决定系数计算器
计算回归模型的决定系数R²，衡量模型拟合优度。
R-squared
0.722500
R-squared vs Correlation Coefficient (r)
公式
How to Calculate the Coefficient of Determination
Formula
R-squared = r^2
R-squared is the square of the Pearson correlation coefficient. It represents the proportion of variance in the dependent variable that is predictable from the independent variable. The remaining 1 - R^2 is unexplained variance.
计算示例
If r = 0.85, how much variance does X explain in Y?
- 01R-squared = 0.85^2 = 0.7225
- 02X explains 72.25% of the variance in Y
- 03Unexplained variance = 1 - 0.7225 = 0.2775 or 27.75%
常见问题
What is a good R-squared value?
It depends on the field. In physical sciences, R^2 > 0.9 is typical. In social sciences, R^2 > 0.3 may be noteworthy. In stock prediction, even R^2 = 0.05 can be valuable.
Can R-squared be negative?
In simple linear regression, R^2 = r^2 and is always between 0 and 1. In multiple regression with poor models, adjusted R-squared can be negative, indicating the model is worse than simply predicting the mean.
What is adjusted R-squared?
Adjusted R-squared penalizes for the number of predictors. It can decrease if a predictor does not improve the model enough to justify the lost degree of freedom. It is preferred for comparing models with different numbers of predictors.
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