The use of R2 to determine the appropriate transformation of regression variables

It is proved that, under certain conditions, the ‘true’ model, from a set of alternative regression specifications involving different transformations of the same dependent variable, is the formulation for which population R² is highest. This theorem, which requires assumptions of normality, is proved through the use of Hermite polynomials. The paper contains an appendix listing the major properties of these polynomials.