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
|
Year
|
Real HousePrice Index
|
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
|
109.0
|
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?