?Locate the?Case Study: How Are Inflation and Unemployment Related??in your textbook on pages 531-532. You will use the data given in the problem to make a complete regression analysis and then predictions based on your analysis. For your convenience, the data sets given in this problem are also given here as an Excel spreadsheet:?Inflation-Unemployment Data (Excel). You can use Excel or a TI calculator to work this problem.

1. Answer the questions 1 through 11 and type your answers on a Word document. Any Excel output, including graphs or numerical summaries, should be cut and paste on the same Word document as your answers.

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 least?squares 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 least?squares 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 least?squares 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.