Enrollment in a particular class for the last four semesters has been 120, 126, 110, and 130 (listed from oldest to most recent).Develop a forecast of enrollment next semester using exponential smoothing with an alpha = 0.2.Assume that an initial forecast for the first semester was 120 (so the forecast and the actual were the same).
A)118.96
B)121.17
C)130
D)120

Question

Quizplus · Accepted Answer

Exponential smoothing with alpha = 0.2 involves using the formula:
Forecast for next period = (1-alpha) * Actual value + alpha * Previous forecast

Using the given information, we can calculate the forecast for the second semester:
Forecast = (1-0.2) * 126 + 0.2 * 120 = 124.8

For the third semester:
Forecast = (1-0.2) * 110 + 0.2 * 124.8 = 114.24

For the fourth semester:
Forecast = (1-0.2) * 130 + 0.2 * 114.24 = 125.792

Therefore, the forecast for the next semester would be:
Forecast = (1-0.2) * Actual value + 0.2 * Previous forecast
         = (1-0.2) * 130 + 0.2 * 125.792
         = 121.17

So, the best choice is B, which is the closest option to the calculated forecast using exponential smoothing.

Enrollment in a Particular Class for the Last Four Semesters