Adjusted R-Squared Calculator — Formule
## Adjusted R-Squared
Adjusted R² modifies R² to penalize for additional predictors that do not improve the model. Unlike R², it can decrease when unhelpful variables are added.
### Formula
**Adj R² = 1 - (1 - R²) × (n - 1) / (n - p - 1)**
where n is the sample size and p is the number of predictors. Adjusted R² is always less than or equal to R². The difference grows larger with more predictors relative to sample size.
Adjusted R² modifies R² to penalize for additional predictors that do not improve the model. Unlike R², it can decrease when unhelpful variables are added.
### Formula
**Adj R² = 1 - (1 - R²) × (n - 1) / (n - p - 1)**
where n is the sample size and p is the number of predictors. Adjusted R² is always less than or equal to R². The difference grows larger with more predictors relative to sample size.
Exemple Résolu
R² = 0.85, n = 50, p = 3 predictors.
- Adj R² = 1 - (1 - 0.85) × 49/46
- Adj R² = 1 - 0.15 × 1.0652 = 1 - 0.1598 = 0.8402
- Penalty = 0.85 - 0.84 = 0.01