Flight Delay Modeling: Binary Target, Features, and Diagnostics

You are modeling the probability that a flight arrives with a delay greater than 15 minutes (binary target: 1 if delay > 15 min, else 0). The current feature set includes:

• day_of_week (encoded as integers 1–7),
• flight_seats (contains negative values due to ETL errors),
• several correlated operational variables (e.g., turnaround_time, taxi_out, gate_occupancy).

The team mistakenly fit an OLS regression to this binary target.

Tasks

1. Target/model choice
   • Explain rigorously why OLS is inappropriate for a binary target and select a correct alternative.
   • For your choice, specify the link function, assumptions, and how you’d check them.
2. Encoding for day_of_week
   • 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 and bias.
4. Multicollinearity
   • Define the Variance Inflation Factor (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 under class imbalance.
   • Describe a time-based cross-validation scheme to avoid temporal leakage.
   • Explain how you would calibrate predicted probabilities.