Diagnose and fix linear regression assumption breaks
Diagnosing and Remedying OLS Assumption Breaks
You are tasked with fitting a linear regression using Ordinary Least Squares (OLS) on a large cross-sectional dataset (n = 10,000). Address the following questions:
1) Core OLS Assumptions
List the standard OLS assumptions that are essential for obtaining unbiased, efficient, and consistent estimates. For each assumption, you must provide:
- One concrete diagnostic method.
- One concrete remedy.
Examples of diagnostics include residual plots, Variance Inflation Factor (VIF), White/Breusch–Pagan tests, Durbin–Watson statistic, and the Regression Equation Specification Error Test (RESET). Examples of remedies include data transformations, robust or clustered standard errors, regularization techniques, and Generalized Linear Models (GLMs).
2) Scenario: Heteroskedasticity and Multicollinearity
Consider a specific scenario with the following characteristics:
- Dataset size (n) = 10,000
- Heteroskedasticity is present, specifically
Var(ε | X) ∝ x1²(the variance of the error term is proportional to the square of predictorx1). - Severe multicollinearity exists between two predictors, with
corr(x2, x3) = 0.98.
Outline the exact steps you would take to:
- Validate these assumption breaks.
- Refit the models using appropriate fixes.
- Compare the performance and properties of the original and refitted models.
- Describe the expected changes to standard errors, confidence intervals, and hypothesis tests as a result of your interventions.
3) Method Choice
Explain when and why you would consider switching from OLS to alternative regression methods such as Ridge regression, LASSO regression, or a Generalized Linear Model (GLM).
AI interview prep
Core dilemma
The central engineering conflict is balancing the theoretical statistical properties of a foundational model (OLS) with the practical realities of messy, real-world data, ensuring valid inference and robust model performance while maintaining interpretability.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Diagnose and fix linear regression assumption breaks
Diagnosing and Remedying OLS Assumption Breaks
You are tasked with fitting a linear regression using Ordinary Least Squares (OLS) on a large cross-sectional dataset (n = 10,000). Address the following questions:
1) Core OLS Assumptions
List the standard OLS assumptions that are essential for obtaining unbiased, efficient, and consistent estimates. For each assumption, you must provide:
- One concrete diagnostic method.
- One concrete remedy.
Examples of diagnostics include residual plots, Variance Inflation Factor (VIF), White/Breusch–Pagan tests, Durbin–Watson statistic, and the Regression Equation Specification Error Test (RESET). Examples of remedies include data transformations, robust or clustered standard errors, regularization techniques, and Generalized Linear Models (GLMs).
2) Scenario: Heteroskedasticity and Multicollinearity
Consider a specific scenario with the following characteristics:
- Dataset size (n) = 10,000
- Heteroskedasticity is present, specifically
Var(ε | X) ∝ x1²(the variance of the error term is proportional to the square of predictorx1). - Severe multicollinearity exists between two predictors, with
corr(x2, x3) = 0.98.
Outline the exact steps you would take to:
- Validate these assumption breaks.
- Refit the models using appropriate fixes.
- Compare the performance and properties of the original and refitted models.
- Describe the expected changes to standard errors, confidence intervals, and hypothesis tests as a result of your interventions.
3) Method Choice
Explain when and why you would consider switching from OLS to alternative regression methods such as Ridge regression, LASSO regression, or a Generalized Linear Model (GLM).