Linear correlations between sets of variables

Abstract

While the traditional multiple correlation coefficient appears to be inherently an asymmetrical statistic, it is actually a special case of a more general measure of linear relationship between twosets of variables. Another symmetric generalization of linear correlation is to the total relatednesswithin a set of variables. Both of these developments rest upon thegeneralized variance of a multivariate distribution, which is seen to be the fundamental concept of linear correlational theory.