Question

Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of gallons) 1 17 2 23 3 14 4 25 5 17 6 16 7 22 8 19 9 21 10 19 11 17 12 23 (a) Compute four-week and five-week moving averages for the time series. If required, round your answers to two decimal places. Week Sales 4 Period Moving Average 5 period Moving Average 1 17 2 23 3 14 4 25 5 17 6 16 7 22 8 19 9 21 10 19 11 17 12 23 (b) Compute the MSE for the four-week and five-week moving average forecasts. If required, round your final answers to three decimal places. MSE for four-week moving average = MSE for five-week moving average = (c) What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Consider that the MSE for the three-week moving average is 11.889. - Select your answer -ThreeFourFiveItem 18

Answer 1

a)

Week	Sales (1,000s of gallons)	4 period	5 period
1	17
2	23
3	14
4	25
5	17	19.75
6	16	19.75	19.2
7	22	18	19
8	19	20	18.8
9	21	18.5	19.8
10	19	19.5	19
11	17	20.25	19.4
12	23	19	19.6

b)

for 4 period :

Week	Sales (A)	4 per (F)	(A-F)^2
1	17
2	23
3	14
4	25
5	17	19.75	7.5625
6	16	19.75	14.0625
7	22	18	16
8	19	20	1
9	21	18.5	6.25
10	19	19.5	0.25
11	17	20.25	10.5625
12	23	19	16
		average	8.961

for 5 period:

Week	Sales (A)		5 period	(A-F)^2
1	17
2	23
3	14
4	25
5	17
6	16		19.2	10.24
7	22		19	9
8	19		18.8	0.04
9	21		19.8	1.44
10	19		19	0
11	17		19.4	5.76
12	23		19.6	11.56
		average	19.257	5.434

hence  MSE for four-week moving average = 8.961

MSE for five-week moving average = 5.434

c)

for MSE for r five-week moving average is smallest ; one should use 5 week moving average