Adjusted R-Squared Calculator Formula
Understand the math behind the adjusted r-squared calculator. Each variable explained with a worked example.
Formulas Used
Adjusted R²
adj_r2 = 1 - (1 - r_squared) * (n - 1) / (n - p - 1)Adjustment Penalty
penalty = r_squared - (1 - (1 - r_squared) * (n - 1) / (n - p - 1))Variables
| Variable | Description | Default |
|---|---|---|
r_squared | R² | 0.85 |
n | Sample Size (n) | 50 |
p | Number of Predictors (p) | 3 |
How It Works
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.
Worked Example
R² = 0.85, n = 50, p = 3 predictors.
r_squared = 0.85n = 50p = 3
- 01Adj R² = 1 - (1 - 0.85) × 49/46
- 02Adj R² = 1 - 0.15 × 1.0652 = 1 - 0.1598 = 0.8402
- 03Penalty = 0.85 - 0.84 = 0.01
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Open Adjusted R-Squared Calculator