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) 1 17 2 21 3 19 4 st 23 5 18 6 16 7 18 8 16 9 20 10 18 11 13 12 20 - for the most recent observation, 1 3 1 (a) Using a weight of 2 your answers to two decimal places.) for the second most recent observation, and 11/ for third most recent observation, compute a three-week weighted moving average for the time series. (Round Week Time Series Value Weighted Moving Average Forecast 1 17 2 21 3 19 4 23 5 18 6 16 7 18 00 8 16 9 20 10 18 11 13 12 20 (b) Compute the MSE for the weighted moving average in part (a). Do you prefer this weighted moving average to the unweighted moving average? The MSE for the unweighted moving average is 9.88. 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 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 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 at least as small for a weighted moving average than for an unweighted moving average? Why or why not? O No, an unweighted moving average always has a smaller MSE than a weighted 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. Yes, a weighted moving average always has a smaller MSE than an unweighted moving average. 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) 1 17 2 21 3 19 4 st 23 5 18 6 16 7 18 8 16 9 20 10 18 11 13 12 20 - for the most recent observation, 1 3 1 (a) Using a weight of 2 your answers to two decimal places.) for the second most recent observation, and 11/ for third most recent observation, compute a three-week weighted moving average for the time series. (Round Week Time Series Value Weighted Moving Average Forecast 1 17 2 21 3 19 4 23 5 18 6 16 7 18 00 8 16 9 20 10 18 11 13 12 20 (b) Compute the MSE for the weighted moving average in part (a). Do you prefer this weighted moving average to the unweighted moving average? The MSE for the unweighted moving average is 9.88. 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 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 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 at least as small for a weighted moving average than for an unweighted moving average? Why or why not? O No, an unweighted moving average always has a smaller MSE than a weighted 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. Yes, a weighted moving average always has a smaller MSE than an unweighted moving average