The comparison between polynomial regression and orthogonal polynomial regression

Guo-Liang Tian

Statistics & Probability Letters, 1998, vol. 38, issue 4, 289-294

Abstract: 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) [greater-or-equal, slanted] 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.

Keywords: Condition; number; Gram-Schmidt; decomposition; Multicollinearity; Optimal; design; Polynomial; regression (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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