Extraneous Variables and the Interpretation of Regression Coefficients

Abstract

This paper addresses some difficulties concerning the interpretation of the regression coefficients in simple and multiple regression models. The root of the problem lies in the fact that the fitted multiple regression equation is the result of transforming raw data of the independent variables into residualized scores. In the standard interpretation of the partial regression coefficients, effects of the residual term have not been explicitly differentiated from those of the regressors. Alternative interpretations of the regression coefficients are proposed. The recognition of residual and residualized effects plays an important role in the evaluation of the obtained values of the regression coefficients, R^2, the overall F tests and the construct validity of the multiple regression model.