ABSTRACT
In Chapter 3, we have taken the basic ideas of MRC about as far as they go in the standard textbook treatments. For (in principle) any number k of IVs, we have discussed their joint relationship to Y (RY, Ry, the generation of the regression equation for Y), the various conceptions of the separate relationship of each Xi to Y (rYi, srit prt, B if (3,, r 2., s r j ,p r j ) , and significance testing and power analysis for these statistics. In the present chapter, we offer an expansion of these ideas from k single IVs to h sets of IVs. It turns out that the basic concepts of proportion of variance accounted for and of correlation (simple, partial, semipar tial, multiple) developed in Chapter 3 for single IVs hold as well for sets of IVs. We shall see that this generalization, that is, the use of sets as units of analysis in MRC, proves to be most powerful for the exploitation of data, and is at the core of our expansion of MRC from its limited past role in psychotechnology (for example, predicting freshman grade point average) to a truly general data-analyt ic system.
