Some Considerations in the Evaluation of Alternate Prediction Equations

Prediction equations constructed from multiple linear regression analyses are often intended for use in predicting response values throughout a region of the space of the predictor variables. Criteria for evaluating prediction equations, however, have generally concentrated attention on mean squared error properties of the estimated regression coefficients or on mean squared error properties of the predictor at the design points. If adequate prediction throughout a region of the space of predictor variables is the goal, neither of these criteria may be satisfactory in assessing the predictor. In this paper integrated mean squared error is used as a criterion to determine when the least squares, principal component, and ridge regression estimators of regression coefficients can produce satisfactory prediction equations in the presence of a multicollinear design matrix.