Statistical Science

Collinearity and Least Squares Regression

G. W. Stewart

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Abstract

In this paper we introduce certain numbers, called collinearity indices, which are useful in detecting near collinearities in regression problems. The coefficients enter adversely into formulas concerning significance testing and the effects of errors in the regression variables. Thus they provide simple regression diagnostics, suitable for incorporation in regression packages.

Article information

Source
Statist. Sci. Volume 2, Number 1 (1987), 68-84.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177013439

Digital Object Identifier
doi:10.1214/ss/1177013439

Mathematical Reviews number (MathSciNet)
MR896260

JSTOR
links.jstor.org

Keywords
Collinearity ill-conditioning linear regression errors in the variables regression diagnostics

Citation

Stewart, G. W. Collinearity and Least Squares Regression. Statist. Sci. 2 (1987), no. 1, 68--84. doi:10.1214/ss/1177013439. http://projecteuclid.org/euclid.ss/1177013439.


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See also

  • See Comment: Donald W. Marquardt. [Collinearity and Least Squares Regression]: Comment. Statist. Sci., Volume 2, Number 1 (1987), 84--85.
  • See Comment: David A. Belsley. [Collinearity and Least Squares Regression]: Comment: Well-Conditioned Collinearity Indices. Statist. Sci., Volume 2, Number 1 (1987), 86--91.
  • See Comment: Ronald A. Thisted. [Collinearity and Least Squares Regression]: Comment. Statist. Sci., Volume 2, Number 1 (1987), 91--93.
  • See Comment: Ali S. Hadi, Paul F. Velleman. [Collinearity and Least Squares Regression]: Comment: Diagnosing Near Collinearities in Least Squares Regression. Statist. Sci., Volume 2, Number 1 (1987), 93--98.
  • See Comment: G. W. Stewart. [Collinearity and Least Squares Regression]: Rejoinder. Statist. Sci., Volume 2, Number 1 (1987), 98--100.