please see attached

9. KEYNES MINICASE

John Maynard Keynes hypothesized that household income was the primary determinant of household spending. To test his theory, 9 regions were selected within the United States based upon average disposable income levels.

The scaled income levels for these regions were 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 and 5.0. Per capita household spending was recorded for each region. The results are given below and are stored in a file called KEYNES.mtw.

ROW

Average

Disposable

Income Levels

Per Capita

Household

Spending

X

Y

1

0.5

4.21

2

1.0

5.93

3

1.5

7.30

4

2.0

8.32

5

2.5

10.64

6

3.0

11.50

7

3.5

11.80

8

4.0

11.95

9

5.0

11.90

Using Minitab, the following information was obtained:

  1. The least square regression line for predicting consumer spending from income is:

Y= 4.563 + 1.847Xˆ

  1. SSR = 58.748 and SST = 68.891

  1. Fitted Line Plot and Residual Plot

  1. The analysis of variance table is of the form:

Source

Degrees of Freedom

Sum of Squares

Mean Squares

Regression

Error

Total

Complete the table and test whether there is a linear regression relationship between consumer spending and income. Discuss.

  1. What is the percentage of variation in consumer spending that is explained by income?

  1. What is the correlation coefficient between Income and Spending?

  1. Compute the standard error of estimate and interpret.

  1. Compute the predicted spending when income is 0, 3, 5, and 6 units.

  2. Does the assumption of a linear model appear to be valid?

Support your answer using the fitted line plots and the residual plots.




10. MEAT MINICASE

An analyst wanted to study the total consumption of processed meats in the U.S. for a period of 12 years. He was able to obtain data on:

Total consumption of processed meat

=

TOTCON

Consumption expenditure on food

Ratio of consumer price indexes of

=

FDEXP

processed meat to all meats

=

RELIND

The data are stored in the file MEAT.MTW, and are tabulated on the following page. TOTCON is in billions of pounds. FDEXP is in billions of constant dollars.

The rationale behind the choice of variables should be apparent. You would expect the consumption of processed meat to be affected by the total expenditure on food. You would also expect that consumption will be affected by the price of processed meat relative to the price of all meats. The variable RELIND (relative index) is a measure of the relative prices of processed meat to all meats.

Before doing any analysis, and to make sure that you have understood the background of the problem,write down the algebraic signs of the regression coefficients that you expect to find when you fit the model

TOTCON = β0 + β1(FDEXP) + β2(RELIND) + ε

to the data. In other words, from what you know about economics, what do you expect the signs of β0, β1 and β2 to be? Plus or minus?










  1. DATA

ROW

TOTCON

FDEXP

RELIND

1

12.572

100.074

0.959

2

11.497

104.470

1.015

3

11.541

107.580

1.062

4

12.813

109.608

1.000

5

13.359

114.213

0.979

6

13.256

115.926

0.979

7

13.741

118.831

0.986

8

15.261

118.916

0.900

9

13.616

112.079

0.941

10

12.219

120.293

1.004

11

14.324

118.912

0.981

12

11.902

121.151

1.079

  1. MINITAB REGRESSION RESULTS

  1. Regression Analysis of TOTCON ON FDEXP

Predictor Coef SE Coef T P

Constant 3.080 4.614 0.67 0.519

FDEXP 0.08756 0.04028 2.17 0.055

Analysis of Variance

Source DF SS MS F P

Regression 1 4.4112 4.4112 4.73 0.055

Residual Error 10 9.3353 0.9335

Total 11 13.7464




  1. Regression Analysis of TOTCON on RELIND

Predictor Coef SE Coef T P

Constant 31.564 4.258 7.41 0.000

RELIND -18.651 4.295 -4.34 0.001

Analysis of Variance

Source DF SS MS F P

Regression 1 8.9834 8.9834 18.86 0.001

Residual Error 10 4.7631 0.4763

Total 11 13.7464

  1. Regression Analysis of TOTCON on FDEXP and RELIND

Predictor Coef SE Coef T P

Constant 21.890 3.762 5.82 0.000

FDEXP 0.07214 0.01893 3.81 0.004

RELIND -17.211 2.826 -6.09 0.000

Analysis of Variance

Source DF SS MS F P

Regression 2 11.9239 5.9619 29.44 0.000

Residual Error 9 1.8226 0.2025

Total 11 13.7464






  1. Write down the fitted regression connecting TOTCON and FDEXP. What percentage of variation in total consumption of processed meat can be explained by expenditure on food along? What is the standard error of estimate?

  1. Write down the fitted regression connecting total consumption of processed meat and the relative price index (RELIND) of the processed meat to the price of all meats. What percentage of the variation is explained by the relative index? What is the standard error of estimate?

  1. Write down the fitted regression connecting total consumption, food expenditure and the relative index. What percentage of the variation in total consumption can be explained by these two variables? What is the standard error of estimate?

  1. Of the three fitted models, which would you use for forecasting the total consumption of processed meat? Justify your answer.