Refer again to the gasoline sales time series data in Table.

a. Use a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for the third most recent to compute a three-week weighted moving average for the time series.

b. Compute the MSE for the weighted moving average in part (a). Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 10.22.

c. Suppose that you are allowed to choose any weights as long as they sum to 1. Could you always find a set of weights that would make the MSE smaller for a weighted moving average than for an unweighted moving average? Why or why not?

TABLE GASOLINE SALES TIMES SERIES

Week Sales (1000s of gallons)

1 ..........17

2 ..........21

3 ..........19

4 ..........23

5 .............18

6 ..........16

7 ..........20

8 ..........18

9 ..........22

10 ............20

11 ............15

12 ..........22