Work out a trend forecast for a time series, whether fitted as a linear or a log-linear trend, from given trend coefficients, and judge the result
The idea
A linear trend model says the series rises by a constant amount each period, so the forecast is the intercept plus the slope times t: y = b0 + b1 × t. A log-linear trend regresses the natural log of the series on t instead, so the series grows at a constant rate and the forecast, converted back from logs, is y = e^(b0 + b1 × t). The implied growth rate per period is e raised to b1, minus 1, which is close to b1 only when b1 is small. Count periods carefully: two periods after a sample that ends at period 48 is period 50, so the forecast uses t of 50. The classic slips are forgetting to convert the log forecast back to the original units and using the next period's t instead of the one asked for.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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