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 Value 18 13 (a) Construct a time series plot. 20T 18 16- 14- Time Series Value O Week 1 2 3 4 5 6 What type of pattern exists in the data? O The data appear to follow a cyclical pattern. O The data appear to follow a trend pattern. 8 6 O The data appear to follow a seasonal pattern. O The data appear to follow a horizontal pattern. Week 1 2 0 1 3 4 5 6 18 13 15 12 (b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.) Time Series Value 16 14 18 + 2 13 15 4 5 6 15 12 16 3 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? 12 16 4 14 Week (c) Use a = 0.2 to compute the exponential smoothing values for the time series. Time Series Value 5 14 Forecast 6 Forecast 7 20 18 16 14 12 WE 10 2 + 7 @o 20 18 0 1 2 3 4 Week 5 6 00 0 1 2 3 4 5 Week 6 7 0° 20 18 16 14- 12- 10- 8 6 0 1 2 3 4 Week 5 6 7 0 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 a = 0.2. Which appears to provide the better forecast based on MSE? Explain. O The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach. O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. O The exponential smoothing using a = 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. (e) Use a = 0.4 to compute the exponential smoothing values for the time series. Time Series Value Week 1 2 3 5 6 18 13 15 12 16 14 Forecast Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. O The exponential smoothing using a = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.2. O The exponential smoothing using @ = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.4. O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.4. O The exponential smoothing using a = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.2.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter13: Regression And Forecasting Models
Section13.7: Exponential Smoothing Models
Problem 29P: The file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building...
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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
Value 18 13
(a) Construct a time series plot.
20T
18
16-
14-
Time Series Value
O
Week
1
2
3
4
5
6
What type of pattern exists in the data?
O The data appear to follow a cyclical pattern.
O The data appear to follow a trend pattern.
8
6
O The data appear to follow a seasonal pattern.
O The data appear to follow a horizontal pattern.
Week
1
2
0 1
3
4
5
6
18
13
15
12
(b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.)
Time Series
Value
16
14
18
+
2
13
15
4 5 6
15 12 16
3
Compute MSE. (Round your answer to two decimal places.)
MSE =
What is the forecast for week 7?
12
16
4
14
Week
(c) Use a = 0.2 to compute the exponential smoothing values for the time series.
Time Series
Value
5
14
Forecast
6
Forecast
7
20
18
16
14
12
WE
10
2 +
7
@o
20
18
0 1 2
3
4
Week
5
6
00
0 1 2
3 4 5
Week
6 7
0°
20
18
16
14-
12-
10-
8
6
0
1
2
3
4
Week
5
6
7
0
Transcribed Image Text: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 Value 18 13 (a) Construct a time series plot. 20T 18 16- 14- Time Series Value O Week 1 2 3 4 5 6 What type of pattern exists in the data? O The data appear to follow a cyclical pattern. O The data appear to follow a trend pattern. 8 6 O The data appear to follow a seasonal pattern. O The data appear to follow a horizontal pattern. Week 1 2 0 1 3 4 5 6 18 13 15 12 (b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.) Time Series Value 16 14 18 + 2 13 15 4 5 6 15 12 16 3 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? 12 16 4 14 Week (c) Use a = 0.2 to compute the exponential smoothing values for the time series. Time Series Value 5 14 Forecast 6 Forecast 7 20 18 16 14 12 WE 10 2 + 7 @o 20 18 0 1 2 3 4 Week 5 6 00 0 1 2 3 4 5 Week 6 7 0° 20 18 16 14- 12- 10- 8 6 0 1 2 3 4 Week 5 6 7 0
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 a = 0.2. Which appears to provide the better forecast based on MSE? Explain.
O The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.
O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach.
O The exponential smoothing using a = 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.
(e) Use a = 0.4 to compute the exponential smoothing values for the time series.
Time Series
Value
Week
1
2
3
5
6
18
13
15
12
16
14
Forecast
Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.
O The exponential smoothing using a = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.2.
O The exponential smoothing using @ = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.4.
O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.4.
O The exponential smoothing using a = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.2.
Transcribed Image Text: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 a = 0.2. Which appears to provide the better forecast based on MSE? Explain. O The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach. O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. O The exponential smoothing using a = 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. (e) Use a = 0.4 to compute the exponential smoothing values for the time series. Time Series Value Week 1 2 3 5 6 18 13 15 12 16 14 Forecast Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. O The exponential smoothing using a = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.2. O The exponential smoothing using @ = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.4. O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.4. O The exponential smoothing using a = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.2.
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