Problem 15-08 (Algorithmic) Refer again to the gasoline sales time series data i
ID: 3148383 • Letter: P
Question
Problem 15-08 (Algorithmic) Refer again to the gasoline sales time series data in the following table. Sales (1000s of gallons) 17 24 21 25 20 14 19 16 Week 10 16 12 23 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. a. Weighted MovingForecast (Error) Week Sales Average Forecast Error 17 24 21 25 20 14 19 16 10 16 12 23 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-Explanation / Answer
MSE= sum of Error2/9
= 147.2/9
= 16.35
Yes we prefer unweighted moving average as the MSE is less in that case as compared to weighted moving average.
week sales Weighted moving average forecast forcast error (error)2 1 17 2 24 3 21 4 25 (17*(1/6))+ (24*1/3)+(21*1/2)= 21.33 3.67 13.46 5 20 (24*(1/6))+ (21*1/3)+(25*1/2)= 23.50 -3.50 12.25 6 14 (21*(1/6))+ (25*1/3)+(20*1/2)= 20.50 -6.50 42.25 7 19 (25*(1/6))+ (20*1/3)+(14*1/2)= 17.83 1.16 1.34 8 16 (20*(1/6))+ (14*1/3)+(19*1/2)= 17.50 -1.5 2.25 9 22 (14*(1/6))+ (19*1/3)+(16*1/2)= 16.66 5.33 28.40 10 22 (19*(1/6))+ (16*1/3)+(22*1/2)= 19.50 2.50 6.25 11 16 (16*(1/6))+ (22*1/3)+(22*1/2)= 21 -5 25 12 23 (22*(1/6))+ (22*1/3)+(16*1/2)= 19 4 16 Total 147.2