Diagnose and fix a flight-delay modeling setup

A team built a linear regression model for flight delays using predictors such as day_of_week (coded 1–7), flight_seats (which contains negative values due to ETL errors), and several correlated operational variables. The outcome was a binary indicator of delay > 15 minutes, but they still estimated the model with OLS.

Tasks:

1. Target/model choice: Give a rigorous explanation of why OLS is not appropriate for this outcome and choose a suitable alternative. For the model you select, specify the link function, its assumptions, and how you would check them.
2. Encoding: Show why treating day_of_week as numeric can bias the estimates; propose a better encoding and a quick statistical test to assess day-of-week effects.
3. Data quality: Recommend a principled treatment for negative seat counts and missing values; quantify the impact of different strategies on variance and bias.
4. Multicollinearity: Define VIF and derive $VIF = \frac{1}{1 - R_j^2}$. If the VIF for turnaround_time is 12, interpret this value and list three remedies (and their trade-offs), including regularization. Explain how standardization affects coefficient interpretation and multicollinearity diagnostics.
5. Evaluation: Choose metrics aligned with the binary target (with class imbalance). Describe a time-based cross-validation scheme to avoid temporal leakage and how you would calibrate predicted probabilities.

Overview: This question evaluates proficiency in statistical modeling for binary outcomes, including concepts such as appropriate model choice and link functions, categorical encoding, ETL-driven data quality issues, multicollinearity diagnostics (e.g.