Interpret regression metrics and assumptions
Overview
This question evaluates a candidate's mastery of multiple linear regression diagnostics and interpretation, covering standardized coefficient interpretation and significance, R²/adjusted R² and out‑of‑fold RMSE comparisons, multicollinearity detection and its effect on coefficients and SEs, heteroskedasticity diagnostics and robust remedies, and implications of intercept omission and partial standardization. Commonly asked in data scientist interviews within the Statistics & Math domain because it probes both conceptual understanding of statistical inference and practical application of model diagnostics and adjustments for reliable prediction and inference.
A multiple linear regression is fit to predict arrival delay with standardized numeric predictors and one‑hot categorical variables. Without seeing the dataset, walk through interpretation and diagnostics: 1) Precisely interpret a coefficient (e.g., tailwind = −0.8, p=0.07) under standardization and discuss statistical vs practical significance. 2) Explain R² vs adjusted R² vs out‑of‑fold RMSE; when can R² increase while adjusted R² decreases, and what decision would you make? 3) Detect multicollinearity (compute/interpret VIF; when to remove vs regularize); explain how coefficients and their standard errors are affected. 4) Diagnose heteroskedasticity from residual plots; propose tests (e.g., Breusch–Pagan) and robust remedies (HC standard errors, transforms). 5) Explain consequences of omitting the intercept or standardizing only some features. 6) Given residuals showing curvature and non‑normal heavy tails, propose modeling changes and quantify expected effect on inference and prediction intervals.