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

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  • David A. Belsley
  • Virginia Klema

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

  • David A. Belsley & Virginia Klema, 1974. "Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition," NBER Working Papers 0066, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0066
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    1. David A. Belsley, 1974. "Estimation of Systems of Simultaneous Equations, and Computational Specifications of GREMLIN," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 551-614, National Bureau of Economic Research, Inc.
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    Cited by:

    1. David A. Belsley, 1976. "Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation," NBER Working Papers 0154, National Bureau of Economic Research, Inc.
    2. Irene Aldridge & Payton Martin, 2022. "ESG In Corporate Filings: An AI Perspective," Papers 2212.00018, arXiv.org.

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