Brief Report: The Use of Highly Correlated Predictors in Regression Analysis

It is commonly believed that the multiple correlation cannot be increased appreciably by adding a predictor which is highly correlated with another predictor. This is based on the assumption that such a variable is redundant. An obvious exception occurs when the added variable is a suppressor variable, Le., it is correlated nearly zero with the criterion. A more general class of variables can be shown to exist which can bring the multiple correlation arbitrarily close to one. This emphasizes the importance of considering variables in combination rather than independently.