方法对比

	调整R方 (R²_adj)	均方误差 (MSE)
领域	模型评估	模型评估
方法族	MCDM	MCDM
起源年份	1961	1809
提出者	Henri Theil	Carl Friedrich Gauss
类型	Penalized goodness-of-fit metric	Squared-error loss function
开创性文献	Theil, H. (1961). Economic Forecasts and Policy. Amsterdam: North-Holland Publishing Company.	Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.
别名	Adjusted R², R²_adj	MSE, L2 error, quadratic error
相关	5	4
摘要	Adjusted R² is a corrected version of the coefficient of determination that accounts for the number of predictors in a regression model. Introduced by Henri Theil in 1961, it addresses the fundamental limitation of standard R²: the tendency to increase whenever any predictor is added, regardless of whether that predictor contributes meaningfully to explaining the target variable.	Mean Squared Error is the foundational loss function for regression models, measuring the average squared deviation between predictions and observations. Originating from Gauss and Legendre's method of least squares (1805-1809), MSE is the basis for ordinary least squares regression and remains central to modern machine learning optimization.