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Collinearity and least squares regression. (English) Zbl 0643.62049

This paper deals with the problem of diagnosing near collinearities in the least-squares regression. The linear model considered here is \[ y(n\times 1)=x(n\times p)b(p\times 1)+e(n\times 1),\quad rank(x)=p,\quad E (e)=0,\quad var(e)=\sigma^ 2I. \] Certain numbers, called collinearity indices, are introduced which are quite useful in detecting near collinearities in regression problems. The collinearity indices introduced here are simply the square roots of the corresponding variance inflation factors, and are invariant under any column scaling of x.
The author also discusses the effects of near collinearity on significance testing, and the value of collinearity indices in estimating the effects of errors in the regression variables. The paper contains some illustrative examples, and very useful comments and discussions at the end by D. Marquardt, D.Belsley, R. Thisted, A. Hadi and P. Velleman.
Reviewer: D.V.Chopra

MSC:

62J05 Linear regression; mixed models
62J99 Linear inference, regression
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