If we fit a linear trend to 10 observations on time-series data that are growing exponentially, then it is most likely that:
A)the fitted trend will be too high at t = 1 and t = 10.
B)the fitted trend will be too low in the middle.
C)the forecasts (if extrapolated) will be too low.
D)the residuals will show a pattern like - - - + + + + - - -.

Question

Quizplus · Accepted Answer

Fitting a linear trend to exponentially growing data will result in the fitted trend being too low in the beginning and too high at the end. Therefore, the forecasts (if extrapolated) will be too low. Choice A and B are incorrect because the trend will not necessarily be too high or low in the middle, and Choice D is unlikely because the residuals should show a random pattern rather than a systematic one.

If We Fit a Linear Trend to 10 Observations on Time-Series