Regression model
多元线性回归
多元线性回归（MLR）是一种参数回归模型，它将一个连续结果变量表示为两个或多个预测变量的加权线性组合加上一个随机误差项。未知权重（回归系数）通过普通最小二乘法（OLS）估计，该方法最小化残差平方和。该方法可以追溯到弗朗西斯·高尔顿1886年关于遗传身高的研究，并由卡尔·皮尔逊奠定了坚实的数学基础；1966年，德雷珀和史密斯的教科书将其确立为应用回归的标准框架。
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来源
- Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263. DOI: 10.2307/2841583 ↗
- Pearson, K., & Lee, A. (1908). On the generalised probable error in multiple normal correlation. Biometrika, 6(1), 59–68. DOI: 10.1093/biomet/6.1.59 ↗
- Draper, N. R., & Smith, H. (1966). Applied Regression Analysis (1st ed.). John Wiley & Sons. ISBN: 9780471221708
- Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis (5th ed.). John Wiley & Sons. ISBN: 9780470542811
如何引用本页
ScholarGate. (2026, June 3). Multiple Linear Regression (Ordinary Least Squares). ScholarGate. https://scholargate.app/zh/statistics/multiple-linear-regression
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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