方法对比

	多项式回归	普通最小二乘法 (OLS) 回归	岭回归（Ridge Regression）
领域	统计学	计量经济学	机器学习
方法族	Regression model	Regression model	Machine learning
起源年份	2012	2019	1970
提出者	Montgomery, Peck & Vining (textbook treatment); classical least squares	Wooldridge (textbook treatment); classical least squares	Hoerl, A.E. & Kennard, R.W.
类型	Linear regression in transformed predictors	Linear regression	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	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	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	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
相关	4	5	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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.