These data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.

Week	Sales (1,000s 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

(a)Using a weight of

1

2

for the most recent observation,

1

3

for the second most recent observation, and

1

6

for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.)

Week	Time Series Value	Weighted Moving Average Forecast
1	17
2	21
3	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22

(b)Compute the MSE for the weighted moving average in part (a). (Round your answer to two decimal places.)

MSE =

Do you prefer this weighted moving average to the unweighted moving average? The MSE for the unweighted moving average is 10.22.

The weighted moving average is preferred because it has a larger MSE compared to the unweighted moving average.

The unweighted moving average is preferred because it has a larger MSE compared to the weighted moving average.

The weighted moving average is preferred because it has a smaller MSE compared to the unweighted moving average.

The unweighted moving average is preferred because it has a smaller MSE compared to the weighted moving average.

(c)Suppose 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 at least as small for a weighted moving average than for an unweighted moving average? Why or why not?

No, an unweighted moving average always has a smaller MSE than a weighted moving average.

Yes, a weighted moving average always has a smaller MSE than an unweighted moving average.

No, sometimes you need to let the weights sum to a number higher/lower than 1 in order to get a smaller MSE than the one for an unweighted moving average.

Yes, because an unweighted moving average is just a weighted moving average where the weights are equal.