Adjusted R-Squared Calculator
Correcting R² for a Model-Building Trick
Plain R² has a well-known flaw: adding any predictor to a regression model, even a column of random noise, can never decrease it and will usually nudge it upward. That makes R² alone a poor guide when comparing models with different numbers of predictors. Adjusted R² fixes this by introducing a penalty tied to the number of predictors relative to the sample size, so it only rises when a new variable adds genuine explanatory value.
The Formula
where n = sample size, k = number of predictors
Worked Examples
Starting from the same R² = 0.75, adjusted R² drops as more predictors compete for the same sample, and rises again as the sample grows to support them:
| R² | n (sample size) | k (predictors) | Adjusted R² |
|---|---|---|---|
| 0.75 | 30 | 3 | 0.7212 |
| 0.75 | 30 | 8 | 0.6548 |
| 0.75 | 100 | 3 | 0.7422 |
| 0.90 | 20 | 5 | 0.8643 |
Each row computed directly from the adjusted R² formula.
Notice the second row: keeping R² fixed at 0.75 but tripling the predictor count from 3 to 8, with the same 30 observations, pulls the adjusted figure down by nearly 7 percentage points — the penalty for spreading a limited sample across more parameters.
Why This Matters for Model Selection
- Comparing nested models — when deciding whether to add a variable, an increase in adjusted R² is a much better signal than an increase in raw R², which is guaranteed to occur regardless of whether the variable is meaningful.
- Guarding against overfitting — models with many predictors relative to sample size tend to fit the training data suspiciously well while generalizing poorly; adjusted R² flags this directly.
- Reporting — journals and technical reports in economics, biostatistics, and social science routinely require adjusted R² alongside R² for exactly this reason.
How to Use This Calculator
- Enter R² from your regression output (a decimal between 0 and 1).
- Enter the sample size (n) used to fit the model.
- Enter the number of predictors (k) in the model.
- Select Calculate to get the adjusted R² value.
Related Calculations
Compute the base R² first with the R-Squared Calculator, or fit the underlying model with the Linear Regression Calculator.