Diagnostic conclusion
Scale-Location plot
The vertical axis shows the selected square-root absolute residual transformation.
Model diagnostics
| Rank | Model | N | Mean residual | MAE | RMSE | Residual SD | Fitted range | Scale range | Trend equation | Trend R² | Spread correlation | Spread CV | Variance ratio | Flagged | Assessment |
|---|
Heteroscedasticity tests
These tests support the visual diagnosis. They do not replace model-specific judgment.
| Model | Test | Statistic | p-value | Decision |
|---|
Binned spread summary
Compare variance and transformed spread across fitted-value intervals.
| Model | Bin | Range | Count | Mean transformed spread | Residual variance |
|---|
Calculated observations
Search, sort, inspect warnings, and export every computed record.
| # | Model | Label | Group | Dataset | Actual | Predicted | Raw residual | Standardized | Selected residual | √|residual| | Leverage | Cook's D | Status |
|---|
Interpretation and suggested actions
Data and calculation options
Use actual and predicted values, or supply fitted values and residuals directly. Multiple model names create comparison traces.
Formula used
Raw residual: eᵢ = yᵢ − ŷᵢ
Standardized residual: rᵢ = (eᵢ − mean(e)) / sₑ
Scale-Location response: zᵢ = √|rᵢ|
Internally studentized residual: tᵢ = eᵢ / (sₑ√(1 − hᵢ))
A stable residual spread creates a nearly horizontal smoothing line. A widening or narrowing pattern suggests nonconstant error variance. Formal tests should be interpreted with the chart and model assumptions.
How to use
- Select the input mode and residual transformation.
- Enter rows manually, import CSV, or load sample data.
- Add model, group, leverage, weight, or Cook’s distance values when available.
- Choose smoothing, warning, binning, and chart options.
- Calculate, inspect the pattern, review tests, and export results.
CSV column guide
Headers are case-insensitive. Common names are mapped automatically.
model,label,group,dataset,actual,predicted,residual,customResidual,weight,leverage,cooks Linear A,Row 1,North,Train,12.4,11.9,,1.1,1,0.08,0.02
Example data
| Model | Observed | Predicted | Interpretation |
|---|---|---|---|
| Stable model | 20.1 | 20.5 | Small residual at a moderate fitted value. |
| Stable model | 35.2 | 34.8 | Similar spread at a larger fitted value. |
| Funnel model | 62.0 | 55.0 | Larger residual at a high fitted value. |
Frequently asked questions
What does a Scale-Location plot measure?
It shows how residual spread changes across fitted values. The vertical axis usually uses square-root absolute standardized residuals.
What pattern indicates constant variance?
Look for points with similar vertical spread throughout the horizontal range. The smoothing line should remain approximately flat.
What does a funnel shape mean?
A widening funnel suggests variance increases with fitted values. A narrowing funnel suggests variance decreases.
Should raw or standardized residuals be used?
Standardized or studentized residuals improve comparability. Raw residuals remain useful when the outcome scale matters directly.
Why include leverage values?
Leverage adjusts studentized residuals for unusual predictor locations. Accurate leverage requires information from the fitted regression model.
What does the Breusch–Pagan test add?
It tests whether squared residuals relate to fitted values. A small p-value supports evidence of nonconstant variance.
Can several models be compared?
Yes. Assign model names to rows and the calculator creates separate traces, summaries, tests, and rankings.
How should outliers be handled?
Investigate data quality, model specification, leverage, and influence. Do not remove observations solely because they appear unusual.
What can correct heteroscedasticity?
Consider target transformations, weighted least squares, robust standard errors, nonlinear terms, or a model with a suitable variance structure.