Approximating the Distribution of the Sample R 2 in Best Subset Regressions

This note presents research on the problem of determining the distribution of the usual sample R2 statistic in multiple regression studies where the variables to be included in the regression equation are the subset of k variables, from a set of m variables, which maximize the sample R2 value or satisfy some similar criterion. A Monte-Carlo approach was used to estimate certain percentile points of the distribution of R2 under the null hypothesis of independence between the dependent variable and the m independent variables. A function has been developed which appears to provide a good approximation to percentile points of the R2 distribution.