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| 多元线性回归× | 多项式回归× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1886 | 2012 |
| 提出者≠ | Francis Galton; formalized by Karl Pearson | Montgomery, Peck & Vining (textbook treatment); classical least squares |
| 类型≠ | Parametric linear model | Linear regression in transformed predictors |
| 开创性文献≠ | Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263. DOI ↗ | Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811 |
| 别名≠ | MLR, OLS regression, multiple regression, linear regression with multiple predictors | polynomial least squares, curvilinear regression, Polinom Regresyonu |
| 相关≠ | 8 | 4 |
| 摘要≠ | Multiple linear regression (MLR) is a parametric regression model that expresses a continuous outcome as a weighted linear combination of two or more predictor variables plus a random error term. The unknown weights (regression coefficients) are estimated by ordinary least squares (OLS), which minimises the sum of squared residuals. The method traces to Francis Galton's 1886 work on hereditary stature and was placed on firm mathematical footing by Karl Pearson; Draper and Smith's 1966 textbook established it as the standard framework for applied regression. | 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. |
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