Consider the following gasoline sales time series data. Click onthe datafile logo to reference the data.
| Week | Sales (1000s of gallons) |
| 1 | 17 |
| 2 | 21 |
| 3 | 19 |
| 4 | 24 |
| 5 | 18 |
| 6 | 15 |
| 7 | 21 |
| 8 | 19 |
| 9 | 22 |
| 10 | 19 |
| 11 | 15 |
| 12 | 23 |
a. Using a weight of 1/2 for the most recentobservation,1/3 for the second most recent observation, and 1/6third the most recent observation, compute a three-week weightedmoving average for the time series (to 2 decimals). Enter negativevalues as negative numbers.
Week |
Time-Series Value | Weighted Moving
Average Forecast | Forecast
Error | |
(Error)2 |
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| | | | | Total | |
b. Compute the MSE for the weighted movingaverage in part (a).
MSE =
Do you prefer this weighted moving average to the unweightedmoving average? Remember that the MSE for the unweighted movingaverage is 14.39 .
Prefer the unweighted moving average here; it has a - Select youranswer -greatersmallerItem 42 MSE.
c. Suppose you are allowed to choose anyweights as long as they sum to 1. Could you always find a set ofweights that would make the MSE at least as small for a weightedmoving average than for an unweighted moving average?
- Select your answer -YesNoItem 43
