Question

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

Week	Sales (1000s of gallons)
1	17
2	22
3	19
4	23
5	19
6	16
7	21
8	18
9	22
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	22
   3	19
   4	23
   5	19
   6	16
   7	21
   8	18
   9	22
   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 11.54.
   
   (three/four/five)

Answer 1

FORECAST = SIGMA(PREVIOUS N DEMANDS) / N

WHERE N = 4

FORECAST 5 = (17 + 22 + 19 + 23) / 4 = 20.25

FORECAST 6 = (22 + 19 + 23 + 19) / 4 = 20.75

FORECAST 7 = (19 + 23 + 19 + 16) / 4 = 19.25

FORECAST 8 = (23 + 19 + 16 + 21) / 4 = 19.75

FORECAST 9 = (19 + 16 + 21 + 18) / 4 = 18.5

FORECAST 10 = (16 + 21 + 18 + 22) / 4 = 19.25

FORECAST 11 = (21 + 18 + 22 + 21) / 4 = 20.5

FORECAST 12 = (18 + 22 + 21 + 14) / 4 = 18.75

FORECAST ERROR

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	DEVIATION ^2
1	17
2	22
3	19
4	23
5	19	20.25	-1.25	1.5625
6	16	20.75	-4.75	22.5625
7	21	19.25	1.75	3.0625
8	18	19.75	-1.75	3.0625
9	22	18.5	3.5	12.25
10	21	19.25	1.75	3.0625
11	14	20.5	-6.5	42.25
12	22	18.75	3.25	10.5625
SIGMA			-4	98.375

MSE = SIGMA(DEVIATIONS^2) / N, WHERE N = 8

MSE = 98.375 / 8 = 12.3

2. FORECAST 5 MA

FORECAST = SIGMA(PREVIOUS N DEMANDS) / N

WHERE N = 5

FORECAST 6 = (17 + 22 + 19 + 23 + 19) / 5 = 20

FORECAST 7 = (22 + 19 + 23 + 19 + 16) / 5 = 19.8

FORECAST 8 = (19 + 23 + 19 + 16 + 21) / 5 = 19.6

FORECAST 9 = (23 + 19 + 16 + 21 + 18) / 5 = 19.4

FORECAST 10 = (19 + 16 + 21 + 18 + 22) / 5 = 19.2

FORECAST 11 = (16 + 21 + 18 + 22 + 21) / 5 = 19.6

FORECAST 12 = (21 + 18 + 22 + 21 + 14) / 5 = 19.2

FORECAST ERROR

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	DEVIATION ^2
1	17
2	22
3	19
4	23
5	19
6	16	20	-4	16
7	21	19.8	1.2	1.44
8	18	19.6	-1.6	2.56
9	22	19.4	2.6	6.76
10	21	19.2	1.8	3.24
11	14	19.6	-5.6	31.36
12	22	19.2	2.8	7.84
SIGMA			-2.8	69.2

MSE = SIGMA(DEVIATIONS^2) / N, WHERE N = 7

MSE = 69.2 / 7 = 9.89

3. BASED ON THE MSE VALUES, 5R MONTH MOVING AVERAGE APPEARS TO BE BETTER.

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