Question

Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.

Week	Sales (1,000s of gallons)
1	15
2	19
3	17
4	21
5	16
6	14
7	22
8	20
9	24
10	22
11	17
12	24

(a)Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.)

Week	Time Series Value	Weighted Moving Average Forecast
1	15
2	19
3	17
4	21
5	16
6	14
7	22
8	20
9	24
10	22
11	17
12	24

(b)Compute the MSE for the weighted moving average in part (a).

MSE = ____

Answer 1

a)

period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	15
2	19
3	17
4	21	17.33	3.67	3.67	13.44
5	16	19.33	-3.33	3.33	11.11
6	14	17.83	-3.83	3.83	14.69
7	22	15.83	6.17	6.17	38.03
8	20	18.33	1.67	1.67	2.78
9	24	19.67	4.33	4.33	18.78
10	22	22.33	-0.33	0.33	0.11
11	17	22.33	-5.33	5.33	28.44
12	24	19.83	4.17	4.17	17.36

b) MSE=   Σ(et)²/n =    16.08