Coefficient of Determination Calculator
Enter observed and predicted values to measure model fit using the coefficient of determination (R²).
R-squared
0.9455
Total sum of squares (SStot): 6.9720
Residual sum of squares (SSres): 0.3800
How to Use This Calculator
- Enter actual (observed) values in the left box.
- Enter predicted values from your model in the right box.
- Review R-squared and the associated sums of squares.
- Use R² to assess how well your model explains variation in the data.
Formula
SStot = Σ (yi − ȳ)²
SSres = Σ (yi − ŷi)²
R² = 1 − (SSres / SStot)
ȳ is the mean of actual values; ŷi are predicted values. R² ranges from −∞ to 1; negative values indicate poor fit compared to the mean-only model.
Full Description
The coefficient of determination measures how well predicted values approximate actual outcomes. Values near 1 indicate excellent fit, while values near 0 (or negative) suggest little explanatory power.
Use adjusted R² for models with multiple predictors to account for overfitting and compare models with different numbers of predictors.
Frequently Asked Questions
Can R² be negative?
Yes. When SSres exceeds SStot, the model performs worse than predicting the mean.
Is higher R² always better?
A higher R² indicates better explanatory power, but check for overfitting and consider adjusted R² for multivariate models.
Do actual and predicted values need to be sorted?
No. Input pairs should correspond row-wise, but order is arbitrary.
How many pairs do I need?
At least two pairs to compute variance; more observations improve reliability.