By Richard William Farebrother (auth.)
This e-book is meant for college students of mathematical records who're drawn to the early heritage in their topic. It supplies special algebraic descriptions of the correct of linear relationships by way of the strategy of least squares (L ) and the comparable least absolute 2 deviations (L ) and minimax absolute deviations (Loo) strategies. those conventional line J becoming systems are, after all, additionally addressed in traditional statistical textbooks, however the dialogue in their old heritage is generally tremendous mild, if no longer solely absent. the current booklet enhances the research of those approaches given in S.M. Stigler'S first-class paintings The background of information: The Quantification of Uncertainty prior to 1900. in spite of the fact that, the current e-book offers a extra particular account of the algebraic constitution underlying those conventional becoming strategies. it really is expected that readers of the current ebook will receive a transparent figuring out of the historic heritage to those and different prevalent statistical techniques. additional, a cautious attention of the wide range of distinctive methods to a selected subject, equivalent to the strategy of least squares, will provide the reader priceless insights into the basic nature of the chosen topic.
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Additional info for Fitting Linear Relationships: A History of the Calculus of Observations 1750–1900
Example text
Gauss explicitly followed the latter course in 1809 and Laplace followed it implicitly in 1818. I know of no early reference for the compromise suggested by Grattan-Guinness (1994, p. 47). 2This procedure is also sometimes named for Pafnuti Lvovic Chebyshev (1821-1894) in honour of his widespread use of it in his practical work. There does not seem to have been a contemporary name for this procedure. It was generally known by its location in Section 39 of the second volume of Laplace's Traite de Mecanique Celeste.
For ease of reference in this section, we shall temporarily adopt de la Vallee Poussin's nomenclature and refer to the observed errors as residuals and to the optimality criterion itself as the criterion of minimal approximation. In the case of three unknowns, we have to choose values X, Y, and Z for the three unknowns x, y, and z, respectively, in such a way that the largest in absolute value of the n residuals atX + bJi + CiZ - mi = Vi i = 1,2, ... , n is as small as possible. In this context de la Vallee Poussin (1911), like Laplace (1786) before him, shows that the solution to this problem is characterised by a set of four (or more) residuals which are larger in absolute size than the other residuals and which share a common 9This procedure may be regarded as a variant of Mayer's elimination procedure for solving systems of linear equations adapted for use with systems of linear inequality constraints.
Had his remarks been published in a work better known and more accessible to naturalists, a detailed refutation of Reaumur and Krenig [by Glaisher] a hundred and thirteen years later would have been rendered superfluous. " Even if we allow that Boscovich could write in Latin with considerable facility, it seems inconceivable to a modern reader that he should have chosen to devote so much of his time to writing a detailed commentary on a poem in Latin hexameters by a kinsman and colleague. But that is precisely what he did choose to do.