Calculator Input
Enter one row per line in this format: actual, fitted, leverage.
Example Data Table
| Actual | Fitted | Leverage | Comment |
|---|---|---|---|
| 12.0 | 11.4 | 0.08 | Low leverage observation |
| 15.0 | 14.1 | 0.11 | Moderate fit error |
| 18.0 | 17.2 | 0.09 | Stable prediction point |
| 21.0 | 20.0 | 0.14 | Higher leverage effect |
| 24.0 | 22.8 | 0.16 | Largest residual here |
Formula Used
The PRESS statistic measures how well a regression model predicts each point when that point is left out during validation.
Residual: ei = yi − ŷi
Leave-one-out residual: ei,LOO = ei / (1 − hii)
PRESS: PRESS = Σ(ei,LOO2) = Σ[(ei / (1 − hii))2]
Predicted R²: 1 − PRESS / SST, where SST = Σ(yi − ȳ)2
Smaller PRESS values usually indicate stronger out-of-sample prediction behavior. Large leverage values can magnify small residuals, so both inputs matter.
How to Use This Calculator
- Prepare your regression output with actual values, fitted values, and diagonal leverage values.
- Enter one observation per line using commas between the three values.
- Click the calculate button to generate PRESS, predicted R², and row-level diagnostics.
- Review the result block above the form for the summary metrics.
- Export the output with the CSV or PDF buttons if needed.
- Compare several datasets or model versions to judge predictive robustness.
Frequently Asked Questions
What does PRESS mean?
PRESS stands for Predicted Residual Error Sum of Squares. It estimates how a regression model performs when each point is predicted from a model fitted without that point.
Why is leverage required?
Leverage adjusts each ordinary residual into a leave-one-out residual. High leverage observations can increase predictive error more than ordinary residuals alone suggest.
Is a lower PRESS always better?
Usually yes, because it indicates smaller prediction errors under leave-one-out validation. Still, compare PRESS values on similar datasets and sample sizes for fair interpretation.
What is predicted R²?
Predicted R² uses PRESS instead of ordinary residual error. It tells you how well the model is expected to predict unseen observations relative to the data mean.
Can leverage equal one?
No. The leave-one-out residual formula divides by 1 minus leverage. A leverage of one would make the denominator zero and the calculation invalid.
Can I paste many rows at once?
Yes. The calculator accepts multiple comma-separated rows in the text area. Each row must contain actual, fitted, and leverage values in that order.
What does PRESS ÷ SSE show?
This ratio compares leave-one-out prediction error against ordinary fitted error. A much larger ratio can suggest weaker generalization or influential observations.
When should I use this metric?
Use it while comparing regression models, checking overfitting risk, or validating model reliability when full external test sets are small or unavailable.