b l e s P h y s i c s 9 1 L.G. X 2 Mathematics 91 L.G. X3 I.Q.-100 Mean Values of v a r i a b l e s . Y 136.77 X L 5.68 X 2 5.58 (68.39$) Standard d e v i a t i o n of v a r i a b l e s X3 20.61 y 25.82 x-, 1,56 x 2 1.03 X 3 6.01 (12.91$) C o e f f i c i e n t of c o r r e l a t i o n . f o r s i n g l e Independent v a r i a b l e s r y l .282 r y 2 .LL85 S i g n i f i c a n t beyond 10$ _ . 1.0$ r y 3 .1+80 1.0$ A n a l y s i s of m u l t i p l e r e g r e s s i o n Source of Degrees" of Sum of v a r i a t i o n freedom squares Mean square Regression 3 6,765.90 R e s i d u a l s 27 13,231.35 2,255.30 1L90.05 T o t a l 30 19,997.25 F3 - 4*77 which i s s i g n i f i c a n t beyond 1$ R 'p, .582 S.E. 22.13 or 11.07$ Regression equation • .. ; Y = 1.7911X! + 7.1190X2 + I.5275X3 + 5 5 . 3 9 0 5 ' R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X± Physics 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q. Percent 9.02$ ' 40.52$ ,50.46$ Advantage of addip I n d i c a t e d v a r i a b l e s  Advantage due t o the S i g n i f i c a n c e s of these a d d i t i o n of . . a d d i t i o n s X 1 Physics 91 L.G. P value not s i g n i f i c a n t X2 Mathematics 91 L.G. P value 2.99 s i g n i f i c a n t beyond 10$ X 0 I.Q. P value 4*18 s i g n i f i c a n t beyond 5$ 120 TABULAR SUMMARY 16 (continued) RUN ON 31 ROWS OP DATA THROUGH PHYSICS 101 U.B.C. MEAN VALUES OP VARIABLES 5 .677419E-00 5.5806I4.5E-00 2.061290E+01 PHYSICS 91 L.G. MATH. 91 L.G. I.Q.-100 C O V A R I A N C E S R O W 1 2.1L25806E-00 R O W 2 8.268817E-01 | L L E - ( ROW 7 . 3 7 6 3 1 L L L E - 0 1 ROW J4. 1.135806E+01 8.268817E-01 1.051612E-00 2.532258E-00 1.283548E+01 S T A N D A R D D E V I A T I O N S 1..557500E-00 1.0251L81E-00 C O R R E L A T I O N C O E P P I C I E N T S ROW 1 liOOOOOOOO ROW 2 .51771104 ROW 3 .07881128 ROW % .28245542 .51771104 1.00000010 .41091813 .4.84794.86 REGRESSION COEPPICIENTS I.79IO52E-OO 7.118999E-00 CONSTANT TERM . . = 5.539050E+01 RESIDUAL VARIANCE = 4*900524E+02 R. SQUARED = 3.383438E-01 7.376344E-01 2.532258E-00 3.611182E+01 7 .450967E+01 6.0093HE - 0 0 .07881128 . 4 1 0 9 1 8 1 3 1 . 0 0 0 0 0 0 0 0 . 4 8 0 2 4 3 6 4 1.527515E-00 1.367741E+02 PHYSICS 155 156 1.135806E+01 1.283548E+01 7.450967E+01 6.665806E+02 2.581822E+01 . 2 8 2 4 5 5 4 2 . 4 8 4 7 9 4 8 6 . 4 8 0 2 4 3 6 4 1 . 0 0 0 0 0 0 0 0 121 TABULAR SUMMARY 17 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 155 AND 156 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 155 and 156 * Number of cases 10 P r e d i c t i o n v a r i a b l e s X± Physics 91 L.G. X 2 Mathematics 91 L.G. X 3 I.Q.