A Note on the Maximization of

The maximization of RI (corrected multiple correlation coefficient) as the statistical criterion of choosing among various regression specifications is now in common use by econometricians, yet there are many practitioners who would arrive at the maximum RI by trial and error, trying all possible permutations of the hypothesized explanatory variables. The more experienced econometricians are aware of the fact that the maximization of K2 (which is equivalent to the minimization of the estimated regression variances 2 s... ) is achieved by retaining all regression coefficients whose associated t-statistics are larger than unity and discarding all which are not. Only a few appear to know whether or not this relationship between t and K2 is exact, and I am no-t aware of any proof in print. The purpose of this note is to establish the exact relationship between R2 and the t-statistics associated with the regression coefficients, and to show some applications of this relationship.