Diagnose and interpret regression assumptions
Overview
This question evaluates proficiency in regression diagnostics and model selection for count outcomes, including OLS assumption checks, log-transformation back-transformation and coefficient interpretation, heteroskedasticity testing and robust standard errors, multicollinearity (VIF), autocorrelation, and the choice between OLS and Poisson/Negative Binomial GLMs; it falls under Statistics & Math for Data Scientist roles and tests both conceptual understanding and practical application of statistical modeling. Such questions are commonly asked to assess a candidate's ability to validate model assumptions, interpret transformed and categorical effects, and justify appropriate modeling choices based on diagnostic evidence, reflecting the statistical reasoning needed in real-world data science work.
OLS for Signups with Diagnostics and Alternatives
You are given a cleaned dataset with the following columns:
- signups: non-negative integer count target
- spend: numeric
- clicks: integer
- cpc: numeric (cost per click)
- region: categorical
Task: Using Python and statsmodels, draw a 100,000-row sample without replacement and fit an OLS model to predict signups using spend, clicks, cpc, and region dummies. Then:
- If you use log1p(signups) as the dependent variable, show how to back-transform predictions to the original scale and interpret the spend coefficient.
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Check model assumptions using:
- Residuals vs fitted plot
- Q–Q plot
- Breusch–Pagan test for heteroskedasticity
- Durbin–Watson test for autocorrelation
- VIFs to assess multicollinearity
- If heteroskedasticity is present, refit with HC3 robust standard errors and comment on how p-values and confidence intervals change.
- Report adjusted R², the 95% CI for the spend coefficient, and interpret the region dummy coefficients relative to the baseline.
- Explain when a Poisson or Negative Binomial GLM would be preferable for signups and how to test for overdispersion.
Provide minimal code necessary to reproduce these diagnostics.
Solution
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