手法を比較

	最小二乗法（OLS）	Multiple Linear Regression
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1805	1886
提唱者	Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809)	Francis Galton; formalized by Karl Pearson
種類	Linear parameter estimation	Parametric linear model
原典	Legendre, A.-M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Firmin Didot, Paris. [Appendix: Sur la Méthode des moindres quarrés, pp. 72–80.]	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.
別名	OLS, OLS regression, linear least squares, classical linear regression	MLR, OLS regression, multiple regression, linear regression with multiple predictors
関連	8	8
概要	Ordinary Least Squares (OLS) is the canonical method for estimating the parameters of a linear regression model by minimizing the sum of squared differences between observed and predicted values. First published by Adrien-Marie Legendre in 1805 and independently developed by Carl Friedrich Gauss (who claimed priority from 1795), OLS is provably optimal under the Gauss-Markov theorem: given its assumptions, it yields the Best Linear Unbiased Estimator (BLUE) of the regression coefficients.	Multiple linear regression (MLR) is a parametric regression model that expresses a continuous outcome as a weighted linear combination of two or more predictor variables plus a random error term. The unknown weights (regression coefficients) are estimated by ordinary least squares (OLS), which minimises the sum of squared residuals. The method traces to Francis Galton's 1886 work on hereditary stature and was placed on firm mathematical footing by Karl Pearson; Draper and Smith's 1966 textbook established it as the standard framework for applied regression.