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

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... dictor 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.