Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition

53 Pages Posted: 11 Apr 2004 Last revised: 20 Apr 2022

See all articles by David A. Belsley

David A. Belsley

Boston College; National Bureau of Economic Research (NBER)

Virginia Klema

National Bureau of Economic Research (NBER)

Date Written: December 1974

Abstract

This paper presents a means for detecting the presence of multicollinearity and for assessing the damage that such collinearity may cause estimated coefficients in the standard linear regression model. The means of analysis is the singular value decomposition, a numerical analytic device that directly exposes both the conditioning of the data matrix X and the linear dependencies that may exist among its columns. The same information is employed in the second part of the paper to determine the extent to which each regression coefficient is being adversely affected by each linear relation among the columns of X that lead to its ill conditioning.

Suggested Citation

Belsley, David A. and Klema, Virginia, Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition (December 1974). NBER Working Paper No. w0066, Available at SSRN: https://ssrn.com/abstract=259379

David A. Belsley (Contact Author)

Boston College ( email )

Department of Economics
Chestnut Hill, MA 02167
United States
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National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
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Virginia Klema

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Computer Research Center
Cambridge, MA 02138
United States

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