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Abstract The optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points. As the number of regressors grows large, the Sp criterion provides an asymptotically optimal rule for the number of variables to enter. Key Words: RegressionStepwise regressionBest subsets regressionPrediction error
Breiman et al. (1983) studied this question.