Linear least squares regression: a different view
Journal
Statistics & Probability Letters
Date Issued
August 1996
Author(s)
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.