On the identification of the significant independent variables in linear models

Abstract

Methods for the identification of the significant independent variables in multiple linear regression and in the multiple regression approach to non-orthogonal analysis of variance and covariance are discussed. “Forward Ranking” and “Backward Ranking” (by order of importance) of the independent variables are defined, and the backward method is shown to avoid the disadvantageous effects of “Compounds” upon the ranking. For non-orthogonal analysis of variance, a unique orthogonal decomposition of the regression sum of squares (due to all ANOVA effects) is shown to be possible when the groups of independent variables (representing the effects) are ranked by the criterion of “Non-Significance” and under “Restricted Admissibility.” A computer program is outlined which incorporates the proposed methods.