Comparative R Squared

Abstract

This paper proposes a simple statistic for testing statistical significance of R squared. This statistic, called "comparative R squared," also tests statistical significance of the difference of R squared between null and alternative models with additional explanatory variables. The asymptotic distribution of the test statistic is a chi square distribution with the degree of freedom equal to the number of (additional) explanatory variables. Unlike the F test, this statistic is useful when dealing with non-normality. Simulations show that the test statistic behaves well and has no distortion of size, even in small samples.