PREDICTING MULTIVARIATE RESPONSES IN MULTIPLE LINEAR-REGRESSION

We look at the problem of predicting several response variables from t he same set of explanatory variables. The question is how to take adva ntage of correlations between the response variables to improve predic tive accuracy compared with the usual procedure of doing individual re gressions of each response variable on the common set of predictor var iables. A new procedure is introduced called the curds and whey method . Its use can substantially reduce prediction errors when there are co rrelations between responses while maintaining accuracy even if the re sponses are uncorrelated. In extensive simulations, the new procedure is compared with several previously proposed methods for predicting mu ltiple responses (including partial least squares) and exhibits superi or accuracy. One version can be easily implemented in the context of s tandard statistical packages.