Refer again to the gasoline sales time series data in the following table. Week 1 Sales (1000s of gallons) 17 2 22 3 21 4 23 5 19 6 17 7 19 8 19 9 23 10 22 11 12 13 22 a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate colculations. Week Sales Weighted Moving Average Forecast Forecast Error (Error)2 1 17 2 22 3 21 4 23 x 5 19 x 6 17 x 7 19 8 19 9 23 a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate colculations. Week Sales Weighted Moving Average Forecast Forecast Error (Error)2 1 17 2 22 3 21 4 23 x 5 19 x 6 17 x 7 19 8 19 9 23 10 22 11 13 12 22 Total 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. Round your answer to two decimal places. MSE- Prefer the moving average here. 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? The input in the box below will not be graded, but may be reviewed and considered by your instructor.