手法を比較

	最小二乗法（OLS）	加重最小二乗法 (WLS)
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1805	1935
提唱者	Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809)	Alexander Craig Aitken
種類	Linear parameter estimation	Weighted linear estimator
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.]	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
別名	OLS, OLS regression, linear least squares, classical linear regression	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares
関連	8	3
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.	Weighted Least Squares is a generalization of Ordinary Least Squares (OLS) regression that assigns each observation a weight inversely proportional to its error variance, thereby down-weighting high-variance data points and up-weighting precise ones. Introduced in its general matrix form by Alexander Craig Aitken in 1935, WLS is the canonical remedy when heteroscedasticity is present and the error variance structure is known or can be reliably estimated.