Best linear composites with a specified structure

Least squares linear composites of predictors for estimating several criteria are derived, satisfying the restriction that the composites have an arbitrary specified intercorrelation matrix. These composites are compared with the usual unrestricted regression composites. An illustrative example is provided. The derivation depends on a general result, given in an appendix, about best-fitting orthonormal transformations.This research was done while the author was a Fellow at The Center for Advanced Study in the Behavioral Sciences. The investigation was supported by a Public Health Service fellowship, 1 F3 MH-28, 495-01 (PS), from the National Institute of Mental Health. Preparation of the paper was supported in part by Grant MH 07722 from the National Institute of Mental Health, Public Health Service, for work done at Carnegie-Mellon University.