The following table, reproduced from the chapter introduction, presents the inflation rate and unemployment rate, both in percent, for the years 1981-2008. Year Inflation Unemployment Year Inflation Unemployment 1981 8.9 7.6 1995 2.5 5.6 1982 3.8 9.7 1996 3.3 5.4 1983 3.8 9.6 1997 1.7 4.9 1984 3.9 7.5 1998 1.6 4.5 1985 3.8 7.2 1999 2.7 4.2 1986 1.1 7.0 2000 3.4 4.0 1987 4.4 6.2 2001 1.6 4.7 1988 4.4 5.5 2002 2.4 5.8 1989 4.6 5.3 2003 1.9 6.0 1990 6.1 5.6 2004 3.3 5.5 1991 3.1 6.8 2005 3.4 5.1 1992 2.9 7.5 2006 2.5 4.6 1993 2.7 6.9 2007 4.1 4.6 1994 2.7 6.1 2008 0.1 5.8 Source: Bureau of Labor Statistics We will investigate some methods for predicting unemployment. First, we will try to predict the unemployment rate from the inflation rate. 1. Construct a scatterplot of unemployment versus inflation 2. Compute the leastsquares line for predicting unemployment from inflation. Page 532 . Do you detect any strong nonlinearity? 3. Predict the unemployment in a year when inflation is 3.0%. 4. Compute the correlation coefficient between inflation and unemployment. The relationship between inflation and unemployment is not very strong. However, if we are interested in predicting unemployment, we would probably want to predict next year's unemployment from this year's inflation. We can construct an equation to do this by matching each year's inflation with the next year's unemployment, as shown in the following table. This Year's Next Year's This Year's Next Year's Year Inflation Unemployment Year Inflation Unemployment 1981 8.9 9.7 1995 2.5 5.4 1982 3.8 9.6 1996 3.3 4.9 1983 3.8 7.5 1997 1.7 4.5 1984 3.9 7.2 1998 1.6 4.2 1985 3.8 7.0 1999 2.7 4.0 1986 1.1 6.2 2000 3.4 4.7 1987 4.4 5.5 2001 1.6 5.8 1988 4.4 5.3 2002 2.4 6.0 1989 4.6 5.6 2003 1.9 5.5 1990 6.1 6.8 2004 3.3 5.1 1991 3.1 7.5 2005 3.4 4.6 1992 2.9 6.9 2006 2.5 4.6 1993 2.7 6.1 2007 4.1 5.8 1994 2.7 5.6 Source: Bureau of Labor Statistics 5. Compute the leastsquares line for predicting next year's unemployment from this year's inflation. 6. Predict next year's unemployment if this year's inflation is 3.0%. 7. Compute the correlation coefficient between this year's inflation and next year's unemployment. If we are going to use data from this year to predict unemployment next year, why not use this year's unemployment to predict next year's unemployment? A model like this, in which previous values of a variable are used to predict future values of the same variable, is called an autoregressive model. The following table presents the data needed to fit this model. This Year's Next Year's This Year's Next Year's Year Unemployment Unemployment Year Unemployment Unemployment 1981 7.6 9.7 1995 5.6 5.4 1982 9.7 9.6 1996 5.4 4.9 1983 9.6 7.5 1997 4.9 4.5 1984 7.5 7.2 1998 4.5 4.2 1985 7.2 7.0 1999 4.2 4.0 1986 7.0 6.2 2000 4.0 4.7 1987 6.2 5.5 2001 4.7 5.8 1988 5.5 5.3 2002 5.8 6.0 1989 5.3 5.6 2003 6.0 5.5 1990 5.6 6.8 2004 5.5 5.1 1991 6.8 7.5 2005 5.1 4.6 1992 7.5 6.9 2006 4.6 4.6 1993 6.9 6.1 2007 4.6 5.8 1994 6.1 5.6 Source: Bureau of Labor Statistics 8. Compute the leastsquares line for predicting next year's unemployment from this year's unemployment. 9. Predict next year's unemployment if this year's unemployment is 5.0%. 10. Compute the correlation coefficient between this year's unemployment and next year's unemployment. 11. Which of the three models do you think provides the best prediction of unemployment, the one using inflation in the same year, the one using inflation in the previous year, or the one using unemployment in the previous year? Explain. Year Inflation Unemploym Next year's Unemployment 1981 8.9 7.6 9.7 1982 3.8 9.7 9.6 1983 3.8 9.6 7.5 1984 3.9 7.5 7.2 1985 3.8 7.2 7 1986 1.1 7 6.2 1987 4.4 6.2 5.5 1988 4.4 5.5 5.3 1989 4.6 5.3 5.6 1990 6.1 5.6 6.8 1991 3.1 6.8 7.5 1992 2.9 7.5 6.9 1993 2.7 6.9 6.1 1994 2.7 6.1 5.6 1995 2.5 5.6 5.4 1996 3.3 5.4 4.9 1997 1.7 4.9 4.5 1998 1.6 4.5 4.2 1999 2.7 4.2 4 2000 3.4 4 4.7 2001 1.6 4.7 5.8 2002 2.4 5.8 6 2003 1.9 6 5.5 2004 3.3 5.5 5.1 2005 3.4 5.1 4.6 2006 2.5 4.6 4.6 2007 4.1 4.6 5.8 2008 0.1 5.8