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Article: The comparison between polynomial regression and orthogonal polynomial regression

TitleThe comparison between polynomial regression and orthogonal polynomial regression
Authors
Tian, GL
KeywordsCondition Number
Gram-Schmidt Decomposition
Multicollinearity
Optimal Design
Polynomial Regression
Issue Date1998
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/stapro
Citation
Statistics And Probability Letters, 1998, v. 38 n. 4, p. 289-294 How to Cite?
AbstractIn 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.
Persistent Identifierhttp://hdl.handle.net/10722/172379
ISSN
0167-7152
2023 Impact Factor: 0.9
2023 SCImago Journal Rankings: 0.448
ISI Accession Number ID
WOS:000074314000001
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorTian, GLen_US
dc.date.accessioned2012-10-30T06:22:14Z-
dc.date.available2012-10-30T06:22:14Z-
dc.date.issued1998en_US
dc.identifier.citationStatistics And Probability Letters, 1998, v. 38 n. 4, p. 289-294en_US
dc.identifier.issn0167-7152en_US
dc.identifier.urihttp://hdl.handle.net/10722/172379-
dc.description.abstractIn 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.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/staproen_US
dc.relation.ispartofStatistics and Probability Lettersen_US
dc.subjectCondition Numberen_US
dc.subjectGram-Schmidt Decompositionen_US
dc.subjectMulticollinearityen_US
dc.subjectOptimal Designen_US
dc.subjectPolynomial Regressionen_US
dc.titleThe comparison between polynomial regression and orthogonal polynomial regressionen_US
dc.typeArticleen_US
dc.identifier.emailTian, GL: gltian@hku.hken_US
dc.identifier.authorityTian, GL=rp00789en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0032119408en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0032119408&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume38en_US
dc.identifier.issue4en_US
dc.identifier.spage289en_US
dc.identifier.epage294en_US
dc.identifier.isiWOS:000074314000001-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridTian, GL=25621549400en_US
dc.identifier.issnl0167-7152-

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