मुफ्त R-वर्ग कैलकुलेटर
R² (निर्धारण गुणांक) की गणना करें। मॉडल कितना अच्छा फिट है यह जानें।
R² (Coefficient of Determination)
0.8000
R² (Coefficient of Determination) vs Regression Sum of Squares (SSR)
सूत्र
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).
हल किया गया उदाहरण
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
अक्सर पूछे जाने वाले प्रश्न
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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