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An alternative look at the linear regression model

Author

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  • Oskar Maria Baksalary

    (Adam Mickiewicz University)

  • Götz Trenkler

    (Dortmund University of Technology)

Abstract

An alternative look at the linear regression model is taken by proposing an original treatment of a full column rank model (design) matrix. In such a situation, the Moore–Penrose inverse of the matrix can be obtained by utilizing a particular formula which is applicable solely when a matrix to be inverted can be columnwise partitioned into two matrices of disjoint ranges. It turns out that this approach, besides simplifying derivations, provides a novel insight into some of the notions involved in the model and reduces computational costs needed to obtain sought estimators. The paper contains also a numerical example based on astronomical observations of the localization of Polaris, demonstrating usefulness of the proposed approach.

Suggested Citation

  • Oskar Maria Baksalary & Götz Trenkler, 2022. "An alternative look at the linear regression model," Statistical Papers, Springer, vol. 63(5), pages 1499-1509, October.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:5:d:10.1007_s00362-021-01280-x
    DOI: 10.1007/s00362-021-01280-x
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    References listed on IDEAS

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    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. Baksalary, Oskar Maria & Trenkler, Götz, 2021. "On formulae for the Moore–Penrose inverse of a columnwise partitioned matrix," Applied Mathematics and Computation, Elsevier, vol. 403(C).
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