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	Multiple Linear Regression	多項式回帰
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1886	2012
提唱者	Francis Galton; formalized by Karl Pearson	Montgomery, Peck & Vining (textbook treatment); classical least squares
種類	Parametric linear model	Linear regression in transformed predictors
原典	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811
別名	MLR, OLS regression, multiple regression, linear regression with multiple predictors	polynomial least squares, curvilinear regression, Polinom Regresyonu
関連	8	4
概要	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.	Polynomial regression is a regression method that models non-linear relationships by including squared and higher-degree terms of an explanatory variable, and it is a core tool of response surface analysis. As developed in Montgomery, Peck and Vining's Introduction to Linear Regression Analysis (2012), it remains linear in its parameters even though the fitted curve bends.