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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.
Rencher et al. (Fri,) studied this question.
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