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Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Sales (1,000s of gallons) Week 17 21 3 19 4 23 18 16 21 19 23 10 21 11 16 12 23 (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.) Time Series Weighted Moving Value Week Average Forecast 1 17 2 21 19 23 18 16 21

Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Sales (1,000s of gallons) Week 17 21 3 19 4 23 18 16 21 19 23 10 21 11 16 12 23 (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.) Time Series Weighted Moving Value Week Average Forecast 1 17 2 21 19 23 18 16 21

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Sales (1,000s of gallons) Week 1 17 2 21 3 19 23 5 18 6 16 7 21 8 19 9 23 10 21 11 16 12 23 (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.) Time Series Value Weighted Moving Average Forecast Week 1. 17 2 21 19 4 23 5 18 6 16 7 21
Transcribed Image Text:Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Sales (1,000s of gallons) Week 1 17 2 21 3 19 23 5 18 6 16 7 21 8 19 9 23 10 21 11 16 12 23 (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.) Time Series Value Weighted Moving Average Forecast Week 1. 17 2 21 19 4 23 5 18 6 16 7 21
21 19 23 18 6 16 7 21 8 19 23 10 21 11 16 12 23 (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 10.91. O 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. O The weighted moving average is preferred because it has a larger MSE compared to the unweighted moving average. O 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? O No, an unweighted moving average always has a smaller MSE than a weighted moving average. O Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. O Yes, a weighted moving average always has a smaller MSE than an unweighted 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. in
Transcribed Image Text:21 19 23 18 6 16 7 21 8 19 23 10 21 11 16 12 23 (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 10.91. O 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. O The weighted moving average is preferred because it has a larger MSE compared to the unweighted moving average. O 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? O No, an unweighted moving average always has a smaller MSE than a weighted moving average. O Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. O Yes, a weighted moving average always has a smaller MSE than an unweighted 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. in
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