The Rise and Fall of Multiple Regression

Abstract

The rise and fall and rise of multiple regression is chronicled in the literature by examining its initial impetus and popularity, followed by the acknowledgement of potential problematic issues such as violation of assumptions and overzealous usage, and the subsequent resurgence of the technique as the problems are addressed and procedures clarified. Jacob Cohen brought to the attention of many researchers that multiple regression can be used as a general data-analytic system. With the increasing availability of mainframe computers and programs to perform statistical analysis, journal editors were inundated with an avalanche of regression analyses. The assumptions underlying the analyses were emphasized, considered, and often found to be unmet. Two major problems of using stepwise regression were identified: (1) incorrect degrees of freedom were specified when evaluating changes in explained variance and, (2) incorrect interpretation of stepwise results when a few variables are selected from many. Subsequently, many different regression models have been developed for different situations, especially when assumptions are violated. These models include ridge regression, robust regression, and nonlinear regression.