方法对比

	主成分回归 (PCR)	多元线性回归
领域	机器学习	统计学
方法族	Machine learning	Regression model
起源年份	1982	1886
提出者	Principal-component regression literature (Jolliffe and others)	Francis Galton; formalized by Karl Pearson
类型	Unsupervised dimension reduction + regression	Parametric linear model
开创性文献	Jolliffe, I. T. (1982). A note on the use of principal components in regression. Journal of the Royal Statistical Society: Series C (Applied Statistics), 31(3), 300–303.	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.
别名	PCR, PCA regression, temel bileşenler regresyonu	MLR, OLS regression, multiple regression, linear regression with multiple predictors
相关	3	8
摘要	Principal components regression first compresses a set of correlated predictors into a few principal components — the directions of greatest variance — and then regresses the response on those components. By discarding low-variance directions, PCR stabilizes estimation in the presence of multicollinearity and high dimensionality, at the cost of choosing components without reference to the response.	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.