Multiple regression as a general data-analytic system

Abstract

Techniques for using multiple regression (MR) as a general variance-accounting procedure of great flexibility, power, and fidelity to research aims in both manipula-tive and observational psychological research are presented. As a prelude, the identity of MR and fixed-model analysis of variance/covariance (AV/ACV) is sketched. This requires an exposition of means of expressing nominal scale (qualita-tive) data as independent variables in MR. Attention is given to methods for handling interactions, curvilinearity, missing data, and covariates, for either un-correlated or correlated independent variables in MR. Finally, the relative roles of AV/ACV and MR in data analysis are described, and the practical advantages of the latter are set forth. If you should say to a mathematical statistician that you have discovered that linear multiple regression analysis and the analysis of variance (and covariance) are identical systems, he would mutter something like, "Of course—general linear model, " and you might have trouble maintaining his atten-tion. If you should say this to a typical psy-chologist, you would be met with incredulity, or worse. Yet it is true, and in its truth lie possibilities for more relevant and therefore more powerful exploitation of research data. That psychologists would find strange the claimed equivalence of multiple regression (MR) and the fixed-model analysis of variance (AV) and covariance (ACV) is readily under-standable. The textbooks in "psychological" statistics treat these matters quite separately, with wholly different algorithms, nomencla-ture, output, and examples. MR is generally illustrated by examples drawn from the psychotechnology of educa-tional or personnel selection, usually the pre-diction of some criterion (e.g., freshman grade point average) from predictors (e.g., verba