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Study of apple yield relationships in 1969 in the Okanagan area of British Columbia Lee, Ewon

Abstract

The purpose of the study is to determine which factors contributed to the production of apples in the Okanagan area during the year 1969. Regression analysis is used in an attempt to quantify yield relationships. A comparison is made among different tree-size categories in order to determine whether it is necessary to fit separate regression equations instead of using the data for the three groups in a single regression equation. For this purpose an Equality of Slope Test is performed. The outcome of the test shows that there are no significant differences among corresponding coefficients in the equations for tree-size categories. Hence it is feasible to combine them into one equation. For the regression analysis, two different types of yield relationships are employed: one is a Cobb-Douglas function linear in the logarithms and the other is a quadratic function. Both functions include a dependent variable, namely, yield per acre and seven independent variables; that is, density, age, value of fertilizer applied, value of spray applied, pruning and thinning labour hours, geographical dummy, and tree-size index. These independent variables are measured on a per-acre basis except in the case of age, geographical dummy and tree-size index. The data, which consists of cross-section informa- tion for 1969 represents one hundred and nineteen sample apple plots. It was derived from personal interviews with apple growers. The quadratic function poses a problem arising from cross-terms in the equation. It was necessary to modify the function in such a manner that the cross-terms included in the regression equation were justified on biological or economic grounds. The regression results for each type of function used in the analysis are discussed and estimates of coefficients and related standard errors shown. It seems desirable that data should be broken down into apple variety groups because different varieties of apple may well have distinct bearing characteristics. Apple trees in the specific plots under study, however, are made up of a mixture of varieties, thus it is extremely difficult to draw a clear map of acreages occupied by each variety. In attempting to obtain variety data, notwithstanding the mixture of varieties in stands, the original data is broken down under certain assumptions. Also in decomposing apple yields into grade constituents similar problems arise. Despite these difficulties, tests of differences among average yields are made under stated conditions for varietal, tree-size, apple-grade, and regional categories. These tests reveal that there are no significant differences in average apple yields for varieties, apple grades and regions., but there are significant differences in the case of different tree sizes. The results of these Tests are presented in Chapter VI. The quadratic form of function seems, within the theoretical framework, to be able to represent satisfactorily the apple yield relationship with the selected independent variables. But, in practice, it does not conform well to the empirical situation; it produces a serious multicolline-arity problem from the point of view of statistical inference. The Cobb-Douglas function, however, does not cause such a problem. Apart from this, its application brought in almost all the coefficients corresponding to the basic independent variables except for the coefficient of the tree-size index variable. On this evidence, a tentative conclusion was made in favour of the Cobb-Douglas function for the representation of an apple yield relationship in the Okanagan in 1969.

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