At Least Squares

Abstract

This chapter focuses on the next important mathematical invention: the method of least squares. First, it sets the historical context for its invention by describing the events in France and Germany leading up to the French Revolution. Next, the chapter describes how the method of least squares was invented twice, first by Adrien-Marie Legendre (as an appendix to his celestial investigations in Nouvelles méthodes pour la détermination des orbites des comètes), and then in a more sophisticated version by Carl Gauss, in Disquisitiones Arithmeticae. After that, an easy-to-understand description of method itself is given. Thus, the chapter goes from observation to probability and on to prediction, through regression, discussing ordinary least squares (OLS), intercepts, and slopes.