Business Context
FinEdge, a B2B payments company, needs a simple near-term forecast for next quarter's revenue to support budgeting. The finance team wants a statistically grounded baseline using recent quarterly results rather than a purely judgment-based estimate.
Problem Statement
Use a linear trend model to forecast next quarter's revenue and quantify uncertainty around the forecast. Assume quarterly revenue follows an approximately linear trend over the last 8 quarters.
Given Data
| Quarter Index t | Revenue ($M) |
|---|
| 1 | 48.2 |
| 2 | 50.1 |
| 3 | 51.4 |
| 4 | 53.0 |
| 5 | 54.6 |
| 6 | 56.1 |
| 7 | 57.9 |
| 8 | 59.3 |
You should forecast revenue for quarter t=9. Use a 95% confidence level.
Requirements
- Fit a simple linear regression of revenue on quarter index.
- Estimate the slope and intercept.
- Compute the point forecast for quarter 9.
- Calculate the residual standard error.
- Construct a 95% prediction interval for quarter 9 revenue.
- Briefly explain whether this forecast is appropriate for financial planning.
Assumptions
- The relationship between time and revenue is approximately linear over these 8 quarters.
- Residuals are independent with constant variance.
- No major structural break, pricing change, or acquisition occurred during the period.
- A prediction interval, not just a mean estimate, is needed because finance cares about planning risk.
