Enter prediction data
Use the row editor, paste lists, or upload a CSV file. Blank rows are ignored.
Formula used
Residual: ei = yi − ŷi
MAE: Σ|ei| ÷ n
MSE: Σei2 ÷ n
RMSE: √MSE
Residual standard error: √[SSE ÷ (n − p)]
Studentized residual: ei ÷ [RSE√(1 − hii)]
A positive residual means the model predicted too low. A negative residual means the model predicted too high. A zero residual represents an exact prediction match.
How to use this calculator
- Select standard, weighted, or diagnostic analysis.
- Enter actual and predicted values for each observation.
- Add optional weights, leverage values, and labels.
- Choose outlier, tolerance, precision, and sorting settings.
- Press calculate to view metrics, tables, and charts.
- Copy results or export them as CSV or PDF.
Example data
| Label | Actual | Predicted | Weight | Leverage |
|---|---|---|---|---|
| Sample A | 12.0 | 11.4 | 1.0 | 0.10 |
| Sample B | 18.5 | 19.2 | 1.3 | 0.12 |
| Sample C | 25.0 | 23.8 | 0.8 | 0.08 |
| Sample D | 32.0 | 35.5 | 1.5 | 0.18 |
| Sample E | 41.0 | 40.2 | 1.0 | 0.11 |
Residual interpretation guide
| Pattern | Possible meaning | Suggested check |
|---|---|---|
| Residuals centred near zero | Limited overall prediction bias | Inspect spread and outliers |
| Mostly positive residuals | Systematic underprediction | Review intercept and calibration |
| Mostly negative residuals | Systematic overprediction | Review target scaling |
| Funnel-shaped spread | Possible heteroscedasticity | Transform targets or model variance |
| Curved residual pattern | Possible missing nonlinearity | Add features or nonlinear terms |
| Large isolated residual | Potential outlier or data issue | Validate the observation carefully |
Frequently asked questions
What is a residual error?
A residual is actual value minus predicted value. It measures one prediction error. Its sign shows prediction direction.
Why can residuals be positive or negative?
Positive values indicate model underprediction. Negative values indicate model overprediction. Zero means both values match.
What is the difference between residual and absolute residual?
A residual preserves the error direction. An absolute residual removes the sign. Absolute values support MAE calculations.
How does RMSE differ from MAE?
RMSE squares errors before averaging them. Large errors receive greater influence. MAE treats errors more evenly.
When should I use weighted residuals?
Use weights when observations have different importance. Larger weights increase an observation’s influence. Weights must remain positive.
What is a standardized residual?
It divides each residual by residual spread. This creates a scale-free comparison. Large magnitudes may identify unusual predictions.
What is a studentized residual?
It adjusts residuals using leverage and model error. Regression diagnostics often use it. Leverage values must stay below one.
Can percentage residual be calculated when actual equals zero?
No reliable percentage exists with a zero denominator. The calculator displays unavailable instead. Other error measures remain valid.
Does a low mean residual guarantee a good model?
No, positive and negative errors may cancel. Review MAE, RMSE, charts, and outliers. Multiple diagnostics provide stronger evidence.