Flexible Regression

Abstract

Marketing researchers who want to do multiple regression often have data in which some of the standard regression assumptions are violated. Flexible regression is a new method for performing a nonparametric multiple regression while relaxing several of the standard assumptions of regression. In particular the assumptions of linearity, normal errors, and homoskedasticity are relaxed. The approach is based on nonparametric density estimation, which results in a more synergistic and less parametrically constrained method of analysis. Asymptotic properties of estimators are explored and necessary conditions are established for the rejection of significance tests that correspond to the major tests of regression. In addition, a necessary condition for rejection of a significance test is provided to determine whether or not to use flexible regression instead of conventional multiple regression. The advantages of the method are illustrated with several examples.