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Ordinary Least Squares Regression

The treatment of errors has a long tradition with attempts to combine repeated measurements in astronomy and geodesy in the early 18th century. In 1805, Adrien-Marie Legendre introduced the method of least squares as a tool for using models with specification errors to fit data collected to determine the shape and circumference of the earth. Specifying the earth's shape to be a sphere, he had to estimate three parameters using five observations from the 1795 survey of the French meridian arc. With three unknowns and five equations, any estimate of the unknown parameters led to errors, when fitted to the five observations. He then proposed to choose those estimates that make “the sum of squares of the errors a minimum” (Legendre, 1805, pp. 72–73).

A formal ...

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