Question
Refer to the gasoline sales time series data in the given table. Click on the datafile...
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Refer to the gasoline sales time series data in the given table. Click on the datafile logo to reference the data.
|
Homework Answers
Answer #1
a)first of all calculating the 4 week moving average as shown in below table and computing the squared error as follows:
| Week | Time Series Value (Sales) | Computation for MA | 4 period MA | Error (Sales - MA ) | Error^2 |
| 1 | 17 | ||||
| 2 | 21 | ||||
| 3 | 19 | ||||
| 4 | 23 | ||||
| 5 | 18 | (17+21+19+23)/4 = | 20 | -2 | 4 |
| 6 | 16 | (21+19+23+18)/4 = | 20.25 | -4.25 | 18.06 |
| 7 | 20 | (19+23+18+16)/4 = | 19 | 1 | 1 |
| 8 | 18 | (23+18+16+20)/4 = | 19.25 | -1.25 | 1.56 |
| 9 | 22 | (18+16+20+18)/4 = | 18 | 4 | 16 |
| 10 | 20 | (16+20+18+22)/4 = | 19 | 1 | 1 |
| 11 | 15 | (20+18+22+20)/4 = | 20 | -5 | 25 |
| 12 | 22 | (18+22+20+15)/4 = | 18.75 | 3.25 | 10.56 |
| Total | 77.18 | ||||
| Average | 9.65 |
the following is the five week moving average and computation of error
| Week | Time Series Value (Sales) | Computation for MA | 5 period MA | Error (Sales - MA ) | Error^2 |
| 1 | 17 | ||||
| 2 | 21 | ||||
| 3 | 19 | ||||
| 4 | 23 | ||||
| 5 | 18 | ||||
| 6 | 16 | (17+21+19+23+18)/5 = | 19.6 | -3.6 | 12.96 |
| 7 | 20 | (21+19+23+18+16)/5 = | 19.4 | 0.6 | 0.36 |
| 8 | 18 | (19+23+18+16+20)/5 = | 19.2 | -1.2 | 1.44 |
| 9 | 22 | (23+18+16+20+18)/5 = | 19 | 3 | 9 |
| 10 | 20 | (18+16+20+18+22)/5 = | 18.8 | 1.2 | 1.44 |
| 11 | 15 | (16+20+18+22+20)/5 = | 19.2 | -4.2 | 17.64 |
| 12 | 22 | (20+18+22+20+15)/5 = | 19 | 3 | 9 |
| Total | 51.84 | ||||
| Average | 7.41 |
b) mean squared error for 4 week
Mean squared error =MSE = 
=77.18/(12-4) = 77.18/8 = 9.65
mean squared error for 4 week = 9.65
MSE for 5 week moving average
MSE=
=51.84/(12-5) =51.84/7 =7.41
mean squared error for 5 week = 7.41
c) Five weeks appears to be best, because the five-week moving average provides the smallest MSE.
since mse for 5 week moving average is less so it is recommended to use 5 week moving average.
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