Business Context
A Product Growth Analyst at Didi Chuxing is reviewing whether exposure to a Didi Ride promo banner in the app causes higher same-day ride booking, or whether the observed relationship is only correlation driven by confounding factors such as user activity level.
Problem Statement
You are given aggregated data from 8 user segments. First, measure the association between promo exposure rate and same-day booking rate. Then evaluate whether that association supports a causal claim after accounting for average prior weekly app opens, a likely confounder.
Given Data
| Segment | Promo Exposure Rate x | Same-Day Booking Rate y | Avg Prior Weekly App Opens z |
|---|
| 1 | 0.10 | 0.050 | 1.0 |
| 2 | 0.20 | 0.070 | 2.0 |
| 3 | 0.30 | 0.090 | 3.0 |
| 4 | 0.40 | 0.110 | 4.0 |
| 5 | 0.50 | 0.130 | 5.0 |
| 6 | 0.60 | 0.150 | 6.0 |
| 7 | 0.70 | 0.170 | 7.0 |
| 8 | 0.80 | 0.190 | 8.0 |
Assume a significance level of α=0.05.
Requirements
- Compute the Pearson correlation between promo exposure rate and booking rate.
- Test whether the correlation is significantly different from 0.
- Fit a simple linear regression of booking rate on promo exposure rate.
- Explain why the regression coefficient alone does not prove causation.
- Refit the model conceptually after controlling for prior weekly app opens, and determine whether a causal interpretation is justified.
- State what additional evidence or design would be needed to make a causal claim.
Assumptions
- Each segment is independent.
- Rates are measured without material logging error.
- Linear association is a reasonable first-pass approximation.
- Prior weekly app opens may affect both promo exposure and booking propensity.
