Residual Calculator
Enter observed values alongside predicted values to compute residuals, mean residual, standard deviation, and sum of squared residuals.
| Observed | Predicted | Residual (obs − pred) |
|---|---|---|
| 10 | 9.5 | 0.5000 |
| 14 | 13.3 | 0.7000 |
| 18 | 17.8 | 0.2000 |
| 21 | 20.2 | 0.8000 |
| 25 | 24.7 | 0.3000 |
Count: 5
Mean residual: 0.5000
Residual standard deviation: 0.2550
Sum of squared residuals: 1.5100
How to Use This Calculator
- Enter observed outcomes and corresponding predicted values from your model.
- Review individual residuals to identify large deviations or patterns.
- Use the summary statistics to evaluate overall model accuracy.
- Consider plotting residuals (outside this tool) for diagnostic purposes.
Formula
Residual ri = observedi − predictedi
Mean residual = Σri / n
Residual standard deviation = √[Σ(ri − r̄)² / (n − 1)]
Sum of squared residuals (SSR) = Σri²
Full Description
Residuals measure the discrepancy between observed and predicted values. They are central to regression diagnostics, model selection, and goodness-of-fit assessments.
Ideally, residuals should be randomly scattered around zero. Systematic patterns suggest model misspecification, heteroscedasticity, or outliers that warrant further investigation.
Frequently Asked Questions
What does a residual of zero mean?
The model predicted the observation exactly.
Why examine residual standard deviation?
It summarizes typical prediction errors and approximates the model’s root mean squared error (RMSE).
Do residuals indicate bias?
A non-zero mean residual suggests systematic over- or under-prediction, indicating bias.
Should residuals be normal?
Normality is desirable for inference in linear regression but not strictly required for prediction accuracy.