-100 Mean values of v a r i a b l e s * T 123.40 ___ 5.00 x 2 5.00 x 3 119.70 Standard d e v i a t i o n of v a r i a b l e s : 7 *1 .94 x 2 1.05 x 3 5.034 C o e f f i c i e n t o f c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y l ry2 r73' S i g n i f i c a n t beyond - -A n a l y s i s of m u l t i p l e r e g r e s s i o n Source of Degrees of Sum of v a r i a t i o n freedom squares Mean square Regression 3 Residuals 6 72.16 P3,6 1*98 .'not s i g n i f i c a n t R y l 2 3 .7056 = 13.57$ Regression equation R e l a t i v e importance o f v a r i a b l e s i n . p r e d i c t i o n of c r i t e r i o n V a r i a b l e Xj^ Physics 91 L.G. X 2 Mathematics 91 L.G. X- I.Q, Percent - - -Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due t o the S i g n i f i c a n c e s of these a d d i t i o n of a d d i t i o n s X-_ Physics 91 L.G. not s i g n i f i c a n t X 2 Mathematics 91 L.G. not s i g n i f i c a n t X 3 I.Q. not s i g n i f i c a n t 122 TABULAR SUMMARY 17 (continued) RUN ON 10 ROWS OP DATA MEAN VALUES OP VARIABLES 5.000000E-00 5.000000E-00 PHYSICS 91 L.G. MATH. 91 L.G. COVARIANCES ROSf 1 8.888888E-01 ROW 2 -.000000E-99 ROW 3 -9.999999E-01 ROW k -1.888888E-00 -.OOOOOOE-99 l . l l l l l l E - 0 0 1.888888E-00 1.800000E+01 STANDARD DEVIATIONS 9.428090E-01 1.051i092E-00 CORRELATION COEPPICIENTS ROW 1 1.00000000 ROW 2 .OOOOOOOO ROW 3 -.21068561 ROW k -.06ii28l88 .OOOOOOOO 1.00000000 .35594780 .5I+7898OO REGRESSION COEPPICIENTS 1.240777E-00 1.111393E+01 CONSTANT TERM " = 2.687937E-00 RESIDUAL VARIANCE = 7.315812E+02 R SQUARED = 4.979083E-01 1.970000E+01 1.234000E+02 I.Q.-100 PHYSICS 155 156 •9.999999E-01 1.888888E-00 2.534l4,i+4E+01 9.557777E+01 • .21068561 .35594780 1.00000000 .60914610 2.991802E-00 •1.888888E-00 1.800000E+01 9.557777E+01 9.713777E+02 5.0314.326E-00 3.H6693E+01 -.O6I428188 .54789800 .6O91I4.6IO 1.00000000 123 TABULAR SUMMARY 18 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 155 AND 156 ON PHYSICS 101 U.B.C, MATHEMATICS 101 U.B.C AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 155 and 156 P r e d i c t i o n v a r i a b l e s X-,^  Physics 101 U.B.C, X 2 Mathematics 101 U.B.C I.Q.-100 Mean values of v a r i a b l e s • • - -Number of cases 31 Y 36.77 x x I O I L . I O C2 113.71 X 3 20.68 Standard d e v i a t i o n of v a r i a b l e s 25.82 y d^.Od. x-j_ I i i . 12 A 2 A ^ C o e f f i c i e n t o f c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s 18.11 6702 y i 7529" S i g n i f i c a n t beyond 0.1$ A n a l y s i s of m u l t i p l e r e g r e s s i o n T 2 .369 5.$ r y 3 .IL74 2.