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Abstract

Our summary of least squares given in Sections 1.3–1.5 shows that the core problem is one of solving the set of linear equations (1.3). In some accounts of regression, therefore, we are led directly to this algebraic problem.

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References

  • Chambers, J. M. (1971) Regression updating. J. Amer. Statist. Assoc., 66, 744–748.

    Article  Google Scholar 

  • Chambers, J. M. (1977) Computational Methods for Data Analysis. Wiley, New York.

    Google Scholar 

  • Clark, C. W. (1982) Elementary Mathematical Analysis, 2nd edn. Wadsworth Publishers of Canada Ltd, Belmont, CA.

    Google Scholar 

  • Goodnight, J. H. (1979) A tutorial on the SWEEP operator. Amer. Statist., 33, 149–158.

    Google Scholar 

  • Mandel, J. (1982) Use of the singular value decomposition in regression analysis. Amer. Statist., 36, 15–24.

    Google Scholar 

  • Rao, C. R. (1965) Linear Statistical Inference and Its Applications. Wiley, New York.

    Google Scholar 

  • Ruhe, A. (1980) Eigenvalues and eigenvectors by Rayleigh quotient iteration. APL Quote Quad, 10 (3), 29–30. [Corrigenda. APL Quote Quad, 10 (4), 18.]

    Google Scholar 

  • Seber, G. A. F. (1977) Linear Regression Analysis. Wiley, New York.

    Google Scholar 

  • Sparks, D. N. and Todd, A. D. (1973) Algorithm AS60. Latent roots and vectors of a symmetric matrix. Appl. Statist., 22, 260–265.

    Article  Google Scholar 

  • Stewart, G. W. (1973) Introduction to Matrix Computations. Academic Press, London.

    Google Scholar 

  • Strang, G. (1980) Linear Algebra with Its Applications, 2nd edn. Academic Press, London.

    Google Scholar 

  • Wilkinson, J. H. and Reinsch, C. (1971) Linear Algebra. Vol. II of Handbook for Automatic Computation (eds F. L. Bauer, A. S. Householder, F. W. J. Olver, H. Rutishauser, K. Samelson, E. Stiegel). Springer-Verlag, New York.

    Google Scholar 

Further reading

  • Clarke, M. R. B. (1981) Algorithm AS163. A Gauss algorithm for moving from one linear model to another without going back to the data. Appl. Statist., 30, 198–203.

    Article  Google Scholar 

  • Clarke, M. R. B. (1982) The Gauss-Jordan SWEEP operator with detection of collinearity. Appl. Statist., 31, 166–168.

    Article  Google Scholar 

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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). Obtaining least squares solutions. In: Regression Analysis with Applications. Monographs on Statistics and Applied Probability. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4105-2_3

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  • DOI: https://doi.org/10.1007/978-94-009-4105-2_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8322-5

  • Online ISBN: 978-94-009-4105-2

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