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The comparison between polynomial regression and orthogonal polynomial regression

โœ Scribed by Guo-Liang Tian

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
270 KB
Volume
38
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

In this paper, the relationship between X, the structure matrix in a polynomial reyression (PR) model, and Z, the structure matrix in an orthoyonalpolynomial reyression (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.

๐Ÿ“œ SIMILAR VOLUMES

A BASIC program for orthogonal polynomia
A BASIC program for orthogonal polynomials and retrieval of regression coefficients for original model
โœ Hugh Tyson; Mary Ann Fieldes ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› Elsevier Science โš– 352 KB

A fast, short method for calculating orthogonal polynomials has been programmed in BASIC. This is combined with the retrieval of b coefficients for the original, non-orthogonal model in, for example, a curvilinear regression. The program may be used alone, or in conjunction with a package of BASIC p