PRINCIPAL COVARIATES REGRESSION .1. THEORY

A method for multivariate regression is proposed that is based on the simultaneous least-squares minimization of Y residuals and X residuals by a number of orthogonal X components. By lending increasing weight to the X variables relative to the Y variables, the procedure moves from ordinary least-squares regression to principal component regression, forming a relatively simple alternative for continuum regression. Analogies and differences with this and other biased regression techniques are discussed. Possible extensions to multi-block problems and nonlinear relationships are indicated.