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Contribution of individual variables to the regression sum of squares

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Contribution of individual variables to the regression sum of squares. / Shabuz, Zillur R; Garthwaite, Paul H.
In: Model Assisted Statistics and Applications, Vol. 14, No. 4, 23.12.2019, p. 281-296.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Shabuz, ZR & Garthwaite, PH 2019, 'Contribution of individual variables to the regression sum of squares', Model Assisted Statistics and Applications, vol. 14, no. 4, pp. 281-296. https://doi.org/10.3233/mas-190468

APA

Shabuz, ZR., & Garthwaite, PH. (2019). Contribution of individual variables to the regression sum of squares. Model Assisted Statistics and Applications, 14(4), 281-296. https://doi.org/10.3233/mas-190468

Vancouver

Shabuz ZR, Garthwaite PH. Contribution of individual variables to the regression sum of squares. Model Assisted Statistics and Applications. 2019 Dec 23;14(4):281-296. doi: 10.3233/mas-190468

Author

Shabuz, Zillur R ; Garthwaite, Paul H. / Contribution of individual variables to the regression sum of squares. In: Model Assisted Statistics and Applications. 2019 ; Vol. 14, No. 4. pp. 281-296.

Bibtex

@article{3b516eb0c9fb4c37a54dd97ee5567a5f,
title = "Contribution of individual variables to the regression sum of squares",
abstract = "In applications of multiple regression, one of the most common goals is to measure the relative importance of each predictor variable. If the predictors are uncorrelated, quantification of relative importance is simple and unique. However, in practice, predictor variables are typically correlated and there is no unique measure of a predictor variable{\textquoteright}s relative importance. Using a transformation to orthogonality, new measures are constructed for evaluating the contribution of individual variables to a regression sum of squares. The transformation yields an orthogonal approximation of the columns of the predictor scores matrix and it maximizes the sum of the covariances between the cross-product of individual regressors and the response variable and the cross-product of the transformed orthogonal regressors and the response variable. The new measures are compared with three previously proposed measures through examples and the properties of the measures are examined.",
author = "Zillur R Shabuz and Paul H Garthwaite",
year = "2019",
month = dec,
day = "23",
doi = "10.3233/mas-190468",
language = "English",
volume = "14",
pages = "281--296",
journal = "Model Assisted Statistics and Applications",
issn = "1574-1699",
publisher = "IOS Press BV",
number = "4",

}

RIS

TY - JOUR

T1 - Contribution of individual variables to the regression sum of squares

AU - Shabuz, Zillur R

AU - Garthwaite, Paul H

PY - 2019/12/23

Y1 - 2019/12/23

N2 - In applications of multiple regression, one of the most common goals is to measure the relative importance of each predictor variable. If the predictors are uncorrelated, quantification of relative importance is simple and unique. However, in practice, predictor variables are typically correlated and there is no unique measure of a predictor variable’s relative importance. Using a transformation to orthogonality, new measures are constructed for evaluating the contribution of individual variables to a regression sum of squares. The transformation yields an orthogonal approximation of the columns of the predictor scores matrix and it maximizes the sum of the covariances between the cross-product of individual regressors and the response variable and the cross-product of the transformed orthogonal regressors and the response variable. The new measures are compared with three previously proposed measures through examples and the properties of the measures are examined.

AB - In applications of multiple regression, one of the most common goals is to measure the relative importance of each predictor variable. If the predictors are uncorrelated, quantification of relative importance is simple and unique. However, in practice, predictor variables are typically correlated and there is no unique measure of a predictor variable’s relative importance. Using a transformation to orthogonality, new measures are constructed for evaluating the contribution of individual variables to a regression sum of squares. The transformation yields an orthogonal approximation of the columns of the predictor scores matrix and it maximizes the sum of the covariances between the cross-product of individual regressors and the response variable and the cross-product of the transformed orthogonal regressors and the response variable. The new measures are compared with three previously proposed measures through examples and the properties of the measures are examined.

U2 - 10.3233/mas-190468

DO - 10.3233/mas-190468

M3 - Journal article

VL - 14

SP - 281

EP - 296

JO - Model Assisted Statistics and Applications

JF - Model Assisted Statistics and Applications

SN - 1574-1699

IS - 4

ER -