R-Squared Calculator
Calculate the coefficient of determination R² from the sum of squares of regression and total sum of squares.
R² (Coefficient of Determination)
0.8000
R² (Coefficient of Determination) vs Regression Sum of Squares (SSR)
公式
## R-Squared (Coefficient of Determination) R² measures the proportion of variance in the dependent variable that is explained by the regression model. ### Formula **R² = SSR / SST = 1 - SSE / SST** where SSR is the regression sum of squares, SST is the total sum of squares, and SSE is the residual sum of squares. R² ranges from 0 (model explains nothing) to 1 (perfect fit).
计算示例
A regression with SSR = 800 and SST = 1000.
- 01R² = 800 / 1000 = 0.80
- 02The model explains 80% of the variance in y.
- 03SSE = 1000 - 800 = 200
- 04R = sqrt(0.80) = 0.8944
常见问题
What is a good R² value?
It depends on the field. In physics, R² > 0.99 is expected. In social sciences, R² > 0.3 may be meaningful. In finance, R² > 0.5 is often good. Context and theory matter more than arbitrary thresholds.
Can R² decrease when adding predictors?
No. R² can only increase (or stay the same) with more predictors. This is why adjusted R² was invented, which penalizes for extra parameters and can decrease if a predictor does not improve the model enough.
Does high R² mean the model is correct?
No. R² only measures linear fit, not whether the model is appropriate. A polynomial may give higher R² but overfit the data. Always check residual plots for patterns indicating model misspecification.
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