$ . Source of v a r i a t i o n Degrees of freedom Sum o f squares Mean square Regression R e s i d u a l s 3 27 10,060.80 9,934.92 3,320.27 367.96 T o t a l 30 19,995.72 P 3,27 R y l 2 3 Regression equation 9.12 .7088 s i g n i f i c a n t beyond 1$ S.E. 12.bj.7° 9699X-L + .088096X 2 + 1.3293X 3 - 101.7 Q21L Y = R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X, Physics 101 U.B.C. X 2 Mathematics 101 X, I.Q, U B C Percent 66.28$ li . 5 3 $ * * 29.19$ Advantage of addip i n d i c a t e d v a r i a b l e s ; Advantage due to the S i g n i f i c a n c e s of these a d d i t i o n of a d d i t i o n s X-k Physics 101 U.B.C P value 13.56 s i g n i f i c a n t beyond 1$ X 2 Mathematics 101 U.B.C F value 3.73 s i g n i f i c a n t beyond 10$ x 3 I.C P value 3.80 s i g n i f i c a n t beyond 124 T A B U L A R S U M M A R Y 1 8 (continued) M E A N V A L U E S O P V A R I A B L E S 1 . 0 1 L 0 9 6 7 E + 0 2 1 . 1 3 7 0 9 6 E + 0 2 P H Y S I C S 1 0 1 U . B . C . C O V A R I A N C E S R O W 1 1.993569E+02 R O W 2 7 . 9 6 2 9 0 3 E + 0 1 R O W 3 2 . 1 6 6 5 5 9 E+01 R O W 11 2 . 2 9 1 8 9 2 E + 0 2 M A T H . 1 0 1 U . B . C . 7 . 9 6 2 9 0 3 E + 0 1 3 . 2 7 8 1 2 9 E + 0 2 1+.993655E+01 I.724989E+02 S T A N D A R D D E V I A T I O N S 1 . 1 L 1 1 9 3 8 E+01 1.8lO*J'60E+01 C O R R E L A T I O N - C O E P P I C I E N T S R O W 1 1.00000000 R O W 2 . 31ll|.8898 R O W •• 3 .25471032 R O W 4 .62871262 . 3 1 1 1 + 8 8 9 8 1 . 0 0 0 0 0 0 0 0 . 4 5 7 8 2 2 7 0 2.0677i|.lE+01 3.6771L19E+01 I .Q. . . -100 P H Y S I C S 155 156 2 .166559E+01 1+.993655E+01 3.6292I+7E+OI 7 . 3 6 5 8 0 6 E + 0 1 .36901756 R E G R E S S I O N C O E P P I C I E N T S 9.699&98E-0I 8.809637E-02 C O N S T A N T T E R M = -1.017021+E+02 R E S I D U A L V A R I A N C E = 3.679550E+02 R S Q U A R E D = 5.031966E-01 .251+.71032 .1+5782270 1.00000000 .47357I63' 1.329295E-00 2 . 2 9 1 8 9 2 E + 0 2 1.721+989E+02 7 .365806E+O1 6 . 6 6 5 8 0 6 E + 0 2 6.021+323E-00 2.58I822E+01 .62871262 .36901756 47357163 1.00000000 125 TABULAR SUMMARY 19 PERTINENT VALUES POR ANALYSIS OP LINEAR REGRESSION OP PHYSICS 155 AND 156 ON PHYSICS 101 G. 13, MATHEMATICS 101 G. .13 AND I.Q, C r i t e r i o n and p r e d i c t i o n v a r i a b l e s . C r i t e r i o n Y Physics 155 and 156 Number of cases IcF P r e d i c t i o n v a r i a b l e s ' X _ Physics 101 G. 13 X £ Mathematics 101 G. 13 X3 I.Q.-100 Mean values of v a r i a b l e s -- • • • Y 123.14.O X - _ 72.90 X 2 68.60 X3 119.70 Standard d e v i a t i o n o f v a r i a b l e s y 31T17 *i TTTf x 2 1749 x 3 5.03 " C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s  __. ____ -rg. _ , i 6 Q 9 S i g n i f i c a n t beyond - - -A n a l y s i s of m u l t i p l e r e g r e s s i o n - Source o f Degrees o f Sura of Mean square v a r i a t i o n freedom squares ____ Regression 3 R e s i d u a l s 6 77.93 T o t a l 9 P^ ^ = 1.74 not s i g n i f i c a n t R y l 2 3 = .682 S.E. 27.91 or 13.96$ Regression equation - .. • Y = . W I X ! + . 