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 smaller for a weighted moving average than for an unweighted moving average? Why or why not? Problem 15-08Refer again to the gasoline sales time series data in Table 15.1.GASOLINE SALES TIME SERIESWeekSales (1000s of gallons)172321192318456.1672081822102015221112 a. 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. Userounded for two decimal places values for intermediate colculations.Weighted MovingForecast(Error)2WeekSalesAverage ForecastError117221319423518616720818922102011151222Totalb. 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 unweightedmoving average is 10.22. Round your answer to two decimal places.MSE =

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Description: 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 smaller for a weighted moving average than for an unweighted moving average? Why or why not? Problem 15-08Refer aga

Given, Gasoline sales time series data: We have to use the weight of 1/2 for the most recent…

Answered: Suppose you are allowed to choose any…

Math

Advanced Math

Suppose you are allowed to choose any weights

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

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 smaller for a weighted moving average than for an unweighted moving average? Why or why not?

Problem 15-08
Refer again to the gasoline sales time series data in Table 15.1.
GASOLINE SALES TIME SERIES
Week
Sales (1000s of gallons)
17
2
3
21
19
23
18
4
5
6.
16
7
20
8
18
22
10
20
15
22
11
12

a. 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.
Weighted Moving
Forecast
(Error)2
Week
Sales
Average Forecast
Error
1
17
2
21
3
19
4
23
5
18
6
16
7
20
8
18
9
22
10
20
11
15
12
22
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 =

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