Linear Regression Diagnostics AI Prompt

Diagnose and validate a fitted linear regression model.

Model: {{model_description}} (outcome, predictors, n)
Fitted model output: {{model_output}}

1. The four core OLS assumptions (LINE):

   L — Linearity:
   - Residuals vs fitted values plot: should show random scatter around zero
   - Pattern in residuals = non-linearity → add polynomial terms, interaction terms, or transform predictors
   - Partial regression plots (added variable plots): check linearity of each predictor separately

   I — Independence of errors:
   - By design: is this a cross-sectional dataset (no natural ordering)?
   - For time series or clustered data: Durbin-Watson test for serial autocorrelation (target: DW near 2)
   - If observations are clustered: use clustered standard errors or mixed effects model

   N — Normality of residuals:
   - Q-Q plot of standardized residuals: points should fall on the diagonal
   - Shapiro-Wilk test for normality (reliable for n < 2000)
   - Note: normality of residuals is the LEAST critical assumption for large samples (CLT)
   - Skewed residuals suggest: log-transform the outcome, or consider a GLM with appropriate family

   E — Equal variance (homoscedasticity):
   - Scale-location plot (sqrt(|standardized residuals|) vs fitted): should be flat
   - Breusch-Pagan test: p < 0.05 indicates heteroscedasticity
   - Fix: use heteroscedasticity-consistent (HC) standard errors (HC3 is robust in small samples)
   - Or: weighted least squares if variance structure is known

2. Influential observations:
   - Leverage (h_ii): measures how far an observation's predictor values are from the mean
     High leverage: h_ii > 2(k+1)/n
   - Cook's Distance: measures overall influence of each observation on all fitted values
     Influential if D_i > 4/n (rule of thumb)
   - DFFITS and DFBETAS: influence on fitted values and specific coefficients
   - Action: investigate (not automatically remove) flagged observations

3. Multicollinearity:
   - Variance Inflation Factor (VIF) per predictor
   - VIF > 5: concerning, VIF > 10: severe multicollinearity
   - Fix: remove redundant predictors, combine correlated predictors via PCA, or use ridge regression

4. Model fit assessment:
   - R-squared: proportion of variance explained (note: always increases with more predictors)
   - Adjusted R-squared: penalizes for adding unhelpful predictors
   - AIC/BIC: for model comparison (lower is better)
   - RMSE on a holdout set: most honest measure of predictive accuracy

Return: assumption check results per criterion, influential observation list, multicollinearity report, and model fit summary.