55 7*P_ + 2.312ILX 3 + 7.0085 R e l a t i v e importance of v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X - , Physics 101 Gr.13 X 2 Mathematics 101 X , I.Q. Gr.13 . ' Percent - -Advantage o f addip i n d i c a t e d v a r i a b l e s  Advantage due to the S i g n i f i c a n c e s of these a d d i t i o n s a d d i t i o n of X - _ Physics 101 G.13 not s i g n i f i c a n t X 2 Mathematics 101 G.13 not s i g n i f i c a n t X3 I.Q,. not s i g n i f i c a n t 126 TABULAR SUMMARY 19 (continued) RUN ON 10 ROWS OP DATA MEAN VALUES OP VARIABLES 7.290000E+O1 6.86000QE+01 PHYSICS 101 G.I3 COVARIANCES ROW 1 5.11+3333E+01 ROW 2 8.017777E+OI ROW 3 -2.730000E+01 ROW i i 1.308222E+O2 MATH. 101 G.13 8.017777E+01 3.06O1LLLLLE+02 4.442222E+01 3.091777E+02 STANDARD DEVIATIONS 7.I7I703E-OO 1.7i|-9l|12E+01 CORRELATION COEPPICIENTS ROW 1 1.00000000 ROW 2 .63905678 ROW 3 .75613430 ROW k .58528191 .63905678 1.00000000 .504390211 .56705080 REGRESSION COEPPICIENTS 4 .47H79E-01 5.574469E-01 CONSTANT TERM = 7.008468E-00 RESIDUAL VARIANCE = 7.792699E+02 R SQUARED = 4*651790E-01 1.970000E+01 1.234000E+02 I.Q.-100 PHYSICS 155 156 2.730000E+01 4.442222E+01 2.53Wt4E + 01 9.557777E+01 5.034326E-00 .75613430 .50439024 1.00000000 .60914610 2.312476E-00 1.308222E+02 3.091777E+02 9.557777E+01 9.713777E+02 3.116693E+01 .58528191 .56705080 .60914610 1.00000000 TABULAR SUMMARY 20 PERTINENT VALUES FOR ANALYSIS OF LINEAR'REGRESSION OF PHYSICS 200 ON PHYSICS 9 1 L.G., MATHEMATICS 9 1 L.G. AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s ] C r i t e r i o n Y P h y s i c s 200 Number of cases 3 1 P r e d i c t i o n v a r i a b l e s ' ' '  X X P h y s i c s 91 L.G. X 2 Mathematics 91 L.G. X3 I.Q,-100 Mean v a l u e s of v a r i a b l e s - • - • - Y 110.39 X X 5.935 X 2 ^' 1^ Z X3 2 3 , 2 3 Standard d e v i a t i o n o f v a r i a b l e s ^ ; 7 2 9 . 8 1 x j 1.11 ' x 2 1 . 3 8 X 3 7.11 C o e f f i c i e n t o f c o r r e l a t i o n f o r s i n g l e independent" v a r i a b l e s  r~j[ ,526 TyJ .606 »775 S i g n i f i c a n t beyond 1.0$ . 0.1$ 0.1$ A n a l y s i s o f m u l t i p l e r e g r e s s i o n ; ' Source o f Degrees o f Sum o f Mean square v a r i a t i o n freedom . squares • '• - R e g r e s s i o n 3 16,428.00 5,476.00 v R e s i d u a l s 27 10,223.00 378.6  T o t a l 30 26,651.00  F 3 , 2 7 = l4»4°4 S i g n i f i c a n t beyond 1$ R - .7851 S.E. 1 2 . 9 7 $ yi23 . R e g r e s s i o n e q u a t i o n - • -• - • • - •  Y = 3 . 5 3 3 1 X 1 + . 8 7 I I X 2 + 2.873OX3 + 17.6794 ' R e l a t i v e importance o f v a r i a b l e s i n . p r e d i c t i o n o f c r i t e r i o n V a r i a b l e X1 P h y s i c s 9 1 L.G. X 2 Mathematics 9 1 L.G. X3 I.Q. Percent. 