Barbara Lynch, the product manager for a line of skiwear produced by HeathCo Industries, has been working on developing sales forecasts for the skiwear that is sold under the Northern Slopes and Jacque Monri brands. She has had various regression-based forecasting models developed (see Exercises 7 and 8 in Chapter 4 and Exercises 6 and 7 in Chapter 5). Quarterly sales for 1998 through 2007 are as follows:

a. Prepare a time-series plot of the data, and on the basis of what you see in the plot, write a brief paragraph in which you explain what patterns you think are present in the sales series.
b. Smooth out seasonal influences and irregular movements by calculating the centered moving averages. Add the centered moving averages to the original data you plotted in part (a). Has the process of calculating centered moving averages been effective in smoothing out the seasonal and irregular fluctuations in the data? Explain.
c. Determine the degree of seasonality by calculating seasonal indices for each quarter of the year. Do this by finding the normalized average of the seasonal factors for each quarter, where the seasonal factors are actual sales divided by the centered moving average for each period. If you have done Exercise 7 in Chapter 5, explain how these seasonal indices compare with the seasonality identified by the regres¬sion model.
d. Determine the long-term trend in the sales data by regressing the centered moving average on time, where T = 1 for Mar-98. That is, estimate the values for bo and b for the following model:
CMAT = b0 + b1(T)
Plot this equation, called the centered moving-average trend (CMAT), along with the raw data and the CMA on the same plot developed in part (a),
e. Find the cycle factor (CF) for each quarter by dividing the CMA by the CMAT. Plot the cycle factors on a new graph and project (CF) forward through Dec-08.
f. Develop a forecast for Ms. Lynch for the four quarters of 2008 by calculating the product of the trend, the seasonal index, and the cycle factor. Given that actual sales (in thousands of dollars) were 334,271, 328,982, 317,921, and 350,118 for quarters 1 through 4, respectively, calculate the RMSE for this model based only on the 2008 forecast period.
g. If you have done Exercises 7 and 8 in Chapter 4 and Exercises 6 and 7 in Chapter 5, write a comparison of your findings.

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Quarterly Sales ($000) at End-Month of Quarter Year March June September December 81,921 117,129 153,907 100,144 180,440 202,415 211,780 182,556 253,142 218,755 257,156 202,568 289,321 266,095 315,011 142,161 151,402 128,497 220,818 200,135 243,700 253,653 229,879 322,052 301,479 72,962 2 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 97,729 114,159 123,242 162,665 163,710 198,990 225,422 224,482 262,938 264,939 145,592 176,076 174,200 313,769