Business Context
FinEdge, a B2B SaaS company, tracks quarterly revenue growth to guide hiring and budget planning. The CFO wants a simple statistical forecast for next quarter based only on recent growth history.
Problem Statement
You are given the last 8 quarterly revenue growth rates. Estimate the expected growth rate for the next quarter and justify the method statistically.
Given Data
| Quarter | Revenue Growth |
|---|
| Q1 | 4.2% |
| Q2 | 5.1% |
| Q3 | 4.8% |
| Q4 | 5.4% |
| Q5 | 4.9% |
| Q6 | 5.3% |
| Q7 | 5.0% |
| Q8 | 5.2% |
Assume quarterly growth rates are independent draws from a stable distribution with no trend or seasonality, and that a normal model is reasonable for short-term forecasting.
Requirements
- Compute the sample mean growth rate as the point forecast for next quarter.
- Compute the sample standard deviation of historical growth rates.
- Construct a 95% confidence interval for the population mean growth rate using the t-distribution.
- State the expected next-quarter growth rate and explain why the sample mean is appropriate under the assumptions.
- Briefly comment on whether the historical variability is low or high for planning purposes.
Assumptions
- No structural break, trend, or seasonal pattern across these 8 quarters
- Growth rates are measured consistently across quarters
- Historical quarters are representative of the near future
- Small sample size implies using the t-distribution rather than the normal approximation
