Business Context
FinSight, a B2B SaaS company, needs a simple near-term forecast for next quarter's revenue to set sales targets and cash planning. You are given the last 8 quarters of revenue and asked to build a baseline statistical forecast.
Problem Statement
Use a linear trend model to forecast revenue for quarter 9 and quantify uncertainty around the forecast. Assume revenue follows a roughly linear trend over these 8 quarters with independent residual errors.
Given Data
| Quarter | Revenue ($M) |
|---|
| 1 | 4.2 |
| 2 | 4.5 |
| 3 | 4.9 |
| 4 | 5.1 |
| 5 | 5.4 |
| 6 | 5.8 |
| 7 | 6.0 |
| 8 | 6.3 |
Use quarter number as the predictor variable and revenue in millions as the response.
Requirements
- Fit a simple linear regression model: revenue = a + b \times quarter.
- Calculate the slope and intercept manually.
- Forecast revenue for quarter 9.
- Compute the residual standard error from the fitted model.
- Construct an approximate 95% prediction interval for quarter 9 using a t-critical value of 2.447 (df = 6).
- Briefly explain whether this forecast is strong enough for financial planning and what risks remain.
Assumptions
- Linear trend is a reasonable approximation over these 8 quarters.
- Residuals are independent with constant variance.
- No major seasonality, pricing changes, or one-time shocks are included.
- Use the standard prediction interval for a new observation, not just the mean forecast.
