Jacob Cohen New York University
By now, it is widely appreciated that multiple regression/correlation analysis (MRC) can be used as a general data-analytic system ( J. Cohen, 1968, 1982a; J. Cohen & P. Cohen, 1983; Pedhazur, 1982). As a realization of the univariate general linear model, it incorporates the analysis of variance (ANOVA) and the analysis of covariance (ANCOVA) as special cases, and is not constrained to the neat balanced layouts or categorical independent variables ("treatments," "diagnosis") that characterizes their textbook presentation. With MRC, one can use graduated ("continuous") independent variables, study interactions and other nonlinear relationships involving such variables, and represent missing data as positive information. Moreover, one can readily generalize the notion of "adjusting" for covariates," used in ANCOVA for categorical independent variables, to graduated variables in "the analysis of partial variance" (APV). MRC also offers the obvious benefit of a common framework for apparently diverse techniques, with a common effect size measure (proportion of variance accounted for), and is replete with least squares parameter estimation, hypothesis testing, and power analysis.
The versatility of MRC as a general data-analytic method is largely due to the use of sets of independent variables representing research factors as the units of analysis, and the varied use of partialling.
Virtually any information can be represented by a suitably chosen set of quantitative variables: nominal (qualitative, categorical) scales, curvilinearly related