Inflation of R ² in Best Subset Regression

Abstract

When subset selection is used in regression the expected value of R 2 is substantially inflated above its value without selection, especially when the number of observations is less than the number of predictor variables. The extent of this increase was investigated by a Monte Carlo simulation. Tables are given with average values and percentage points of R 2 for the null case of independence between the response variable and the predictor variables. Approximation formulas are provided to supplement the coverage in the tables.