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	頑健な重回帰分析	Multiple Linear Regression
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1964–1980s	1886
提唱者	Peter J. Huber (M-estimators, 1964); extended by Rousseeuw, Yohai, and Maronna	Francis Galton; formalized by Karl Pearson
種類	Robust linear regression	Parametric linear model
原典	Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73–101.	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.
別名	robust MLR, M-estimator regression, resistant multiple regression, robust OLS	MLR, OLS regression, multiple regression, linear regression with multiple predictors
関連	6	8
概要	Robust multiple linear regression estimates the linear relationship between a continuous outcome and several predictors while being resistant to outliers and violations of the normality assumption. Instead of minimising the sum of squared residuals, it uses a bounded loss function — most commonly Huber's or Tukey's bisquare — so that extreme observations receive limited influence on the estimated 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.