Methoden vergleichen

	Polynomiale Regression	Lasso-Regression	Methode der kleinsten Quadrate (OLS)
Fachgebiet	Statistik	Maschinelles Lernen	Ökonometrie
Familie	Regression model	Machine learning	Regression model
Entstehungsjahr	2012	1996	2019
Urheber	Montgomery, Peck & Vining (textbook treatment); classical least squares	Tibshirani, R.	Wooldridge (textbook treatment); classical least squares
Typ	Linear regression in transformed predictors	Regularized linear regression (L1 penalty)	Linear regression
Wegweisende Quelle	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811	Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
Aliasnamen	polynomial least squares, curvilinear regression, Polinom Regresyonu	LASSO Regresyonu, lasso, L1-regularized regression, L1 regularization	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
Verwandt	4	4	5
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.	Lasso regression, introduced by Robert Tibshirani in 1996, is a linear regression method that adds an L1 penalty to the loss so that it shrinks coefficients and performs variable selection at the same time, producing a sparse model. By driving some coefficients exactly to zero it keeps only the predictors that matter.	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).