Business Context
BrightAds, a mobile commerce company, reviewed recent campaign data and concluded that increasing daily ad spend causes higher same-day revenue because the two variables move together strongly.
Problem Statement
You are given 10 days of campaign data. The analyst reported a high positive correlation between ad spend and revenue and concluded that raising spend will increase revenue. Analyze the dataset and identify the logical flaw in that conclusion.
Given Data
| Day | Ad Spend ($000) | Revenue ($000) |
|---|
| 1 | 10 | 100 |
| 2 | 12 | 108 |
| 3 | 14 | 116 |
| 4 | 16 | 124 |
| 5 | 18 | 132 |
| 6 | 20 | 140 |
| 7 | 22 | 148 |
| 8 | 24 | 156 |
| 9 | 26 | 164 |
| 10 | 28 | 172 |
A manager states: "The correlation is nearly perfect, so higher ad spend clearly causes higher revenue."
Requirements
- Compute the sample correlation between ad spend and revenue.
- Test whether the correlation is statistically different from 0 at α=0.05.
- Explain whether statistical significance of correlation is enough to support a causal claim.
- Identify the logical flaw in the manager's conclusion.
- State what additional analysis or experimental design would be needed to support causality.
Assumptions
- Treat the 10 daily observations as paired measurements.
- Use a two-sided hypothesis test for correlation.
- Assume approximate linearity for the purpose of computing Pearson correlation.
- You may assume no arithmetic error in the reported data, but you should question the inference drawn from it.
