Prediction, Explanation, Multicollinearity, and Validity Concentration in Multiple Regression

Abstract

Recommendations from popular statistics texts regarding avoidance of predictor variable multicollinearity in the use of OLS multiple regression are considered from the perspective of the alternate purposes of explanation and prediction. Under the conditions considered, in the case of relative or absolute prediction accuracy, it is shown that multicollinearity has no effect on OLS prediction. Moreover, in regard to prediction accuracy, not only does multicollinearity not disadvantage OLS, but indeed, it is, in most data conditions presented, advantageous to model prediction accuracy, as it allows validity concentration to become large enough for alternative non-OLS methods to exceed OLS.