Diagnose and fix a flight-delay modeling setup

A team modeled flight delays with linear regression using features including day_of_week (encoded as 1–7), flight_seats (contains negatives due to ETL errors), and several correlated operational variables. The target they used was a binary indicator of delay>15 minutes, but they still fit OLS. Tasks:

1. Target/model choice: Explain rigorously why OLS is inappropriate here and select a correct alternative. For your choice, specify the link function, assumptions, and how you’d check them.
2. Encoding: Show why treating day_of_week as numeric can bias estimates; propose an appropriate encoding and a quick statistical test to assess day effects.
3. Data quality: Propose a principled treatment for negative seat counts and missing values; quantify the impact of different strategies on variance/bias.
4. Multicollinearity: Define VIF and derive VIF = 1/(1 − R_j^2). If 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.