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

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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.)

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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