ABSTRACT
In the basic linear regression model, the regressors X1,…,Xm are taken to be fi xed constants, with our primary objective being to make inferences about or predict values of the explained variable Y. In this instance, only Y is random because the error term ε is random. Furthermore, under the assumptions of the strong classical linear regression model, ε : N(0, σε), σε constant. In the case of a single fi xed regressor X, the sample coeffi cient of correlation between X and Y, R x y x yi i i i= ∑ ∑ ∑/ 2 2 , is a purely descriptive measure of the linear association between X and Y. Here correlation only serves to measure (through R2 = SSR/SST) the goodness of fi t of the sample linear regression equation; it only refl ects the proportion of the variation in Y explained by the linear infl uence of X.
