Following table gives annual data on the Consumer Price Index (CPI) and the Wholesale Price Index (WPI), also called Producer Price Index (PPI), for the U.S. economy for the period 1980€“2006.

a. Plot the CPI on the vertical axis and the WPI on the horizontal axis. A priori, what kind of relationship do you expect between the two indexes? Why?
b. Suppose you want to predict one of these indexes on the basis of the other index. Which will you use as the regressand and which as the regressor? Why?
c. Run the regression you have decided in (b). Show the standard output. Test the hypothesis that there is a one-to-one relationship between the two indexes.
d. From the residuals obtained from the regression in (c), can you entertain the hypothesis that the true error term is normally distributed? Show the tests you use.

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PPI (Total Finished Goods) CPI Total 1980 1981 88.0 82.4 90.9 96.1 1982 96.5 100.0 1983 99.6 101.6 103.9 1984 103.7 1985 107.6 104.7 103.2 105.4 1986 109.6 1987 1988 113.6 118.3 108.0 113.6 1989 124.0 1990 130.7 119.2 1991 136.2 121.7 1992 123.2 140.3 1993 144.5 124.7 1994 148.2 125.5 127.9 152.4 1995 1996 156.9 131.3 1997 160.5 131.8 130.7 1998 163.0 1999 166.6 133.0 2000 172.2 138.0 177.1 2001 140.7 2002 179.9 138.9 2003 184.0 143.3 188.9 2004 148.5 2005 195.3 155.7 2006 201.6 160.3