Regression Residual Plot
Chart overview
The residuals-vs-fitted plot is the primary diagnostic for linear regression, revealing patterns that indicate heteroscedasticity, nonlinearity, or influential outliers that violate ordinary least squares assumptions.
Key points
- Any systematic trend or funnel shape in the residuals signals that the model is misspecified or that variance stabilization is needed.
- It is a required figure in applied statistics, econometrics, and ecological modeling papers.
Example Visualization
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"Create a regression residual plot from my fitted values and residuals. Scatter residuals against fitted values, add a horizontal dashed reference line at zero, overlay a LOESS smoothed trend line to reveal patterns, color-code or label outlier points beyond 3 standard deviations, and add a horizontal band showing plus or minus 1 and 2 standard deviations."
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Python Code Example
Console Output
Figure saved: plotivy-regression-residual-plot.png
Common Use Cases
- 1Diagnosing heteroscedasticity in a linear model of environmental contaminant concentrations
- 2Checking for nonlinear trends missed by a linear climate regression model
- 3Identifying influential outliers in a pharmacokinetic dose-response regression
- 4Validating that generalized linear model residuals show no systematic pattern
Pro Tips
Add a LOESS smoother to quantify systematic trends not visible from the scatter alone
Label the 5 most extreme residual points by observation ID for follow-up investigation
Plot standardized residuals on the y-axis so plus or minus 2 thresholds correspond to approximate 95% bands
Use a scale-location plot (sqrt of absolute residuals vs fitted) as a companion to detect heteroscedasticity
Scientific Chart Selection Cheat Sheet
Not sure whether to use a Violin Plot, Box Plot, or Ridge Plot? Download our single-page reference mapping the most-used scientific chart types, exactly when to use them, and the core Matplotlib/Seaborn functions.