Groping Toward Linear Regression Analysis: Newton's Analysis of Hipparchus' Equinox Observations

Details Groping Toward Linear Regression Analysis: Newton's Analysis of Hipparchus' Equinox Observations Groping Toward Linear Regression Analysis: Newton's Analysis of Hipparchus' Equinox Observations

2008-10-27

arxiv.org/abs/0810.4948v1

Physics

History and Philosophy of Physics

30 pages, 7 figures, 3 images, 2 tables

Scientific paper

In 1700, Newton, in designing a new universal calendar contained in the manuscripts known as Yahuda MS 24 from Jewish National and University Library at Jerusalem and analyzed in our recent article in Notes & Records Royal Society (59 (3), Sept 2005, pp. 223-54), attempted to compute the length of the tropical year using the ancient equinox observations reported by a famous Greek astronomer Hipparchus of Rhodes, ten in number. Though Newton had a very thin sample of data, he obtained a tropical year only a few seconds longer than the correct length. The reason lies in Newton's application of a technique similar to modern regression analysis. Actually he wrote down the first of the two so-called "normal equations" known from the Ordinary Least Squares method. Newton also had a vague understanding of qualitative variables. This paper concludes by discussing open historico-astronomical problems related to the inclination of the Earth's axis of rotation. In particular, ignorance about the long-range variation in inclination and nutation of the axis is likely responsible for the wide variety in the lengths of the tropical year assigned by different 17th century astronomers - the problem that led Newton to Hipparchus and to an "embryonic" regression analysis.

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