Please help. Im stuck

OTHER 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 (1,000s of gallons) 17 2 21 3 19 23 5 18 6 16 7 20 8 18 22 10 20 11 15 12 22 (a) Using a weight of - for the most recent observation, - for the second most recent observation, and _ 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 Weighted Moving Value Average Forecast 17 2 21 3 19 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). MSE = Do you prefer this weighted moving average to the unweighted moving average? The MSE for the unweighted moving average is 10.22. The unweighted moving average is preferred because it has a smaller MSE compared to the weighted 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 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. (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. 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 weighted moving average always has a smaller MSE than an unweighted moving average. Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. Need Help? Read It Talk to a Tutor