1. The following data show U.S. retail sales of canoes from 1991 through 2008, with data in thousands of boats. Source: National Marine Manufacturers Association, 2008 Recreational Boating Statistical Abstract, p. 72.
Sales Sales
Year (thousands) Year (thousands)
|
1991
|
72.3
|
2000
|
111.8
|
|
1992
|
78.0
|
2001
|
105.8
|
|
1993
|
89.7
|
2002
|
100.0
|
|
1994
|
99.8
|
2003
|
86.7
|
|
1995
|
97.8
|
2004
|
93.9
|
|
1996
|
92.9
|
2005
|
77.2
|
|
1997
|
103.6
|
2006
|
99.9
|
|
1998
|
107.8
|
2007
|
99.6
|
|
1999
|
121.0
|
2008
|
73.7
|
a. Construct a graph of the time series. Does the overall trend appear to be upward or downward?
b. Construct a three-year centered moving average for this series.
c. Using the constant a 5 0.3, ?t an exponentially smoothed curve to the original time series.
d. Repeat part (c) using a 5 0.7. How has the new value for the constant affected the smoothness of the ?tted curve?