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Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply over 11 years are as follows: 4, 6, 4, 7, 8, 10, 12, 17, 13, 17, 19.

1. Develop a 3-year moving average to forecast sales.

2. Estimate demand again with a weighted moving average, where sales in the most recent year are given a weight of 2 and sales in the other 2 years are each given a weight of 1.

3. Find the MSE (Mean Squared Error) value for this weighted moving averages forecast.

Choose one of the following options for the MSE value:

a. 11.773
b. 3.149
c. 5.653
d. 8.215
e. 9.757

Answer :

Answer:

e.

Explanation:

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Final answer:

The 3-year moving average and weighted moving average use past data to forecast future sales, the latter assigning more weight to more recent data. The Mean Squared Error (MSE) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.

Explanation:

The 3-year moving average forecasts are calculated by adding the number of sales from three consecutive years and dividing by three. For example, the forecast for year 4 would be the average of the sales from years 1, 2, and 3. This process is repeated for the subsequent years. The weighted moving average follows a similar concept, but assigns more importance, or weight, to certain instances. In this case, more recent years are given more weight. So, for the weighted average forecast for year 4, the sales for year 3 are multiplied by 2, while the sales for years 1 and 2 are multiplied by 1. These products are added together and then divided by the sum of the weights. Lastly, the MSE, or Mean Squared Error, is found by subtracting the actual sales values from the forecasted values, squaring these differences, summing them all up, and then dividing by the number of forecasts made.

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