Diagnose profit drop via mix decomposition

Q: Diagnose profit drop via mix decomposition

The question evaluates a data scientist's competency in profit decomposition, attribution, experiment design, and diagnostic dashboarding within the Analytics & Experimentation domain.

Q: How do I approach Analytics & Experimentation interview questions?

Analytics & Experimentation questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master analytics & experimentation interviews.

Q: What difficulty level is this interview question?

This is a hard difficulty Analytics & Experimentation question, commonly asked during Technical Screen rounds at Capital One.

Q: What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Capital One during technical interviews.

Question

Profit Decomposition, Attribution, Experiment Design, and Diagnostics

Context and Assumptions (to make the task self-contained)

We analyze why daily profit fell on a “mixed” coupon day even though the restaurant had more tables and higher average spend per table. We define daily profit as contribution margin = net revenue after discounts/commissions minus variable costs, ignoring fixed costs.

Assumptions (typical coupon economics; adjust if your prior scenario differs):

Variable cost rate (food + variable labor) = 40% of gross spend.
Non-coupon table revenue = 100% of gross spend.
Coupon economics: customer receives 50% off; the platform takes 20% commission on the discounted amount. Net to the restaurant = 0.5 × (1 − 0.20) = 40% of gross spend.
Baseline day: 20 tables, average gross spend $30, no coupons.
Mixed day: 25 tables, average gross spend $36, with 10/25 coupon tables.

Tasks

Decompose the change in daily profit into volume effect, spend effect, and mix effect using a stepwise counterfactual:
- (a) Baseline: 20 tables, $30, no coupons
- (b) Change only tables to 25 (keep $30, no coupons)
- (c) Change only spend to $36 (25 tables, no coupons)
- (d) Apply observed mix: 10/25 coupon tables at $36 Quantify each step’s contribution and verify the final profit difference.
Attribute the loss primarily to which factor(s) with numeric justification.
Design an experiment to measure cannibalization and long-term value of coupon customers. Specify:
- Randomization unit (e.g., day-of-week within store, ZIP-level or DMA holdout)
- Treatments (e.g., discount depth, commission share, minimum spend, new-customer-only)
- Primary metric (e.g., daily contribution margin), guardrails (e.g., utilization, service time), and sample-size/duration assumptions.
Propose a diagnostic dashboard: daily KPIs and derived ratios to catch issues early and prevent future surprises.

Diagnose profit drop via mix decomposition

Quick Overview

Profit Decomposition, Attribution, Experiment Design, and Diagnostics

Context and Assumptions (to make the task self-contained)

Tasks

Solution

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