Brief Report: Highly Correlated Predictor Variables in Multiple Regression Models

The inclusion in a multiple regression model of a predictor variable which is highly correlated with other prediotor variables is usually not recommended. The argument is that the new predictor variable is accouihing for variance which has already been accounted for in the model. The following discussion is a defense for the procedure of including highly correlated predictor variables under certain circumstances. First, highly correlated variables can be used when there is a requirement that the predictor variables account for a certain number of group membership vectors. A second and more important situation occurs when there is theoretical or empirical justification for the inclusion of such a variable. The following discussion is limited to a very specific kind of highly correlated variable-one that contains the squared elements of one of the original variables.