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The accompanying table, compiled by economists Karl Case and Robert Shiller, lists average U.S. housing prices (in the form of a real, inflation- adjusted index) from 1975 to 2010.
Year
Real HousePrice Index
1975
104.4
1987
118.3
1999
119.5
1976
105.2
1988
122.5
2000
126.6
1977
110.5
1989
125.3
2001
133.5
1978
117.1
1990
121.0
2002
143.4
1979
120.5
1991
114.1
2003
154.5
1980
114.5
1992
111.5
2004
171.4
1981
109.0
1993
2005
191.0
1982
105.1
1994
109.3
2006
194.7
1983
105.4
1995
108.2
2007
181.1
1984
105.5
1996
107.6
2008
146.1
1985
107.5
1997
108.6
2009
130.3
1986
112.7
1998
113.4
2010
128.2
a. Using the years 1975 to 2006 (and denoting the time variable by the integers 1 to 32 for simplicity), estimate the linear time trend of housing prices. Use the same data to estimate an exponential trend. How well does either trend fit the data?
b. Now estimate two separate linear regressions-one for years 1975 to 1996 and one for 1996 to 2006. Does dividing the time series in this way make sense? How much predictive confidence would you put in the time-series regression estimated for 1996 to 2006?
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