11.27$ . 3 .81$ 84.92$ Advantage o f addip i n d i c a t e d v a r i a b l e s Advantage due t o the S i g n i f i c a n c e s o f these a d d i t i o n o f a d d i t i o n s X-L P h y s i c s 91 L.G. F v a l u e 2.99 s i g n i f i c a n t beyond 10$ X 2 Mathematics 91 L.G. F v a l u e not s i g n i f i c a n t X3 I.Q. F v a l u e 4«7° s i g n i f i c a n t beyond 5$ 128 TABULAR SUMMARY 21 PERTINENT VALUES POR ANALYSIS OF LINEAR REGRESSION OP PHYSICS 200 ON PHYSICS 91 L.G., MATHEMATICS 91 L.G. AND I.Q. C r i t e r i o n and p r e d i c t i o n v a r i a b l e s C r i t e r i o n Y Physics 2 0 0 Number of cases 25 P r e d i c t i o n v a r i a b l e s Physics 9 1 L.G. X 2 Mathematics 9 1 L.G. X3 I.Q.-100 Mean values of v a r i a b l e s T 109.96 X-_ 6.08 . X_ 5.84 X3 23.36 Standard d e v i a t i o n of v a r i a b l e s y 30.52 x x 1 . 1 2 x 2 1.31 x 3 7.27 C o e f f i c i e n t of c o r r e l a t i o n f o r s i n g l e independent v a r i a b l e s r y l «560 r y 2 .599 S i g n i f i c a n t beyond 1.0$ 1.0$ r y 3 , 7 8 6 0 . 1 $ A n a l y s i s of m u l t i p l e r e g r e s s i o n Source of Degrees of Sum of v a r i a t i o n freedom .. squares Mean square Regression 3 1_L,176.56 Residuals 2 1 8,18.0... 34 4,725.52 3 8 9 .54 T o t a l 24 22,356.90 P o p i = 12.13 which i s s i g n i f i c a n t • beyond 1 $ R y l 2 3 . 7 9 6 1 S.E. 13 . 1 6 $ Regression equation Y == _L._L861LX1 - . 2 9 6 2 6 X 2 + 2 . 9 4 O I X 3 + 15.7321 R e l a t i v e importance o f v a r i a b l e s i n p r e d i c t i o n of c r i t e r i o n V a r i a b l e X__ Physics 9 1 L.G. X 2 Mathematics L.G. Percent l i t . 1 2 $ 1.18$ 9 1 X3 I.Q. 84.70$ -Advantage of addip i n d i c a t e d v a r i a b l e s Advantage due to the S i g n i f i c a n c e s of these a d d i t i o n of a d d i t i o n s X-_ P h y s i c s 91 L;G. P value not s i g n i f i c a n t X 2 Mathematics 91 L'.G". F value not s i g n i f i c a n t X o r.Q". P value 8.03 s i g n i f i c a n t beyond 1$ 129 T A B U L A R S U M M A R Y 2 1 (continued) R U N O N 25 R O W S O P D A T A T H R O U G H P H Y S I C S 1 0 1 U . B . C . M E A N V A L U E S O P V A R I A B L E S - . 6 . 0 8 0 0 0 0 E - 0 0 5 . 8 1 LO 0 O 0 E - O 0 P H Y S I C S 91 L . G . M A T H , 91 L . G . C O V A R I A N C E S R O W 1 1 .2LL3333ETOO R O W 2 9.716666E-01 R O W 3 4.678333E -O0 R O W 4 1.90lilj.99B+0_l 9.716666E-01 1.723333E-00 6.851666E-00 2.399333E+01 S T A N D A R D D E V I A T I O N S i . i l 5 0 l i 8 E - 0 0 1 .312757E-00' C O R R E L A T I O N C O E P P I C I E N T S R O W 1 1.00000000 R O W 2 .66380256 R O W ,3 . .57727731 R O W I I .55961128 .66380256 1.00000010 .71812279 2 . 