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Inflation of R2 in Best Subset Regression

Alvin C. Rencher and Fu Ceayong Pun
Technometrics
Vol. 22, No. 1 (Feb., 1980), pp. 49-53
DOI: 10.2307/1268382
Stable URL: http://www.jstor.org/stable/1268382
Page Count: 5
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Inflation of  R2 in Best Subset Regression
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Abstract

When subset selection is used in regression the expected value of R2 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 R2 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.

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