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|Title:||Linear least squares regression: a different view||Authors:||Yatracos, Yannis G.||Keywords:||Regression analysis;Parameter estimation||Issue Date:||1996||Publisher:||Elsevier||Source:||Statistics and Probability Letters, 1996, Volume 29, Issue 2, Pages 143-148||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.||URI:||http://ktisis.cut.ac.cy/handle/10488/6673||ISSN:||01677152||DOI:||http://dx.doi.org/10.1016/0167-7152(95)00167-0||Rights:||© 1996 Elsevier B.V. All rights reserved.||Type:||Article|
|Appears in Collections:||Άρθρα/Articles|
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