3 3 6 0 0 0 E + 0 1 I . Q . - 1 0 0 .59883230 R E G R E S S I O N C O E P P I C I E N T S IL.IL86393E-00 - 2 . 9 6 2 5 5 7 E - O I C O N S T A N T T E R M - . = 1.573207E+01 R E S I D U A L V A R I A N C E =-3.8954°4 E +02 R S Q U A R E D . . . . . . = 6.34102.8E-0.1 1+.678333E-00 6.851666E-00 5 . 2 8 2 3 3 3 E + 0 1 1.7I+26IL9E+02 7 . 2 6 7 9 6 6 E - 0 0 .57727731 .71812279 1.00000000 .7855910ii 2..9I4.OIO2E-OO 1 . 0 9 9 6 0 0 E + 0 2 P H Y S I C S 2 0 0 1.90ILIL99E+01 2 . 3 9 9 3 3 3 E + 0 1 1.71+26IL9E+02 9.315399E+02 3.052113E+01 .55961128 .59883230 .78559104 I.6060OOOO 1130 TABULAR SUMMARY 22 PERTINENT VALUES FOR* ANALYSIS OF LINEAR REGRESSION OF PHYSICS 200 ON PHYSICS 101 U.B.C., MATHEMATICS 101 U.B.C. AND I.Q. C r i t e r i o n and pr e d i c t i o n variables C r i t e r i o n Y Physics 200 P r e d i c t i o n variables Number of cases 19 X X Physics 101 U.B.C. X 2 Mathematics 101 U.B.C. X ^ I.Q,.-100 Mean values of variables - _______ Y 109 i l l X__ 115.68 X 2 - 118.00 23.1.2 Standard deviation of variables 31.67 2 l 3 J 2 4 * 5 1 X n x2 7.60 C o e f f i c i e n t of co r r e l a t i o n for single independent variables T l 7 8 2 8 S i g n i f i c a n t beyond 0.1$ Analysis of multiple regression 'y2 .800 r y 3 .787 0.1$ 0.1$ Source of v a r i a t i o n Degrees of freedom Sum of squares Mean square Regression Residuals 3 15 13,678.58 4,373.1.0 4,559.53 291.54 T o t a l 18 18,051.68 F 3,l£ = 15.64 s i g n i f i c a n t beyond 1$ R Y L 2 3 .8704 S.E. 11.33$ Regression equation • • - "  Y = .7603X 1 + .0721LLLX2 + I..5096X3 - 22.7567 ' " Relative importance of variables i n predi c t i o n of c r i t e r i o n Variable X__ Physics 101 U.B.C. X o Mathematics 101 X3 I.Q. U.B.C. Percent 56.49$ 5.92$ 37.59$ Advantage of addip indicated variables Advantage due to the addition of Significances of these additions X]_ Physics 101 U.B.C. F value 4*82 s i g n i f i c a n t beyond 5$ X 2 Mathematics 101 U.B.C. F value not s i g n i f i c a n t Xo I.Q. F value not s i g n i f i c a n t 131 TABULAR SUMMARY 2 2 (continued) RUN ON 1 9 ROWS OP DATA MEAN VALUES OP VARIABLES 1.15681I2E+02 1 . 1 8 0 0 0 0 E + 0 2 PHYSICS 101 U.B.C. COVARIANCES ROW 1 li.6356l)+E+02 ROW 2 )-|J|)|)|)|)|]jlg+02 ROW 3 1.191959E+02 ROW l i 5.6li5906E+02 MATH. 101 U.B.C. 4.444444 E + 0 2 6.008888E+02 1.587222E+02 6.210555E+02 STANDARD DEVIATIONS 2.l530li7+01 2.LL51303E+01 CORRELATION COEPPICIENTS ROW 1 1.00000000 ROW 2 .84210600 ROW 3 .72880815 ROW l i .82804924 .84210600 1.00000000 .85240528 2.342105E+01 i.Q:.-100 .80003592 REGRESSION COEFFICIENTS 7.603342E-01 7.243808E-02 CONSTANT TERM " = -2.275676E+01 RESIDUAL VARIANCE = 2.915453E+02 R SQUARED. = 7.577426E-01 1.191959E+02 1.587222E+02 5.770175E+01 1.892309E+02 7.596167E-00 . 