Residual Distribution Plot
📉 What is this?
The model makes predictions, but predictions are always wrong. How much each prediction is "off" is the residual:
Residual = Actual value − Predicted valueThe residual distribution plot draws all these "errors" as a histogram, overlaid with a normal distribution fit curve, to judge whether the model's error is "healthy".
💡 If the Prediction Scatter Plot looks at "how accurate the prediction is", then the residual distribution plot looks at "whether the errors follow a pattern".
🧐 How to read?
A healthy model's residuals should satisfy three conditions:
| Feature | Healthy behavior | Abnormal behavior and meaning |
|---|---|---|
| Center position | Symmetrically distributed around 0 | Overall offset → the model has a systematic bias (e.g. an important variable was missed) |
| Shape | Close to a normal distribution (bell-shaped) | Bimodal → the data may mix two different populations (e.g. two operating conditions) |
| Width | The narrower the better | Very wide → large prediction error, insufficient model explanatory power |
The chart also displays key statistics:
| Indicator | Meaning |
|---|---|
| R² | Goodness of fit |
| RMSE | Root mean square error, reflecting the actual size of the error |
| Residual mean | Whether it is close to 0, to judge whether there is systematic bias |
| Residual standard deviation | The dispersion of the error |
🛠️ How to use?
Configuration items
| Configuration item | Description |
|---|---|
| Prediction type | Choose the prediction category |
| Target variable | Choose the Y variable to analyze |
Click Fit to generate.
Diagnostic checklist
- [ ] Is the histogram centered on 0? An offset means the model systematically underestimates/overestimates
- [ ] Is it single-peaked and bell-shaped? Bimodality is a warning sign of mixed data
- [ ] Does the fit curve match the histogram? Deviation means the error does not follow a normal distribution, and the premise of ordinary statistical tests may not hold
- [ ] Are RMSE and residual standard deviation within the error range acceptable to the business
- [ ] Is there a long tail? The samples in the long tail are the worst-predicted ones, and deserve separate investigation
💡 What to do when you find a long tail: use the Data Table to find the samples with the largest absolute residuals and see whether they share common features (same batch? same time period?). This often uncovers real process problems.
🎯 Division of labor with other prediction-related charts
| Chart | What to look at | Question it answers |
|---|---|---|
| Prediction Scatter Plot | Predicted vs actual | How accurate overall? Are the points close to the diagonal? |
| Prediction Line Chart | Continuous comparison of predicted and actual values | Which time period did the prediction collapse in? |
| Residual Distribution Plot | The distribution shape of the residuals | Do the errors follow a pattern? Is there systematic bias? |
⚠️ Notes
- Only regression models are supported (PLS / OPLS)——classification models have no concept of continuous residuals
- A residual plot being normal does not mean the model is necessarily good: it must also be judged together with Q², R² and business plausibility
- When the amount of data is too small the histogram shape is unstable; it is recommended to have no fewer than 30 samples before reading the shape