The Bcchtal Tire Company (BTC) is a supplier of automotive tires for U.S. car companies. BTC has hired you to analyze its sales. Data from 1976Q1 through 2007Q4 are given in the following table (in thousands of units):

a. Write a report to Bechtal Tire Company in which you explain what a time-series de-composition analysis shows about its tire sales. Include in your discussion seasonal, cyclical, and trend components. Show the raw data, the deseasonalized data, and the long-term trend on one time-series plot. Also provide a plot of the cycle factor with a projection through 2008.
b. In the last section of your report, show a time-series graph with the actual data and the values that the time-series decomposition model would predict for each quarter from 1986Q3 through 2007Q4, along with a forecast for 2008. If actual sales for 2008 were Ql = 1,445.1, Q2 = 1,683.8, Q3 = 1,586.6, and Q4 = 1,421.3, what RMSE would result from your 2008 forecast?

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BTC Sales of Tires Year Q2 91 о» 1,926 1,656 1,987 2,147 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2,029 1,783 1,974 2,347 2,190 2,276 2,517 2.229 1,546 2,718 2,138 1,709 2,376 2,538 2,727 2,231 1,551 1,576 1,535 1,876 2,251 2,273 2,162 1.49 2,425 2,524 2,451 1,752 1,506 2,025 2,128 2,027 2,155 1,850 1,733 1,401 1,456 1,994 2,042 1,898 1,669 1,927 1,734 1,9702,002 2,081 2,140 1,971 1,515 1,618 1,327 2,122 2,223 2,270 1,875 1,666 1,282 1,494 1,813 1,852 1,672 1,827 1,561 1,763 1,454 1,560 1,973 2,076 2,019 1,878 1,855 2,218 2,247 1,878 1,787 1,898 1,752 1,707 1,706