Title: Linear least squares regression: a different view
Abstract: The main result of this paper is filling an existing gap between the theory of least squares regression and the solution of linear systems of equations. A linear least squares regression problem with p-parameters over n cases is converted, via non-orthogonal transformations, into a k-parameter regression problem through the origin on n − p + k cases, and p − k equations in diagonal form with p − k unknowns, 0 < k < p. As a consequence of this result: (i) tests and confidence intervals can be easily obtained for any subset of the parameters of the model; (ii) the regression problem can be converted into p-univariate regression problems through the origin based on (n − p + 1) cases only; (iii) one may conclude that we can talk about the influence of the observations on any subset of the least squares estimates; (iv) the PC user may provide solutions to regression problems of higher dimension than the ones previously handled.
Publication Year: 1996
Publication Date: 1996-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1
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