About Residual Diagnostics
Residual diagnostics help assess whether the model assumptions are satisfied.
These plots reveal patterns in residuals that may indicate model specification issues,
heteroskedasticity, non-normality, or influential observations.
Available Diagnostic Plots
- Q-Q Plot: Tests normality assumption of residuals
- Residuals vs Fitted: Checks for non-linearity and heteroskedasticity
- Scale-Location: Detects heteroskedasticity (non-constant variance)
- Residuals vs Leverage: Identifies influential observations
- Residual Time Series: Checks for autocorrelation patterns
- Residual Distribution: Shows distribution shape with KDE overlay
- Residual ACF: Autocorrelation function plot (if available)
{% if model_info %}
Model Information
{% if model_info.estimator %}
| Estimator |
{{ model_info.estimator }} |
{% endif %}
{% if model_info.formula %}
| Formula |
{{ model_info.formula }} |
{% endif %}
{% if model_info.nobs %}
| Observations |
{{ model_info.nobs }} |
{% endif %}
{% if model_info.n_entities %}
| Entities |
{{ model_info.n_entities }} |
{% endif %}
{% if model_info.n_periods %}
| Time Periods |
{{ model_info.n_periods }} |
{% endif %}
{% if model_info.r_squared %}
| R-squared |
{{ "%.4f"|format(model_info.r_squared) }} |
{% endif %}
{% endif %}
{% if residual_charts %}
Residual Diagnostic Plots
Interactive diagnostic plots for comprehensive residual analysis.
Hover over data points for detailed information, zoom to focus on specific areas.
{% if residual_charts.qq_plot %}
Q-Q Plot (Quantile-Quantile)
Tests normality assumption. Points should fall along the diagonal line if residuals are normally distributed.
Deviations indicate departures from normality.
{{ residual_charts.qq_plot|safe }}
{% endif %}
{% if residual_charts.residual_vs_fitted %}
Residuals vs Fitted Values
Checks for non-linearity and heteroskedasticity. Should show random scatter around zero
with no clear patterns. LOWESS curve helps identify systematic deviations.
{{ residual_charts.residual_vs_fitted|safe }}
{% endif %}
{% if residual_charts.scale_location %}
Scale-Location Plot
Detects heteroskedasticity (non-constant variance). Horizontal line with equally spread points
indicates homoskedasticity. Upward/downward trends suggest heteroskedasticity.
{{ residual_charts.scale_location|safe }}
{% endif %}
{% if residual_charts.residual_vs_leverage %}
Residuals vs Leverage
Identifies influential observations. Points beyond Cook's distance contours (dashed lines)
are potentially influential and may affect model fit significantly.
{{ residual_charts.residual_vs_leverage|safe }}
{% endif %}
{% if residual_charts.residual_timeseries %}
Residual Time Series
Shows residuals over time to detect autocorrelation patterns. Should appear random
with no systematic trends or cycles.
{{ residual_charts.residual_timeseries|safe }}
{% endif %}
{% if residual_charts.residual_distribution %}
Residual Distribution
Histogram with kernel density estimate (KDE) overlay. Should approximate normal distribution
(bell curve). Deviations indicate non-normality.
{{ residual_charts.residual_distribution|safe }}
{% endif %}
{% if residual_charts.residual_acf %}
Autocorrelation Function (ACF)
Shows correlation between residuals at different lags. Bars should fall within confidence bands
(blue shaded area) if no significant autocorrelation exists.
{{ residual_charts.residual_acf|safe }}
{% endif %}
Chart Interactions
- Hover: Move your mouse over data points to see detailed information
- Zoom: Click and drag to zoom into a region, or use the zoom buttons
- Pan: After zooming, click and drag to pan around
- Reset: Click the "Reset axes" button to restore the original view
- Export: Use the camera icon to download the chart as a PNG image
{% else %}
No diagnostic plots available.
Generate residual diagnostics using the visualization system.
{% endif %}
Interpretation Guide
Q-Q Plot
What to look for: Points should fall along the diagonal reference line.
- ✓ Good: Points closely follow the line
- ✗ Heavy tails: Points curve away at extremes (non-normal)
- ✗ Light tails: S-shaped pattern (non-normal)
- ✗ Skewness: Points systematically above/below line
Residuals vs Fitted Values
What to look for: Random scatter around horizontal zero line.
- ✓ Good: No patterns, random scatter
- ✗ Non-linearity: Curved LOWESS line (add polynomial terms)
- ✗ Heteroskedasticity: Funnel shape (variance increases/decreases)
- ✗ Outliers: Points far from zero line
Scale-Location Plot
What to look for: Horizontal line with equal vertical spread.
- ✓ Good: Horizontal LOWESS line, constant spread
- ✗ Heteroskedasticity: Upward/downward trending line
- ✗ Increasing variance: Spread increases with fitted values
Remedies: Use robust standard errors, WLS, or log transformation.
Residuals vs Leverage
What to look for: Points inside Cook's distance contours.
- ✓ Good: All points inside dashed contours
- ⚠ High leverage: Points far right (influential on fitted values)
- ✗ Influential: Points outside Cook's distance (high leverage + large residual)
Actions: Investigate influential points - data errors? Outliers? Structural breaks?
Residual Time Series
What to look for: Random fluctuation around zero.
- ✓ Good: No visible patterns or trends
- ✗ Autocorrelation: Clusters of positive/negative residuals
- ✗ Trends: Systematic upward/downward movement
- ✗ Cycles: Repeated patterns over time
Remedies: Add lagged dependent variable, use clustered SE, or AR errors.
Residual Distribution
What to look for: Bell-shaped (normal) distribution.
- ✓ Good: Symmetric, bell-shaped histogram
- ✗ Skewness: Long tail on one side
- ✗ Kurtosis: Too peaked or too flat
- ✗ Bimodal: Two peaks (mixture of populations?)
General Recommendations
- Multiple issues: Prioritize fixing the most severe problems first
- Outliers: Investigate before removing - may contain important information
- Heteroskedasticity: Robust standard errors are often sufficient
- Non-normality: Less critical for large samples (CLT applies)
- Autocorrelation: Critical for panel data - use clustered/HAC errors