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.

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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