7 2 8 8 0 8 1 5 . 8 5 2 4 0 5 2 8 1.00000000 .786636II 1.509568E-00 1.091052E+02 PHYSICS 200 5.6459O6E+02 6.210555E+02 1.892309E+02 1 .002877E+02 3.166823E+01 .82804924 .80003592 .78663611 l.OOOOOOOO TABULAR SUMMARY 23 PERTINENT VALUES FOR ANALYSIS OF LINEAR REGRESSION OF PHYSICS 200 ON PHYSICS 101 G. 13, MATHEMATICS 101 G. 13 AND I.Q,. Criterion and prediction variables  Criterion Y Physics 200 ! Number of cases 5" Prediction of variables • . . - . •   X ] _ Physics 101 G. 13 X 2 Mathematics 101 G. 13 X3 I.Q.-100 Mean values of variables.. Y" 112.17 X x 7ii.50 x 2 74.33 X3 22.67 Standard deviation of variables y 29.31 x x 13.85 x 2 15.62 X3 . 6.43 Coefficient of correlation for ; single independent variables r y l .80. ry2 -573 r y 3 - 7 1 7 Significant beyond 10$ 40$ 30$ Analysis of multiple regression Source of Degrees of variation freedom Sum of squares Mean square Regression 3 Residuals 2 4,187.00 107.74 1,395.66 '53.87 Total 5 4,294.74 F o p = 25.91 which is significant ' beyond 1$ R y l 2 3 . »9873 S.E. 7.67$ Regression equation • ..  Y = 3.7365X1 - 2.5957X_ + 2.202OXJ3 - 2.3171 .. Relative importance of variables in prediction ; Variable X± Physics 101 G. 13 X p Mathematics 101 X o I.Q, G 13 Percent 55.50$ " 30.95$ "l3.55$ Advantage of addip indicated variables Advantage-due to the Significances of these addition of additions X^ Physics 101 G. 13 F value 17.96 significant beyond X 2 Mathematics 101 G. 13 F value 10.69 significant beyond Xn I.Q. P value 11.66 significant beyond 10$ 133 TABULAR SUMMARY 23 (continued) RUN ON 6 ROWS OP DATA MEAN VALUES OP VARIABLES 7 . i i i | 9 9 9 9 E + 0 1 7 4 3 3 3 3 3 E +01 P H Y S I C S 101 G.13 C O V A R I A N C E S R O W 1 1 .919000E+02 R O W 2 2 .000000E+02 R O W 3 5.839999E+01 R O W I I 3.265000E+02 MATH. 101 G.13 2 . 0 0 0 0 0 0 E + 0 2 2.IL38666E+02 6.713333E+01 2 . 6 2 1 3 3 3 E + 0 2 STANDARD DEVIATIONS 1 . 3 8 5 2 7 9 E + 0 1 1 . 5 6 1 6 2 3 E + 0 1 CORRELATION COEPPICIENTS ROW 1 1.00000010 ROW 2 . 921L52005 ROW 3 .65467508 ROW 4 .80418794 .92452005 1.00000000 .66759406 2.266666+01 I.Q.-100 5.839999E+01 6.713333E+01 4.146666E+01 1.352666E+02 .57274049 REGRESSION COEPPICIENTS ' 3 . 7 3 6 5 0 6 E - 0 O -2.595668E-00 CONSTANT TERM = -2.317088E+01 RESIDUAL VARIANCE = 5 . 3 8 7 0 2 0 E + 0 1 R SQUARED = 9 . 7 4 9 1 4 0 E - 0 1 .65467508 .66759406 1.00000000 .71672586 2.202024E-00 1 . 1 2 1 6 6 6 E + 0 2 PHYSICS 2 0 0 3.265000E+02 2 . 6 2 1 3 3 3 E + 0 2 1 . 3 5 2 6 6 6 E + 0 2 8.589666E+02 6.439461E-00 2.930813E+01 .80418794 .57274049 .71673586 1.00000000 

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