Understanding Partial Regression Coefficients in the Presence of Correlated Regressors

Abstract

The interpretation of partial regression coefficients in the presence correlated regressors causes difficulty for students in the social sciences. Since correlation among regressors is the typical case in the social sciences, this presents a considerable instructional problem. This article presents an explanation of the partial regression coefficient in the presence of correlated regressors that is a simple and direct extension of the case where regressors are mutually orthogonal. The interpretation presented emphasizes the relationship between the partial regression coefficient and the simple regression coefficient. An example using SAS computer package is provided.