Given data,
| Week |
Sales (1,000s of
gallons) |
| 1 |
17 |
| 2 |
21 |
| 3 |
16 |
| 4 |
24 |
| 5 |
17 |
| 6 |
18 |
| 7 |
22 |
| 8 |
20 |
| 9 |
21 |
| 10 |
19 |
| 11 |
16 |
| 12 |
25 |
Solution:
a) Computing 4-week and 5-week Moving averages.
- 4- Period Moving Average = Sum up the four consective year and
divide by 4.
- 5- Period Moving Average = Sum up the five consective year and
divide by 5.
| Week |
Sales (1,000s of
gallons) |
4 Period
Moving Average |
5 period
Moving Average |
| 1 |
17 |
- |
- |
| 2 |
21 |
- |
- |
| 3 |
16 |
- |
- |
| 4 |
24 |
- |
- |
| 5 |
17 |
(17+21+16+24)/4 |
- |
| 6 |
18 |
(21+16+24+17)/4 |
(17+21+16+24+17)/5 |
| 7 |
22 |
(16+24+17+18)/4 |
(21+16+24+17+18)/5 |
| 8 |
20 |
(24+17+18+22)/4 |
(16+24+17+18+22)/5 |
| 9 |
21 |
(17+18+22+20)/4 |
(24+17+18+22+20)/5 |
| 10 |
19 |
(18+22+20+21)/4 |
(17+18+22+20+21)/5 |
| 11 |
16 |
(22+20+21+19)/4 |
(18+22+20+21+19)/5 |
| 12 |
25 |
(20+21+19+16)/4 |
(22+20+21+19+16)/5 |
Result:
| Week |
Sales (1,000s of
gallons) |
4 Period
Moving Average |
5 period
Moving Average |
| 1 |
17 |
- |
- |
| 2 |
21 |
- |
- |
| 3 |
16 |
- |
- |
| 4 |
24 |
- |
- |
| 5 |
17 |
20.25 |
- |
| 6 |
18 |
19.50 |
19.00 |
| 7 |
22 |
18.75 |
19.20 |
| 8 |
20 |
20.25 |
19.40 |
| 9 |
21 |
19.25 |
20.20 |
| 10 |
19 |
20.25 |
19.6 |
| 11 |
16 |
20.50 |
20 |
| 12 |
25 |
19.00 |
19.6 |
b)
| Week |
Sales (1,000s of
gallons) |
4 Period
Moving Average |
Error |
(Error)^2 |
5 period
Moving Average |
Error |
(Error)^2 |
| 1 |
17 |
- |
- |
- |
- |
- |
- |
| 2 |
21 |
- |
- |
- |
- |
- |
- |
| 3 |
16 |
- |
- |
- |
- |
- |
- |
| 4 |
24 |
- |
- |
- |
- |
- |
- |
| 5 |
17 |
20.25 |
-3.25 |
10.5625 |
- |
- |
- |
| 6 |
18 |
19.50 |
-1.5 |
2.2500 |
19.00 |
-1.00 |
1.0000 |
| 7 |
22 |
18.75 |
3.25 |
12.2500 |
19.20 |
2.80 |
7.8400 |
| 8 |
20 |
20.25 |
-0.25 |
0.0625 |
19.40 |
0.60 |
0.3600 |
| 9 |
21 |
19.25 |
1.75 |
3.0625 |
20.20 |
0.80 |
0.6400 |
| 10 |
19 |
20.25 |
-1.25 |
1.5625 |
19.6 |
-0.60 |
0.3600 |
| 11 |
16 |
20.50 |
-4.50 |
20.25 |
20 |
-4.00 |
16.0000 |
| 12 |
25 |
19.00 |
6.00 |
36 |
19.6 |
5.40 |
29.1600 |
| Total |
|
|
|
86 |
|
|
55.36 |
   Â
MSE for 4-week moving average = 86/8 = 10.75
MSE for 5-week moving average = 55.36/7 = 7.91
c) It is preferred to choose lowest MSE for training and highest
MSE for testing.
Five week moving average.
