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Visual Guides/Regression Diagnostics
UNIT 10: REGRESSION FOUNDATIONS

Regression Diagnostics: When the Model Breaks

Every regression model rests on assumptions. Learn to detect violations (non-linearity, heteroscedasticity, non-normal residuals, and influential outliers) using the four core diagnostic plots.

Viewed healthy model
Viewed problematic model
Removed at least one outlier
Checked VIF table
All 4 plots examined (0/4)

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Select Dataset

No violations detected. Residuals are random, variance is constant, and points follow the linear trend.

Diagnostic Plots

Plot 1: Residuals vs Fitted

6.1716.126.136.046.0-0.60-0.300.000.300.60Fitted ValuesResiduals
✓

Random scatter around zero: linearity assumption met.

Plot 2: Normal Q-Q

-2.07-1.030.001.032.07-2.27-1.060.161.372.58Theoretical QuantilesStd. Residuals
✓

Points near the diagonal: residuals approximately normal.

Plot 3: Scale-Location

6.1716.126.136.046.00.000.440.891.331.78Fitted Values√|Std. Residuals|
✓

Horizontal band: constant variance (homoscedasticity) confirmed.

Plot 4: Leverage vs Residuals

0.000.060.120.180.24-2.50-1.250.001.252.50Leverage (h_ii)Std. Residuals+2-2Lev threshold#9
TIP

Click highlighted points to remove them and see how the model changes.

Outlier & Leverage Point Removal

Toggle flagged points to see how they affect the fitted model. Points with |standardized residual| > 2 or leverage > 4/n are flagged.

Leverage: 0.053Cook's D: 0.122Std. Res: 2.02OUTLIER

Multicollinearity Check (VIF)

The Variance Inflation Factor (VIF) measures how much a predictor's variance is inflated due to correlation with other predictors. VIF > 10 suggests a predictor is nearly a linear combination of others.

VariableVIFStatus
Temperature1.04GOOD
Weekend flag1.03GOOD
VIF < 5Good

No meaningful correlation with other predictors.

5 – 10Acceptable

Moderate correlation; monitor but usually acceptable.

VIF > 10Problematic

High collinearity: standard errors are inflated.

Assumption Check Summary

Status for the currently selected dataset.

✓Linearity

Residuals vs Fitted shows no systematic pattern

✓Homoscedasticity

Scale-Location plot shows a horizontal band

✓Normality of Residuals

Q-Q plot points lie near the diagonal

✓No Influential Outliers

No points with high Cook's distance in leverage plot

Diagnostic Quick Reference

Residuals vs Fitted

✓ Look for

Random cloud around y=0

✗ Bad sign

Curved or funnel-shaped pattern

Normal Q-Q

✓ Look for

Points along the diagonal

✗ Bad sign

S-curve or systematic departure

Scale-Location

✓ Look for

Horizontal flat band

✗ Bad sign

Rising or falling trend

Leverage / Cook's D

✓ Look for

No points outside ±2 or high leverage

✗ Bad sign

Points with Cook's D > 1 or h >> 4/n

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