Inflation of R² 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.

KEY WORDS:

• Regression
• Subset selection
• Multiple correlation coefficient
• Stepwise regression
• Monte Carlo