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	Multiple Linear Regression	ステップワイズ回帰
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1886	1960
提唱者	Francis Galton; formalized by Karl Pearson	M. A. Efroymson
種類	Parametric linear model	Automated variable selection
原典	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.	Efroymson, M. A. (1960). Multiple regression analysis. In A. Ralston & H. S. Wilf (Eds.), Mathematical Methods for Digital Computers (pp. 191–203). Wiley.
別名	MLR, OLS regression, multiple regression, linear regression with multiple predictors	stepwise selection, forward stepwise regression, backward stepwise regression, forward-backward selection
関連	8	5
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.	Stepwise regression is an automated variable selection procedure for multiple linear regression that adds or removes predictor variables one at a time according to a statistical criterion, typically the F-statistic or a p-value threshold. The forward-selection algorithm was formally described by Efroymson (1960) and the bidirectional variant was popularised by Draper and Smith in their landmark 1966 text Applied Regression Analysis. Despite widespread historical use, the method is now widely critiqued, making its documentation essential in any canonical methods library.