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 18 11 14 10 17 12 (a) Construct a time series plot. 20 18 10 8 6 4 2 0 + 16 14 12 W + 20 18 16 14 12 10 8 2 W 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 Week Week Week 20 18 16 14 12 10 H 20 18 16 14 12 Time Series Value 2086420 0 1 2 3 4 5 6 7 Week What type of pattern exists in the data? The data appear to follow a trend pattern. The data appear to follow a horizontal pattern. The data appear to follow a seasonal pattern. The data appear to follow a cyclical pattern. 9 7 (b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.) Week Time Series Forecast (c) Value 1 18 2 11 3 14 4 10 5 17 6 12 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? Use = 0.2 to compute the exponential smoothing values for the time series. Time Series Week Value 1 18 2 11 3 14 4 10 5 17 6 12 Forecast 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 exponential smoothing using = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. 0000 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 smaller MSE than the smoothing approach. The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach. (e) Use = 0.4 to compute the exponential smoothing values for the time series. Time Series Week Value 1 18 2 11 3 14 4 10 5 17 6 12 Forecast Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. 000 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 a = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using = 0.2. 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 = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.4.