Problems of selection with restrictions

Abstract

The paper considers a practically important generalization of the theory of regression. A linear function of a set of variables x₁,..., x_p, called predictor variables, is constructed so as to maximize its correlation with a criterion variable y₁, subject to the condition that its correlations with other criterion variables y₂,..., y_q are non-negative. It is suggested that a linear function so determined is useful when selection of individuals is done on the basis of x₁,..., x_p to achieve the maximum possible progress in the mean of y₁, while ensuring that no deterioration takes place in the mean values of y₂,..., y_a in the selected group, compared with the original group of individuals from which selection is made.