Explain multicollinearity and OLS assumptions
Overview
This question evaluates understanding of ordinary least squares (OLS) assumptions and multicollinearity, covering estimator properties, diagnostic metrics, and implications for the design matrix as core competencies in statistical modeling and numerical linear algebra within the Statistics & Math domain for Data Scientist roles.
Citadel
Jul 27, 2025, 12:00 AM
Data Scientist
Technical Screen
Statistics & Math
0
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Linear Regression Technical Screen: OLS Assumptions and Multicollinearity
Context: You are asked to summarize core OLS assumptions, explain multicollinearity, and discuss diagnostics, remedies, and implications for the design matrix.
Tasks
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List and explain the standard OLS assumptions:
- Linearity in parameters
- Independence / no autocorrelation
- Homoscedasticity
- Normality of errors (for exact small-sample inference)
- No perfect multicollinearity
- Correct specification (including exogeneity)
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Define multicollinearity and describe its effects on:
- Coefficient variance and stability
- Confidence intervals and p-values
- Note that OLS point estimates remain unbiased under exogeneity
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Show how to diagnose multicollinearity:
- Correlation matrix
- Variance Inflation Factors (VIF) and common thresholds
- Condition number
- Eigenvalue-based analysis
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Propose remedies and discuss trade-offs:
- Collect more data
- Drop/combine features
- Center variables and interaction terms
- Regularization (ridge/LASSO/elastic net)
- Dimension reduction (PCA/PLS)
- If two predictors are perfectly collinear, what happens to X'X and how do implementations typically handle it?
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