Suppression situations in multiple linear regression

Abstract

This article proposes alternative expressions for the two most prevailing definitions of suppression without resorting to the standardized regression modeling. The formulation provides a simple basis for the examination of their relationship. For the two-predictor regression, the author demonstrates that the previous results in the literature are incomplete and oversimplified. The proposed approach also allows a natural extension for multiple regression with more than two predictor variables. It is shown that the conditions under which both types of suppression can occur are not fully congruent with the significance of the partial F test. This implies that all the standard variable selection techniques-backward elimination, forward selection, and stepwise regression procedures-can fail to detect suppression situations. This also explains the controversial findings in the redundancy or importance of correlated variables in applied settings. Furthermore, informative visual representations of various aspects of these phenomena are provided.