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| 多項式回帰× | 回帰スプラインと平滑化スプライン× | |
|---|---|---|
| 分野≠ | 統計学 | 機械学習 |
| 系統≠ | Regression model | Machine learning |
| 提唱年≠ | 2012 | 1996 |
| 提唱者≠ | Montgomery, Peck & Vining (textbook treatment); classical least squares | Spline regression literature; P-splines by Eilers & Marx |
| 種類≠ | Linear regression in transformed predictors | Piecewise-polynomial nonparametric regression |
| 原典≠ | Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811 | Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121. DOI ↗ |
| 別名≠ | polynomial least squares, curvilinear regression, Polinom Regresyonu | splines, cubic splines, natural splines, smoothing splines |
| 関連 | 4 | 4 |
| 概要≠ | 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. | Regression splines model a nonlinear relationship by fitting piecewise polynomials that join smoothly at a set of points called knots. Cubic and natural splines are the most common, and smoothing splines add a roughness penalty that automatically balances fit against smoothness. Splines are the standard flexible building block for univariate nonlinear regression and the basis of generalized additive models. |
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