Enrollment in a particular class for the last four semesters has been 120, 126, 110, and 130.Suppose a one-semester moving average was used to forecast enrollment (this is sometimes referred to as a naïve forecast).Thus, the forecast for the second semester would be 120, for the third semester it would be 126, and for the last semester it would be 110.What would the MSE be for this situation?
A)196.00
B)230.67
C)100.00
D)42.00

Question

Quizplus · Accepted Answer

The formula for calculating Mean Squared Error (MSE) is:

MSE = (1/n) * ∑(actual - forecast)^2

Using the given data and the moving average method, the forecasts are:

- For the second semester: forecast = 120 (actual = 126)
- For the third semester: forecast = 126 (actual = 110)
- For the fourth semester: forecast = 110 (actual = 130)

So, the errors are:

- For the second semester: error = actual - forecast = 126 - 120 = 6
- For the third semester: error = actual - forecast = 110 - 126 = -16
- For the fourth semester: error = actual - forecast = 130 - 110 = 20

Then, the MSE can be calculated as:

MSE = (1/3) * [6^2 + (-16)^2 + 20^2] = 230.67

Therefore, the best choice is B.

Enrollment in a Particular Class for the Last Four Semesters