The 60-second answer
State the model y = Xβ + ε and distinguish prediction assumptions from assumptions needed for classical statistical inference. Least squares minimizes squared residuals; with full-rank X the normal-equation solution is (XᵀX)⁻¹Xᵀy, though stable solvers avoid explicit inversion.
Build the answer in this order
State the model y = Xβ + ε and distinguish prediction assumptions from assumptions needed for classical statistical inference.
Least squares minimizes squared residuals; with full-rank X the normal-equation solution is (XᵀX)⁻¹Xᵀy, though stable solvers avoid explicit inversion.
Check nonlinearity, heteroscedasticity, correlated errors, influential points, and multicollinearity.
Use MAE/RMSE/R² according to the product loss and validate on held-out data.
A useful interview mental model
This is the shape of a strong answer—not a script to memorize.
Senior-level signal
- Discuss regularization or robust regression when assumptions fail rather than treating diagnostics as a pass/fail checklist.
- In high dimensions, solver choice and conditioning can dominate numerical behavior.
What the interviewer is really testing
Likely follow-up questions
Common weak-answer patterns
- Reciting a definition without mechanism or assumptions.
- Claiming one technique is always better without a data regime.
- Stopping before failure modes, validation, or deployment implications.