Calculator Inputs
Enter your model statistics, then compute Adjusted R². Use SSE/SST mode if you only have error sums.
Formula used
Adjusted R² penalizes models with more predictors by correcting for degrees of freedom:
- R²: coefficient of determination
- n: sample size (observations)
- p: number of predictors (features)
In SSE/SST mode, R² is computed as 1 − SSE/SST before adjustment.
How to use this calculator
- Select an input method: enter R² or enter SSE and SST.
- Provide n (observations) and p (predictors).
- Click Calculate to see results above the form.
- Use Download CSV for spreadsheets and reports.
- Use Download PDF for quick sharing and archiving.
Example data table
These sample scenarios show how Adjusted R² changes with more predictors at similar R² values.
| Scenario | n | p | R² | Adjusted R² |
|---|---|---|---|---|
| Model A | 120 | 3 | 0.68 | 0.6717 |
| Model B | 120 | 8 | 0.72 | 0.6998 |
| Model C | 60 | 6 | 0.55 | 0.4991 |
| Model D | 250 | 12 | 0.81 | 0.8004 |
| Model E | 40 | 5 | 0.62 | 0.5641 |
Why Adjusted R² matters in model comparison
R² usually rises when you add predictors, even if a feature only fits noise. Adjusted R² corrects this by scaling (1 − R²) with degrees of freedom. With n=120 and p=3, an R² of 0.68 becomes about 0.672, making comparisons fairer when models have different feature counts. If you add redundant variables, the adjusted score may stay flat or fall.
Inputs that drive the adjustment
The key multiplier is (n−1)/(n−p−1). When n is small or p is large, residual degrees of freedom shrink and the penalty grows. For example, n=40 and p=5 gives 39/34=1.147. At R²=0.62 the adjusted value is roughly 0.564. With n=250 and p=5 the multiplier is 249/244=1.020, so Adjusted R² is about 0.612. Count p as estimated slopes, including dummy and interaction terms.
Using SSE and SST when R² is unavailable
Switch to SSE/SST mode when your output provides sums of squares. R² is computed as 1 − SSE/SST, where SSE is residual error and SST is total variation around the mean. If SST=10,000 and SSE=3,200, then R²=0.68. Using n=120 and p=3 produces the same adjusted result as entering R² directly. Useful when you only have an ANOVA table or training logs.
Interpreting results responsibly
Adjusted R² can be negative when a model performs worse than predicting the mean, often signaling leakage, wrong transformations, or over-parameterization. Compare models only on the same split and target definition, and report n and p with the score. If two models are close, favor the simpler one and validate with metrics like MAE or RMSE. Use it as a selection aid, not a guarantee of predictive accuracy; confirm real improvements with holdout evaluation or cross-validation, especially for high-dimensional data.
Workflow tips for reproducible reporting
Use the precision control to match your reporting standard, such as 4 decimals for experiments and 2 for summaries. The CSV export supports audit trails by listing R², Adjusted R², degrees of freedom, and the adjustment amount (R² − Adjusted R²). Use the PDF export for review snapshots. Recompute after feature engineering, because p must match the final predictor set. Store the inputs alongside your model version for traceability.
FAQs
What is the difference between R² and Adjusted R²?
R² measures the proportion of variance explained. Adjusted R² adds a penalty for the number of predictors relative to sample size, so it can decrease when you add weak or redundant features.
Should p include the intercept term?
Typically no. Use p as the number of estimated feature coefficients (slopes). Include dummy variables, interactions, and polynomial terms, because each consumes a degree of freedom.
Why can Adjusted R² be negative?
It can drop below zero when the model fits worse than predicting the mean. Common causes include overfitting, leakage, incorrect target scaling, or too many predictors for the available observations.
When should I use SSE and SST mode?
Use it when your output provides sums of squares instead of R². The calculator computes R² as 1 − SSE/SST and then applies the adjusted formula using your n and p.
Can I compare Adjusted R² across different datasets?
Only with care. Scores are most comparable when the target definition, preprocessing, and evaluation split are the same. Different datasets or time windows can change the baseline variance and distort comparisons.
Does a higher Adjusted R² guarantee better predictions?
No. It summarizes in-sample fit adjusted for complexity. Validate with holdout testing or cross-validation, and consider error-based metrics (MAE, RMSE) and business constraints before deciding.