How to use this calculator
- Enter or choose data.
- The r² updates as you type. Use Copy result or Share to keep it.
Method
R² = 1 − SSres ÷ SStot; adjusted R² = 1 − (1 − R²)(n − 1) ÷ (n − k − 1); F = (SStot − SSres) ÷ (SSres ÷ (n − 2)) on 1 and n − 2 df
- SSres
- Σ(actual − fitted)²
- SStot
- Σ(actual − mean)²
- n
- observations
- k
- number of predictors (1 for a straight line)
Worked example
- The least-squares line is ŷ = 2.2 + 0.6x, leaving SSres = 2.4; SStot = Σ(y − 4)² = 6.
- R² = 1 − 2.4 ÷ 6 = 0.6.
- Adjusted R² = 1 − 0.4 × 4 ÷ 3 = 0.4667; F = 3.6 ÷ 0.8 = 4.5 on 1 and 3 df (p = 0.124).
The straight line explains 60% of the variation in y (adjusted R² 0.47), but the F test is not significant with only five points.
What the result means
R² says how much of the spread the model accounts for, not whether the model is right: a curved relation can have a high R² for a straight line and still be badly specified. Adjusted R² penalises extra predictors. With predictions from another model, a negative R² means the model is worse than predicting the mean every time.
Assumptions and limits
- Fit mode uses ordinary least squares with an intercept; the F test assumes independent, normal, constant-variance residuals.
- Predictions mode uses R² = 1 − SSres ÷ SStot for any model, so it can be negative.
- The F test is not computed for supplied predictions, because their degrees of freedom depend on how the model was fitted.
- R² on the data used to fit a model overstates how well it predicts new data.
Questions
Is R² the same as r squared?
For a straight line fitted by least squares with an intercept, yes: R² equals the square of Pearson’s r. For other models it is not.
What is a good R²?
It depends on the field. Physical measurements often exceed 0.95, while models of human behaviour may be useful at 0.2.