Regression Diagnostics Lab

Regression analysis

Break the assumptions on purpose, spot the damage with diagnostics, then fix it.

Diagnosis

Diagnostic plots

Residuals vs fitted

Look for a funnel (unequal spread) or a curve. Amber band = ±2 SD.

Residuals in order

Long runs above or below zero mean neighbouring errors are linked.

Autocorrelation (ACF)

Bars beyond the dashed lines are significant lags.

Normal Q–Q plot

Points should hug the line. Curved ends mean heavy tails or skew.

Cook’s distance

Red bars rise above 4/n: removing them would change the fit.

Multicollinearity

VIF above 5 is a warning, above 10 is a problem.

Regression results

Fixes

Switch these on and watch the badges, plots and table respond.

Predictors in the model X1 X2 X3 Add a curvature term(X1 − mean)², helps with non-linearity Remedies Log-transform yTames growing spread and skew Robust standard errors (HC3)Valid even when the spread is uneven AR(1) correction (Cochrane–Orcutt)Removes serial correlation from the errors Drop influential pointsRemoves points with Cook’s D above 4/n

Can you trust the p-values? (300 simulations)

Draws 300 fresh datasets with these same problems, fits your current model to each, and checks how often the 95% interval captures the true coefficient. Honest inference gives about 95%.