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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.

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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## Gasoline Sales Data ### Weekly Gasoline Sales in Bennington, Vermont The table below presents the number of gallons of gasoline (in thousands) sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. | Week | Sales (1,000s of gallons) | |------|--------------------------| | 1 | 19 | | 2 | 23 | | 3 | 21 | | 4 | 25 | | 5 | 20 | | 6 | 18 | | 7 | 22 | | 8 | 20 | | 9 | 24 | | 10 | 22 | | 11 | 17 | | 12 | 24 | This dataset is valuable for analyzing sales trends and patterns over a three-month period, which can assist in making informed decisions for inventory management, distribution strategies, and understanding seasonal or demand fluctuations in gasoline sales. Analyzing this data can also reveal peak weeks and dips in sales, which can be correlated with external factors such as holidays, weather conditions, or local events.
Transcribed Image Text:## Gasoline Sales Data ### Weekly Gasoline Sales in Bennington, Vermont The table below presents the number of gallons of gasoline (in thousands) sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. | Week | Sales (1,000s of gallons) | |------|--------------------------| | 1 | 19 | | 2 | 23 | | 3 | 21 | | 4 | 25 | | 5 | 20 | | 6 | 18 | | 7 | 22 | | 8 | 20 | | 9 | 24 | | 10 | 22 | | 11 | 17 | | 12 | 24 | This dataset is valuable for analyzing sales trends and patterns over a three-month period, which can assist in making informed decisions for inventory management, distribution strategies, and understanding seasonal or demand fluctuations in gasoline sales. Analyzing this data can also reveal peak weeks and dips in sales, which can be correlated with external factors such as holidays, weather conditions, or local events.
### Moving Averages and Mean Squared Error Calculation --- #### (a) Weighted Moving Average Calculation Using a weight of \( \frac{1}{2} \) for the most recent observation, \( \frac{1}{3} \) for the second most recent observation, and \( \frac{1}{6} \) for the third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.) | Week | Time Series Value | Weighted Moving Average Forecast | |------|--------------------|----------------------------------| | 1 | 19 | | | 2 | 23 | | | 3 | 21 | | | 4 | 25 | | | 5 | 20 | | | 6 | 18 | | | 7 | 22 | | | 8 | 20 | | | 9 | 24 | | | 10 | 22 | | | 11 | 17 | | | 12 | 24 | | --- #### (b) Mean Squared Error (MSE) Calculation 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. - [ ] The unweighted moving average is preferred because it has a smaller MSE compared to the weighted moving average. - [ ] The weighted moving average is preferred because it has a larger MSE compared to the unweighted moving average. - [ ] The unweighted moving average is preferred because it has a larger MSE compared to the weighted moving average. - [ ] The weighted moving average is preferred because it has a smaller MSE compared to the unweighted moving average. --- #### (c) Choosing Weights for Minimizing MSE 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? - [ ] **Yes,** a weighted moving average always has a smaller MSE than an
Transcribed Image Text:### Moving Averages and Mean Squared Error Calculation --- #### (a) Weighted Moving Average Calculation Using a weight of \( \frac{1}{2} \) for the most recent observation, \( \frac{1}{3} \) for the second most recent observation, and \( \frac{1}{6} \) for the third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.) | Week | Time Series Value | Weighted Moving Average Forecast | |------|--------------------|----------------------------------| | 1 | 19 | | | 2 | 23 | | | 3 | 21 | | | 4 | 25 | | | 5 | 20 | | | 6 | 18 | | | 7 | 22 | | | 8 | 20 | | | 9 | 24 | | | 10 | 22 | | | 11 | 17 | | | 12 | 24 | | --- #### (b) Mean Squared Error (MSE) Calculation 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. - [ ] The unweighted moving average is preferred because it has a smaller MSE compared to the weighted moving average. - [ ] The weighted moving average is preferred because it has a larger MSE compared to the unweighted moving average. - [ ] The unweighted moving average is preferred because it has a larger MSE compared to the weighted moving average. - [ ] The weighted moving average is preferred because it has a smaller MSE compared to the unweighted moving average. --- #### (c) Choosing Weights for Minimizing MSE 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? - [ ] **Yes,** a weighted moving average always has a smaller MSE than an
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