Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Week Sales (1,000s of gallons) 1 18 2 22 3 20 4 24 5 19 6 17 7 22 8 20 9 24 10 22 11 17 12 24 (a) Using a weight of 1 2 for the most recent observation, 1 3 for the second most recent observation, and 1 6 for 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 18 2 22 3 20 4 24 5 19 6 17 7 22 8 20 9 24 10 22 11 17 12 24 (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. The unweighted moving average is preferred because it has a larger MSE compared to the weighted moving average.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 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? No, an unweighted moving average always has a smaller MSE than a weighted moving average.Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. 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, a weighted moving average always has a smaller MSE than an unweighted moving average.
Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks. Week Sales (1,000s of gallons) 1 18 2 22 3 20 4 24 5 19 6 17 7 22 8 20 9 24 10 22 11 17 12 24 (a) Using a weight of 1 2 for the most recent observation, 1 3 for the second most recent observation, and 1 6 for 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 18 2 22 3 20 4 24 5 19 6 17 7 22 8 20 9 24 10 22 11 17 12 24 (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. The unweighted moving average is preferred because it has a larger MSE compared to the weighted moving average.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 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? No, an unweighted moving average always has a smaller MSE than a weighted moving average.Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. 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, a weighted moving average always has a smaller MSE than an unweighted moving average.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
Related questions
Question
Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.
Week | Sales (1,000s of gallons) |
---|---|
1 | 18 |
2 | 22 |
3 | 20 |
4 | 24 |
5 | 19 |
6 | 17 |
7 | 22 |
8 | 20 |
9 | 24 |
10 | 22 |
11 | 17 |
12 | 24 |
(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.)
1 |
2 |
1 |
3 |
1 |
6 |
Week | Time Series Value |
Weighted Moving Average Forecast |
---|---|---|
1 | 18 | |
2 | 22 | |
3 | 20 | |
4 | 24 | |
5 | 19 | |
6 | 17 | |
7 | 22 | |
8 | 20 | |
9 | 24 | |
10 | 22 | |
11 | 17 | |
12 | 24 |
(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.
The unweighted moving average is preferred because it has a larger MSE compared to the weighted moving average.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 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?
No, an unweighted moving average always has a smaller MSE than a weighted moving average.Yes, because an unweighted moving average is just a weighted moving average where the weights are equal. 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, a weighted moving average always has a smaller MSE than an unweighted moving average.
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