方法对比

	多元线性回归	协方差分析 (ANCOVA)
领域	统计学	统计学
方法族	Regression model	Hypothesis test
起源年份	1886	1932
提出者	Francis Galton; formalized by Karl Pearson	Ronald A. Fisher
类型	Parametric linear model	Parametric group comparison with covariate control
开创性文献	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574
别名	MLR, OLS regression, multiple regression, linear regression with multiple predictors	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)
相关	8	4
摘要	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.	ANCOVA is a parametric hypothesis test that compares the adjusted means of two or more independent groups while statistically controlling for one or more continuous covariates. By removing the portion of outcome variance explained by the covariate, ANCOVA increases statistical precision and produces fairer group comparisons. The method builds on the general linear model framework consolidated by Fisher in the early 1930s and is described comprehensively by Tabachnick and Fidell (2013).