Problems of Selection with Restrictions

Abstract

SUMMARY The paper considers a practically important generalization of the theory of regression. A linear function of a set of variables x l, …, xp, called predictor variables, is constructed so as to maximize its correlation with a criterion variable y 1 subject to the condition that its correlations with other criterion variables y 2,…,yq are non-negative. It is suggested that a linear function so determined is useful when selection of individuals is done on the basis of x 1,…,xp to achieve the maximum possible progress in the mean of y 1, while ensuring that no deterioration takes place in the mean values of y 2,…,yq in the selected group, compared with the original group of individuals from which selection is made.