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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 16 2 20 3 18 22 17 O 6. 15 O 20 18 9 22 10 20 11 15 12 22 (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 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. 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 smaller 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 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. O Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. O No, an unweighted moving average always has a smaller MSE than a weighted 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 16 2 20 3 18 22 17 O 6. 15 O 20 18 9 22 10 20 11 15 12 22 (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 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. 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 smaller 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 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. O Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. O No, an unweighted moving average always has a smaller MSE than a weighted moving average.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 16 2 20 3 18 4 22 17 6. 15 7 20 18 9 22 10 20 11 15 12 22
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 16 2 20 3 18 4 22 17 6. 15 7 20 18 9 22 10 20 11 15 12 22
(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.) Weighted Moving Average Forecast Time Series Week Value 1 16 2 20 18 4 22 5 17 6 15 7 20 8 18 9 22 10 20 11 15 12 22 (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 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. 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 smaller 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 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. O Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. O No, an unweighted moving average always has a smaller MSE than a weighted moving average.
Transcribed Image Text:(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.) Weighted Moving Average Forecast Time Series Week Value 1 16 2 20 18 4 22 5 17 6 15 7 20 8 18 9 22 10 20 11 15 12 22 (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 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. 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 smaller 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 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. O Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. O No, an unweighted moving average always has a smaller MSE than a weighted moving average.
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