Analyze omitted-variable bias in regression
Overview
This question evaluates understanding of omitted-variable bias and heteroscedasticity in linear regression, testing competency in how omitting a relevant covariate and having non-constant error variance impact OLS point estimation and inference.
Amazon
Oct 13, 2025, 9:49 PM
Data Scientist
Onsite
Statistics & Math
0
0
Omitted-Variable Bias, Heteroscedasticity, and Remedies
Setup
- True data-generating process (DGP): Y = β0 + β1·Temp + β2·Occupancy + ε
- Assumptions: E[ε | Temp, Occupancy] = 0 and Var(ε | Temp, Occupancy) = σ²(Temp) (heteroscedasticity depending on Temp).
- Mistake: You fit OLS on Y ~ Temp only (Occupancy omitted).
Tasks
- Derive the expected (asymptotic) bias of the OLS estimator of β1 when regressing Y on Temp only. Express it in terms of Cov(Temp, Occupancy) and Var(Temp).
- State the sign of the bias when hotter days are more occupied.
- Explain how weighted least squares (WLS) and heteroscedasticity-robust standard errors (robust SEs) affect estimation vs inference in this setting.
- Design a test to detect remaining heteroscedasticity: name the test and its null hypothesis.
- Propose a practical heteroscedasticity diagnostic you would include in a production training report.
Solution
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