Variable subset selection for optimal regression prediction at a specified point

Abstract

It is often desirable to select a subset of regression variables so as to maximise the accuracy of prediction at a pre-specified point. There are a variety of possible mean-square-error-type criteria which could be used to measure the accuracy of prediction and hence to select an optimal subset. We shall show how these can easily be included in existing stepwise regression codes. The performance of the criteria is compared on a data set, where it becomes obvious that not only do different criteria give rise to different subsets at the same prediction point, but the same criterion quite commonly gives rise to different subsets at different prediction points. Thus the choice of a criterion has a major effect on the subset selected, and so requires conscious selection.