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 Ordinary Least Squares (OLS) model to predict signups using spend, clicks, cpc, and region dummy variables.

Then:

1. If you use log1p(signups) as the dependent variable, show how to back-transform predictions to the original scale and interpret the spend coefficient.
2. Check model assumptions using:
   • Residuals vs. fitted plot
   • Q–Q plot
   • Breusch–Pagan test for heteroskedasticity
   • Durbin–Watson test for autocorrelation
   • Variance Inflation Factors (VIFs) to assess multicollinearity
3. If heteroskedasticity is present, refit the model with HC3 robust standard errors and comment on how p-values and confidence intervals change.
4. Report the adjusted R², the 95% confidence interval for the spend coefficient, and interpret the region dummy coefficients relative to the baseline.
5. Explain when a Poisson or Negative Binomial Generalized Linear Model (GLM) would be preferable for signups and how to test for overdispersion.

Provide the minimal code necessary to reproduce these diagnostics.