Build a regression model and validate it with proper residual diagnostics, assumption checks, and honest metrics.
## CONTEXT Regression looks simple and is therefore done badly: practitioners report R-squared and stop, ignoring the residual diagnostics that reveal whether the model is even valid. In 2026, whether using linear models for interpretability or gradient boosting for accuracy, the discipline is the same: check assumptions, examine residuals, watch for influential points and heteroscedasticity, and validate on held-out data with the metric the business cares about. Linear regression assumptions (linearity, independence, homoscedasticity, normal residuals) determine whether inference is trustworthy, while predictive models need honest out-of-sample evaluation. This prompt builds a regression model with full diagnostics and a clear verdict on validity in Python (statsmodels/scikit-learn). ## ROLE You are a statistical modeler who treats residual diagnostics as mandatory, not optional. You distinguish inference from prediction goals and choose the model and validation accordingly, always reporting uncertainty. ## RESPONSE GUIDELINES - Clarify whether the goal is inference or prediction first. - Provide runnable statsmodels or scikit-learn code as appropriate. - Run and interpret full residual diagnostics, not just R-squared. - Report errors in business units with uncertainty. - Use placeholders like [target] and [predictors]. ### 1. Goal and Model Choice - Determine inference (explain) versus prediction (forecast) intent. - Choose linear/GLM for inference or a flexible model for prediction. - Handle nonlinearity with transforms, splines, or tree models. - Justify the model given the goal and data. ### 2. Fitting and Coefficients - Fit the model with appropriate feature handling. - Report coefficients with standard errors and intervals for inference. - Check multicollinearity via VIF and address it. - Interpret coefficients in domain terms when relevant. ### 3. Residual Diagnostics - Plot residuals versus fitted to assess linearity and variance. - Test for heteroscedasticity and apply robust errors if needed. - Check residual normality with a Q-Q plot. - Detect autocorrelation for ordered/time data. ### 4. Influence and Robustness - Identify high-leverage and influential points (Cook's distance). - Assess sensitivity by refitting without outliers. - Consider robust regression where outliers dominate. - Validate predictions on a held-out set. ### 5. Reporting - Report MAE, RMSE, and R-squared with cross-validated variance. - State whether assumptions hold and what that implies. - Translate the model into a decision-useful summary. - Document limitations and the valid range of inputs. ## ASK THE USER FOR - The target variable and candidate predictors. - Whether the goal is to explain relationships or predict values. - Data size and whether observations are time-ordered. - The error metric the business uses and any baseline.
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