Centerville Bikes and Stuff (CBS) sells motorcycles and accessories. The number of helmets sold by CBS per week for the past six weeks follows. Week 1 2 3 4 5 6 Value 17 12 14 10 16 13 (a) Construct a time series plot. A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 17), go down and right to (2, 12), go up and right to (3, 14), go down and right to (4, 10), go up and right to (5, 16), and go down and right to stop at (6, 13). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 15), go down and right to (2, 10), go up and right to (3, 12), go down and right to (4, 8), go up and right to (5, 14), and go down and right to stop at (6, 11). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 11), go up and right to (2, 14), go down and right to (3, 8), go up and right to (4, 12), go down and right to (5, 10), and go up and right to stop at (6, 15). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 13), go up and right to (2, 16), go down and right to (3, 10), go up and right to (4, 14), go down and right to (5, 12), and go up and right to stop at (6, 17). What type of pattern exists in the data? The data appear to follow a horizontal pattern.The data appear to follow a seasonal pattern. The data appear to follow a trend pattern.The data appear to follow a cyclical pattern. (b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.) Week Time Series Value Forecast 1 17 2 12 3 14 4 10 5 16 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (c) Use ? = 0.2 to compute the exponential smoothing values for the time series. Week Time Series Value Forecast 1 17 2 12 3 14 4 10 5 16 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (Round your answer to two decimal places.) (d) Compare the three-week moving average forecast with the exponential smoothing forecast using ? = 0.2. Which appears to provide the better forecast based on MSE? Explain. The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.The exponential smoothing using ? = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach. The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach.The exponential smoothing using ? = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. (e) Use ? = 0.4 to compute the exponential smoothing values for the time series. Week Time Series Value Forecast 1 17 2 12 3 14 4 10 5 16 6 13 Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. The exponential smoothing using ? = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using ? = 0.2.The exponential smoothing using ? = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using ? = 0.2. The exponential smoothing using ? = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using ? = 0.4.The exponential smoothing using ? = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using ? = 0.4.

Centerville Bikes and Stuff (CBS) sells motorcycles and accessories. The number of helmets sold by CBS per week for the past six weeks follows. Week 1 2 3 4 5 6 Value 17 12 14 10 16 13 (a) Construct a time series plot. A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 17), go down and right to (2, 12), go up and right to (3, 14), go down and right to (4, 10), go up and right to (5, 16), and go down and right to stop at (6, 13). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 15), go down and right to (2, 10), go up and right to (3, 12), go down and right to (4, 8), go up and right to (5, 14), and go down and right to stop at (6, 11). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 11), go up and right to (2, 14), go down and right to (3, 8), go up and right to (4, 12), go down and right to (5, 10), and go up and right to stop at (6, 15). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 13), go up and right to (2, 16), go down and right to (3, 10), go up and right to (4, 14), go down and right to (5, 12), and go up and right to stop at (6, 17). What type of pattern exists in the data? The data appear to follow a horizontal pattern.The data appear to follow a seasonal pattern. The data appear to follow a trend pattern.The data appear to follow a cyclical pattern. (b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.) Week Time Series Value Forecast 1 17 2 12 3 14 4 10 5 16 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (c) Use ? = 0.2 to compute the exponential smoothing values for the time series. Week Time Series Value Forecast 1 17 2 12 3 14 4 10 5 16 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (Round your answer to two decimal places.) (d) Compare the three-week moving average forecast with the exponential smoothing forecast using ? = 0.2. Which appears to provide the better forecast based on MSE? Explain. The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.The exponential smoothing using ? = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach. The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach.The exponential smoothing using ? = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. (e) Use ? = 0.4 to compute the exponential smoothing values for the time series. Week Time Series Value Forecast 1 17 2 12 3 14 4 10 5 16 6 13 Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. The exponential smoothing using ? = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using ? = 0.2.The exponential smoothing using ? = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using ? = 0.2. The exponential smoothing using ? = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using ? = 0.4.The exponential smoothing using ? = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using ? = 0.4.

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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Related questions

Question

Centerville Bikes and Stuff (CBS) sells motorcycles and accessories. The number of helmets sold by CBS per week for the past six weeks follows.

Week	1	2	3	4	5	6
Value	17	12	14	10	16	13

(a)

Construct a time series plot.

A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows.

The segments start at (1, 17),
go down and right to (2, 12),
go up and right to (3, 14),
go down and right to (4, 10),
go up and right to (5, 16),
and go down and right to stop at (6, 13).

The segments start at (1, 15),
go down and right to (2, 10),
go up and right to (3, 12),
go down and right to (4, 8),
go up and right to (5, 14),
and go down and right to stop at (6, 11).

The segments start at (1, 11),
go up and right to (2, 14),
go down and right to (3, 8),
go up and right to (4, 12),
go down and right to (5, 10),
and go up and right to stop at (6, 15).

The segments start at (1, 13),
go up and right to (2, 16),
go down and right to (3, 10),
go up and right to (4, 14),
go down and right to (5, 12),
and go up and right to stop at (6, 17).

What type of pattern exists in the data?

The data appear to follow a horizontal pattern.The data appear to follow a seasonal pattern. The data appear to follow a trend pattern.The data appear to follow a cyclical pattern.

(b)

Develop the three-week moving average for this time series. (Round your answers to two decimal places.)

Week	Time Series Value	Forecast
1	17
2	12
3	14
4	10
5	16
6	13

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7?

(c)

Use ? = 0.2 to compute the exponential smoothing values for the time series.

Week	Time Series Value	Forecast
1	17
2	12
3	14
4	10
5	16
6	13

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

(d)

Compare the three-week moving average forecast with the exponential smoothing forecast using

? = 0.2.

Which appears to provide the better forecast based on MSE? Explain.

The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.The exponential smoothing using ? = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach. The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach.The exponential smoothing using ? = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach.

(e)

Use ? = 0.4 to compute the exponential smoothing values for the time series.

Week	Time Series Value	Forecast
1	17
2	12
3	14
4	10
5	16
6	13

Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.

The exponential smoothing using ? = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using ? = 0.2.The exponential smoothing using ? = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using ? = 0.2. The exponential smoothing using ? = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using ? = 0.4.The exponential smoothing using ? = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using ? = 0.4.

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