CORRELATION WEIGHTS IN MULTIPLE REGRESSION

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights. We then derive the least squares weights ( for any set of predictors) that yield the largest drop in R-2 ( the coefficient of determination) when switching to correlation weights. Our findings suggest that two characteristics of a model/data combination are especially important in determining the effectiveness of correlation weights: (1) the condition number of the predictor correlation matrix, R-xx, and ( 2) the orientation of the correlation weights to the latent vectors of R-xx.