Marketing Analytics Case: Funnel, Attribution, Budget Optimization, and Incrementality

You are given a daily-by-channel dataset with the following columns:

• date
• channel
• spend
• visits
• form_starts
• form_completes
• loan_funded
• revenue

Assume each row aggregates that day’s outcomes for a channel. Revenue is recognized at funding (no refunds/chargebacks) and is net of promotions but gross of media cost unless otherwise stated.

Tasks:

1. Funnel and CAC
   • Build a funnel with stage-to-stage conversion rates: visits → form_starts → form_completes → loan_funded.
   • Compute cost-per-stage ("CAC at each milestone"): cost per visit, per start, per complete, and per funded loan.
2. ROAS and Payback under Two Attribution Models
   • Compute ROAS and payback using: a) Last-click attribution b) 7-day first-touch attribution
   • Describe how you would re-attribute using only raw click/impression logs if the provided revenue is not already attributed as required.
3. Next-Month Budget Shifts via Response Curves
   • Fit a simple channel response curve (e.g., logarithmic or Hill function) to link spend to outcomes and estimate marginal ROAS.
   • Recommend how to shift next-month budget by channel based on marginal ROAS.
4. Incrementality Test Design
   • Propose a geo- or time-based holdout experiment to validate recommendations. Specify unit of randomization, sample size approach, contamination risks, success criteria, and analysis plan.
5. Diagnose Likely Non-Incremental Channels
   • Flag channels that look effective but may be non-incremental (e.g., retargeting, brand spillovers).
   • Propose diagnostics to detect non-incrementality.

Provide concrete formulas, any assumptions you must make, and how you would communicate the recommendation with risk bounds.