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Generalized inverse regression

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Book cover Regression Analysis with Applications

Part of the book series: Monographs on Statistics and Applied Probability ((MSAP))

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Abstract

We have just been studying the problems which can arise due to multicollinearities in regression. Examples quite frequently occur when there is an exact, rather than an approximate, linear relationship between the explanatory variables, and the problem we then face is that the matrix in the normal equations which we wish to invert is singular. Examples will be given below. In fact, it is possible to go through with much of least squares theory using what we call generalized inverses.

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References

  • Boot, J. G. C. (1963) The computation of the generalized inverse of singular or rectangular matrices. Amer. Math. Monthly, 70, 302–303.

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Author information

Authors and Affiliations

  1. Department of Statistics, The University of Newcastle upon Tyne, UK

    G. Barrie Wetherill

  2. Applied Statistics Research Unit, University of Kent at Canterbury, UK

    P. Duncombe

  3. Mathematical Institute, University of Kent at Canterbury, UK

    M. Kenward, J. Köllerström & B. J. Vowden

  4. Department of Mathematics and Statistics, University of Windsor, Canada

    S. R. Paul

Authors
  1. G. Barrie Wetherill
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  2. P. Duncombe
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  3. M. Kenward
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  4. J. Köllerström
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  5. S. R. Paul
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  6. B. J. Vowden
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© 1986 G. Barrie Wetherill

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Barrie Wetherill, G., Duncombe, P., Kenward, M., Köllerström, J., Paul, S.R., Vowden, B.J. (1986). Generalized inverse regression. In: Regression Analysis with Applications. Monographs on Statistics and Applied Probability. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4105-2_5

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  • DOI: https://doi.org/10.1007/978-94-009-4105-2_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8322-5

  • Online ISBN: 978-94-009-4105-2

  • eBook Packages: Springer Book Archive

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