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(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 2 3 4 5 6 7 8 9 10 11 12 19 23 21 25 20 18 22 20 24 22 17 24 E (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. O The unweighted moving average is preferred because it has a smaller 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 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 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 t least as small for a weighted moving average than for an unweighted moving average? Why or why not? O Yes, a weighted moving average always has a smaller MSE than an unweighted moving average. O 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.

(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 2 3 4 5 6 7 8 9 10 11 12 19 23 21 25 20 18 22 20 24 22 17 24 E (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. O The unweighted moving average is preferred because it has a smaller 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 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 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 t least as small for a weighted moving average than for an unweighted moving average? Why or why not? O Yes, a weighted moving average always has a smaller MSE than an unweighted moving average. O 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.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.6: Rational Functions
Problem 11SC: Find the mean hourly cost when the cell phone described above is used for 240 minutes.
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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 week Sales (1,000s of gallons) Week 1 2 3 4 5 6 7 8 9 10 11 12 19 23 21 25 20 18 22 20 24 22 17 24
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 week Sales (1,000s of gallons) Week 1 2 3 4 5 6 7 8 9 10 11 12 19 23 21 25 20 18 22 20 24 22 17 24
(a) Using a weight off for the most recent observation, 11/13 for the second most recent observation, and Time Series Value Weighted Moving Average Forecast Week 1 2 3 4 5 6 7 00 8 9 10 11 12 19 23 21 25 20 18 22 20 24 22 17 24 (b) Compute the MSE for the weighted moving average in part (a). MSE = 1/1/ for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.) Do you prefer this weighted moving average to the unweighted moving average? The MSE for the unweighted moving average is 10.22. O The unweighted moving average is preferred because it has a smaller 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 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 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 Yes, a weighted moving average always has a smaller MSE than an unweighted moving average. O No, an unweighted average always has a smaller MSE than a wei oving 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, because an unweighted moving average is just a weighted moving average where the weights are equal.
Transcribed Image Text:(a) Using a weight off for the most recent observation, 11/13 for the second most recent observation, and Time Series Value Weighted Moving Average Forecast Week 1 2 3 4 5 6 7 00 8 9 10 11 12 19 23 21 25 20 18 22 20 24 22 17 24 (b) Compute the MSE for the weighted moving average in part (a). MSE = 1/1/ for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.) Do you prefer this weighted moving average to the unweighted moving average? The MSE for the unweighted moving average is 10.22. O The unweighted moving average is preferred because it has a smaller 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 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 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 Yes, a weighted moving average always has a smaller MSE than an unweighted moving average. O No, an unweighted average always has a smaller MSE than a wei oving 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, because an unweighted moving average is just a weighted moving average where the weights are equal.
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