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Article: The comparison between polynomial regression and orthogonal polynomial regression
Title | The comparison between polynomial regression and orthogonal polynomial regression |
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Authors | |
Keywords | Condition Number Gram-Schmidt Decomposition Multicollinearity Optimal Design Polynomial Regression |
Issue Date | 1998 |
Publisher | Elsevier 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? |
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)≥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 Identifier | http://hdl.handle.net/10722/172379 |
ISSN | 2023 Impact Factor: 0.9 2023 SCImago Journal Rankings: 0.448 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Tian, GL | en_US |
dc.date.accessioned | 2012-10-30T06:22:14Z | - |
dc.date.available | 2012-10-30T06:22:14Z | - |
dc.date.issued | 1998 | en_US |
dc.identifier.citation | Statistics And Probability Letters, 1998, v. 38 n. 4, p. 289-294 | en_US |
dc.identifier.issn | 0167-7152 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/172379 | - |
dc.description.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)≥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.language | eng | en_US |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/stapro | en_US |
dc.relation.ispartof | Statistics and Probability Letters | en_US |
dc.subject | Condition Number | en_US |
dc.subject | Gram-Schmidt Decomposition | en_US |
dc.subject | Multicollinearity | en_US |
dc.subject | Optimal Design | en_US |
dc.subject | Polynomial Regression | en_US |
dc.title | The comparison between polynomial regression and orthogonal polynomial regression | en_US |
dc.type | Article | en_US |
dc.identifier.email | Tian, GL: gltian@hku.hk | en_US |
dc.identifier.authority | Tian, GL=rp00789 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.scopus | eid_2-s2.0-0032119408 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0032119408&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 38 | en_US |
dc.identifier.issue | 4 | en_US |
dc.identifier.spage | 289 | en_US |
dc.identifier.epage | 294 | en_US |
dc.identifier.isi | WOS:000074314000001 | - |
dc.publisher.place | Netherlands | en_US |
dc.identifier.scopusauthorid | Tian, GL=25621549400 | en_US |
dc.identifier.issnl | 0167-7152 | - |