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
Date Written: December 1974
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.
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