Methoden vergleichen

	Polynomiale Regression	Response-Oberflächenmethode (ROM)	Ridge Regression
Fachgebiet	Statistik	Versuchsplanung	Maschinelles Lernen
Familie	Regression model	Hypothesis test	Machine learning
Entstehungsjahr	2012	1951	1970
Urheber	Montgomery, Peck & Vining (textbook treatment); classical least squares	George E. P. Box & K. B. Wilson	Hoerl, A.E. & Kennard, R.W.
Typ	Linear regression in transformed predictors	Second-order polynomial response surface model	L2-regularized linear regression
Wegweisende Quelle	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.
Aliasnamen	polynomial least squares, curvilinear regression, Polinom Regresyonu	RSM, Central Composite Design, Box-Behnken Design, CCD	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
Verwandt	4	7	4
Zusammenfassung	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.