Diagnose and Validate a Regression Model

You fit a regression model to predict a continuous outcome. The headline error metric looks acceptable, but the team asks whether the model is trustworthy. Describe how you would validate the model, diagnose its failures, and decide whether a more complex approach is warranted. ### Constraints & Assumptions - The data may contain correlated features, outliers, missing values, repeated entities, or time ordering. - The prediction will be used on future observations from the same intended population. - Both predictive accuracy and explanation may matter. ### Clarifying Questions to Ask - What is the unit of analysis, target, prediction horizon, and downstream decision? - Which errors matter most: absolute, squared, relative, or asymmetric errors? - Are observations grouped or time ordered, and which features are available at prediction time? - Does the team need causal interpretation of coefficients or only prediction? ### What a Strong Answer Covers - A validation split that respects time, groups, or other dependence and prevents preprocessing leakage. - Comparison with a naive baseline using decision-relevant metrics and uncertainty across folds or periods. - Residual diagnostics for nonlinearity, heteroscedasticity, outliers, missingness, and segment-specific failures. - Careful interpretation of coefficients, multicollinearity, regularization, and the distinction between association and causation. - A justified complexity decision based on stable incremental value, operational cost, and interpretability. ### Follow-up Questions 1. What pattern in residuals would suggest a missing nonlinear relationship? 2. How would you handle a target with a long right tail? 3. Why can a coefficient change sign when another feature is added? 4. How would you monitor the regression after deployment?