Question

Refer to the gasoline sales time series data in the given table.

Week	Sales (1000s of gallons)
1	17
2	20
3	18
4	22
5	17
6	16
7	22
8	17
9	23
10	21
11	14
12	22

1. Compute four-week and five-week moving averages for the time series. Round your answers to two decimal places.
   

   Week	Sales	4-Week Moving Average	5-Week Moving Average
   1	17
   2	20
   3	18
   4	22
   5	17
   6	16
   7	22
   8	17
   9	23
   10	21
   11	14
   12	22

2. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations and final answers to two decimal places.
   
   MSE for four-week moving average =
   
   MSE for five-week moving average =
   
3. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 12.87.
   
   

Answer 1

a) Fromt the givend ata

Week	Sales	4 Week Moving Aveages	5 Week Moving Averages
1	17
2	20
3	18
4	22
5	17	19.25
6	16	19.25	18.80
7	22	18.25	18.60
8	17	19.25	19.00
9	23	18.00	18.80
10	21	19.50	19.00
11	14	20.75	19.80
12	22	18.75	19.40

b) MSE for 4 Week moving averages:

Week	Sales	4 Week Moving Aveages	Absolute Error	Error^2
1	17
2	20
3	18
4	22
5	17	19.25	2.25	5.0625
6	16	19.25	3.25	10.5625
7	22	18.25	3.75	14.0625
8	17	19.25	2.25	5.0625
9	23	18	5	25
10	21	19.5	1.5	2.25
11	14	20.75	6.75	45.5625
12	22	18.75	3.25	10.5625
		Total:	28	118.125

MSE of 4 Week moving average is 118.125/8 = 14.7656

and

MSE for 5 Week moving averages:

Week	Sales	5 Week Moving Aveages	Absolute Error	Error^2
1	17
2	20
3	18
4	22
5	17
6	16	18.80	2.8	7.84
7	22	18.60	3.4	11.56
8	17	19.00	2	4
9	23	18.80	4.2	17.64
10	21	19.00	2	4
11	14	19.80	5.8	33.64
12	22	19.40	2.6	6.76
		Total:	22.8	85.44

MSE of 5 Week moving average is 85.44/7 = 12.2057

c) since MSE of 5 week moving average is smaller than that of 4 week moving average and also 3 week moving average (12.87)

Therefoore, 5 Week moving average is best method to predict the future value for this given data