方法对比

	多项式回归	响应面方法 (RSM)	岭回归（Ridge Regression）
领域	统计学	实验设计	机器学习
方法族	Regression model	Hypothesis test	Machine learning
起源年份	2012	1951	1970
提出者	Montgomery, Peck & Vining (textbook treatment); classical least squares	George E. P. Box & K. B. Wilson	Hoerl, A.E. & Kennard, R.W.
类型	Linear regression in transformed predictors	Second-order polynomial response surface model	L2-regularized linear regression
开创性文献	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811	Box, G. E. P. & Wilson, K. B. (1951). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society, Series B, 13(1), 1–45.	Hoerl, A.E. & Kennard, R.W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
别名	polynomial least squares, curvilinear regression, Polinom Regresyonu	RSM, Central Composite Design, Box-Behnken Design, CCD	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
相关	4	7	4
摘要	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.	Response Surface Methodology is a collection of statistical and mathematical techniques for building an empirical second-order polynomial model that relates a continuous response variable to two or more controllable input factors, and then locating the factor settings that optimize that response. The approach was introduced by George E. P. Box and K. B. Wilson in their landmark 1951 paper and has since become a cornerstone of process optimization across engineering, chemistry, food science, and pharmaceutics.	Ridge Regression is an L2-regularized linear regression method, introduced by Arthur Hoerl and Robert Kennard in 1970, that reduces multicollinearity by adding a penalty on the size of the coefficients. It shrinks coefficients toward zero without setting any of them exactly to zero, producing more stable estimates when predictors are highly correlated.