Mean and variance of R2 in small and moderate samples

Abstract

We derive and use easily computable expressions for the mean and variance of R2 in the standard linear regression model with fixed regressors. In respect to its probability limit R2 is seriously biased upward in small samples; the0 'adjusted' R̄2 does much better. But at sample sizes where these distinctions matter both measures are thoroughly unreliable because of their large dispersion. R2 should not be quoted for samples of less than fifty observations. © 1987.