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In February 1700, Isaac Newton needed a precise tropical year to design a newuniversal calendar that would supersede the Gregorian one. However,17th-Century astronomers were uncertain of the long-term variation in theinclination of the Earth's axis and were suspicious of Ptolemy's equinoxobservations. As a result, they produced a wide range of tropical years. Facingthis problem, Newton attempted to compute the length of the year on his own,using the ancient equinox observations reported by a famous Greek astronomerHipparchus of Rhodes, ten in number. Though Newton had a very thin sample ofdata, he obtained a tropical year only a few seconds longer than the correctlength. The reason lies in Newton's application of a technique similar tomodern regression analysis. Newton wrote down the first of the two so-called'normal equations' known from the ordinary least-squares (OLS) method. In thatprocedure, Newton seems to have been the first to employ the mean (average)value of the data set, while the other leading astronomers of the era (TychoBrahe, Galileo, and Kepler) used the median. Fifty years after Newton, in 1750,Newton's method was rediscovered and enhanced by Tobias Mayer. Remarkably, thesame regression method served with distinction in the late 1920s when thefounding fathers of modern cosmology, Georges Lemaitre (1927), Edwin Hubble(1929), and Willem de Sitter (1930), employed it to derive the Hubble constant.

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