The comparison between polynomial regression and orthogonal polynomial regression

In this paper, the relationship between X, the structure matrix in a polynomial regression (PR) model, and Z, the structure matrix in an orthogonal polynomial regression (OPR) model, is established. We show that C(X)≥C(Z), where C(X) denotes the condition number of X, and OPR is superior to PR under the criteria of A-and E-optimalities in the sense of experimental design. However, the two regressions are equivalent under the criterion of D-optimality. These conclusions are also valid for the general linear regression model with p(> 1) predictor variables. © 1998 Elsevier Science B.V. All rights reserved.link_to_subscribed_fulltex