In: Statistics and Probability
Refer to the gasoline sales time series data in the given table.
Week | Sales (1000s of gallons) |
1 | 18 |
2 | 22 |
3 | 18 |
4 | 24 |
5 | 19 |
6 | 16 |
7 | 21 |
8 | 19 |
9 | 22 |
10 | 19 |
11 | 16 |
12 | 23 |
Week |
Sales |
4-Week Moving Average |
5-Week Moving Average |
1 | 18 | ||
2 | 22 | ||
3 | 18 | ||
4 | 24 | ||
5 | 19 | ||
6 | 16 | ||
7 | 21 | ||
8 | 19 | ||
9 | 22 | ||
10 | 19 | ||
11 | 16 | ||
12 | 23 |
a) Four Week moving average:
Week | Sales | Four week moving Average | Error | Error² | |
1 | 18 | - | - | - | - |
2 | 22 | - | - | - | - |
3 | 18 | - | - | - | - |
4 | 24 | - | - | - | - |
5 | 19 | (18+22+18+24)/4 = | 20.500 | -1.500 | 2.250 |
6 | 16 | (22+18+24+19)/4 = | 20.750 | -4.750 | 22.563 |
7 | 21 | (18+24+19+16)/4 = | 19.250 | 1.750 | 3.063 |
8 | 19 | (24+19+16+21)/4 = | 20.000 | -1.000 | 1.000 |
9 | 22 | (19+16+21+19)/4 = | 18.750 | 3.250 | 10.563 |
10 | 19 | (16+21+19+22)/4 = | 19.500 | -0.500 | 0.250 |
11 | 16 | (21+19+22+19)/4 = | 20.250 | -4.250 | 18.063 |
12 | 23 | (19+22+19+16)/4 = | 19.000 | 4.000 | 16.000 |
Total | -3.000 | 73.750 |
Five Week moving Average :
Month | Sales | Five week moving Average | Error | Error² | |
1 | 18 | - | - | - | - |
2 | 22 | - | - | - | - |
3 | 18 | - | - | - | - |
4 | 24 | - | - | - | - |
5 | 19 | - | - | - | - |
6 | 16 | (18+22+18+24+19)/5 = | 20.200 | -4.200 | 17.640 |
7 | 21 | (22+18+24+19+16)/5 = | 19.800 | 1.200 | 1.440 |
8 | 19 | (18+24+19+16+21)/5 = | 19.600 | -0.600 | 0.360 |
9 | 22 | (24+19+16+21+19)/5 = | 19.800 | 2.200 | 4.840 |
10 | 19 | (19+16+21+19+22)/5 = | 19.400 | -0.400 | 0.160 |
11 | 16 | (16+21+19+22+19)/5 = | 19.400 | -3.400 | 11.560 |
12 | 23 | (21+19+22+19+16)/5 = | 19.400 | 3.600 | 12.960 |
Total | -1.600 | 48.960 |
b)
MSE for four week moving average = ∑(A-F)²/n = 73.75/8 = 9.22
MSE for four week moving average = ∑(A-F)²/n = 48.96/7 = 6.99
c)
5 week moving average is the best.