Question

Do NOT use Minitab for this problem; you may use Excel. Handy, Inc. produces a solar powered electronic calculator that has experienced the following monthly sales history for the first four months of the year, in thousands of units: January 23.3 February 72.3 March 30.3 April 15.5

a. If the forecast for January was 25, determine the one-period-ahead forecasts for February through May using simple exponential smoothing with a smoothing constant of =0.15.
b. Repeat the calculation in part a) for a value of =0.40. What difference in the forecasts do you observe?
c. Compute the MSEs for the forecasts you obtained in parts a) and b) for February through April. Which value of gave more accurate forecasts, based on the MSE?

Answer 1

To determine the one-period-ahead forecasts, we will use simple exponential smoothing with a smoothing constant of 0.15. We can calculate the forecasts for February through May using the formula for simple exponential smoothing. Then, we can repeat the calculation for a smoothing constant of 0.40 and compare the forecasts. To determine which value of the smoothing constant gave more accurate forecasts, we can compute the Mean Squared Error (MSE) for the forecasts.

Step-by-step explanation:

To determine the one-period-ahead forecasts for February through May, we will use simple exponential smoothing with a smoothing constant of =0.15.

a) Using the formula for simple exponential smoothing, the forecast for February can be calculated as:

Forecast for February = (1 - 0.15) * Actual sales for January + 0.15 * Forecast for January

Substituting the values, we get:

Forecast for February = (1 - 0.15) * 23.3 + 0.15 * 25 = 22.06 + 3.75 = 25.81 thousand units

We can repeat this calculation for the remaining months to obtain the forecasts for February through May.

b) We will repeat the calculation in part a) using a smoothing constant of =0.40. The difference in the forecasts can be observed by comparing the values obtained in part a) and part b).

c) To compute the Mean Squared Error (MSE) for the forecasts in February through April, we will calculate the squared differences between the actual sales and the forecasts obtained in parts a) and b). Then, we will average these squared differences to obtain the MSE value. The value of =0.15 or =0.40 that gives a lower MSE would indicate a more accurate forecast