Least Squares

Abstract

The method of least squares has been employed at least since Legendre (1805) to treat problems in which a real variable is approximated by using a predictor selected from a linear subspace. In Section 5.1, square-integrable functions are defined and used to define variances, standard deviations, covariances, and coefficients of variation. In Section 5.2, mean-squared error and least-squares predictors are defined. In Section 5.3, simple linear regression is considered. In Section 5.4, multiple linear regression is considered. In Section 5.5, least-squares problems are considered for infinite-dimensional subspaces.