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Explain multicollinearity and OLS assumptions

CitadelData Scientist · Technical Screen
MediumData ScientistTechnical ScreenStatistics & Math

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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.

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?