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Abstract

A Monte Carlo study was conducted comparing the selection of subsets of multiple regression predictors by the methods of forward selection, backward selection, and a newer method that looks for the “best” possible subset of a given size. Sample correlation matrices were obtained for sample sizes of 25, 150, and 450. Only at the n = 25 case were any significant differences among these three methods observed, and even then the differences were judged to be trivial in terms of practical consequences. The method of stepwise selection (forward selection with statistical tests both for inclusion and deletion of variables) is recommended for naive users, but it will not prevent inflation of reported R²s when n is small.

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Maximum R 2 Improvement and Stepwise Multiple Regression as Related to Over-Fitting

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