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```Table 6.1
Month 1 2 3 4 5 6 7
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Value 24 13 20 12 19 23 15

7. Refer to the gasoline sales time series table in 6.1.
a. Compute four - week and five-week moving averages for the first series.
b. Compute the MSE for the four-week and five-week moving average average forecasts.
c. What appears to be the best number of weels of past data (three, four, or five) to use in the moving average computation? Recall that the MSE for the three-week moving average is 10.22.
Use a = 0.2 to compute the exponential smoothing valuesfor the first series.
Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2.

9. With the gasoline time series data from Table 6.1, show the exponential smoothing forcasts using a = 0.1.
a. Apply the MSE measure of forecast accuracy, would you prefer a smoothing constant of a = 0.1 or a a =0.2 for the gasoline sales time series?
b. Are the results the same if you apply MAE as the measure of accuracy?
c. What are the results if Mape is used?

11. For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83.
a. Compare a time series plot. What type of pattern exsists in the data?
b. Compare a three-month moving average forecast with an exponential smoothing forecast for a = 0.2. Which provides the better forecasts using MSE as the measure of model accuracy?
c. What is the forecast for next month?

16. The Nielsen ratings (percentage of U.S. households that tuned in) for the Masters golf tournament from 1997 through 2008 follow (Golf Magazine, January 2009).
Year Rating
1997 11.2
1998 8.6
1999 7.9
2000 7.6
2001 10.7
2002 8.1
2003 6.9
2004 6.7
2005 8.0
2006 6.9
2007 7.6
2008 7.3
The rating of 11.2 in 1997 indicates 11.2% of U.S. households tumed into watch Tiger Woods win his first major golf tournament and become the first African American to Win the Masters. Tiger Woods also won the Masters in 2001, 2002, and 2005.
a. Construct a time series plot. What type of pattern exsists in the data? Discuss some of the factors that may have resulted in the pattern exhibited in the time series plot for this time series.
b. Given the pattern of the time series plot developed in part (a), do you think the forecasting methods discussed in this section are appropriate to develop forecasts for this time series? Explain.
c. Would you recommend using only the Nielsen ratings for 2002-2008 to forecast the rating for 2009, or should the entire time series from 1997 to 2008 be used? Explain.

19. Consider the following time series.
t 1 2 3 4 5 6 7
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Y1 120 110 100 96 94 92 88

a. Construct a time series plot. What type of pattern exsists in the date?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the t= 8?```