Explain multicollinearity and OLS assumptions
Company: Citadel
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
In linear regression:
1) List and explain the OLS assumptions (linearity, independence/no autocorrelation, homoscedasticity, normality of errors for inference, no perfect multicollinearity, correct specification).
2) Define multicollinearity and describe its effects on coefficient variance, stability, confidence intervals, and p-values while noting that OLS point estimates remain unbiased.
3) Show how to diagnose multicollinearity (correlation matrix, VIF thresholds, condition number, eigenvalue analysis).
4) Propose remedies (collect more data, drop/combine features, center variables and interaction terms, ridge/LASSO/elastic net, PCA/PLS) and discuss their trade-offs.
5) If two predictors are perfectly collinear, what happens to X'X and how do implementations typically handle it?
Quick Answer: Explain multicollinearity and OLS assumptions evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.