Сравнение методов

	Полиномиальная регрессия	Регрессия методом обыкновенных наименьших квадратов (ОНМК)	Методология поверхности отклика (RSM)	Гребневая регрессия
Область	Статистика	Эконометрика	Планирование эксперимента	Машинное обучение
Семейство	Regression model	Regression model	Hypothesis test	Machine learning
Год появления	2012	2019	1951	1970
Автор метода	Montgomery, Peck & Vining (textbook treatment); classical least squares	Wooldridge (textbook treatment); classical least squares	George E. P. Box & K. B. Wilson	Hoerl, A.E. & Kennard, R.W.
Тип	Linear regression in transformed predictors	Linear regression	Second-order polynomial response surface model	L2-regularized linear regression
Основополагающий источник	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	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.
Другие названия	polynomial least squares, curvilinear regression, Polinom Regresyonu	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	RSM, Central Composite Design, Box-Behnken Design, CCD	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
Связанные	4	5	7	4
Сводка	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).	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.