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Julius Weisbach’s pioneering contribution to orthogonal linear regression (1840). (English) Zbl 1436.62014

Authors’ abstract: Orthogonal linear regression is a standard statistical method which is used to fit a line to a scatter plot of data points \((x_i , y_i)\) in situations where both variables have errors. Until now the US American R. J. Adcock has been considered to be the first who published this method, which is based on the method of least squares. We show that J. Weisbach, professor of mathematics and engineering at Bergakademie Freiberg in Saxony (Germany) had already published in 1840 a paper [“Bestimmung des Hauptstreichens und Hauptfallens von Lagerstätten”, Archiv für Mineralogie, Geognosie, Bergbau und Hüttenkunde 4, 159–174 (1840)] in which the method is fully described and applied to an interesting problem. We discuss the context of his discovery in order to understand the type of problems mining surveyors faced in that time and why the use of this method was found to be relevant in geodesy. Weisbach’s method of solution is then explained in all detail. We show that he implicitly used the method of least squares, but presented the solution in terms of geometrical arguments adapted to the readership of the journal in which he published.

MSC:

62-03 History of statistics
51M15 Geometric constructions in real or complex geometry
62J05 Linear regression; mixed models
01A55 History of mathematics in the 19th century
01A70 Biographies, obituaries, personalia, bibliographies
01A74 History of mathematics at institutions and academies (non-university)
86A30 Geodesy, mapping problems

Biographic References:

Weisbach, Julius
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References:

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