a through c is one whole problem

Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks Week Sales (1,000 of gallons) 1 17 2 21 3 19 4 22 5 1 6 16 7 20 8 18 9 22 10 20 11 15 12 22 1 for the most recent observation for the second most recent observation, and for the most recent observation, compute three-week weighted moving average for (a) Unaw of 1 the time series (Round your answers to two decimal places) Week Time Series Weighted Moving Value Average Forecast 1 12 2 21 3 19 4 22 5 10 6 36 2 20 8 22 10 20 6 16 7 20 8 18 9 22 10 20 11 15 12 22 (1) Compute the MSE for the welghted 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 smaller MSE compared to the unweighted moving average. 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 smaller Mse compared to the weighted moving average. o The unweighted moving average is preferred because it has a larger 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 smaller for a weighted moving average than for an unweighted moving average? Why or why not? O 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, a welghted moving average always has a smaller MSE than an unweighted moving average. O No, an unweighted moving average always has a smaller MSE than a weighted moving average No, but you will always be able to make the MSE at least as good as the one for an unweighted average