You collect data on 26 metropolitan areas to analyze average monthly debt paymen

Question

You collect data on 26 metropolitan areas to analyze average monthly debt payments in terms of income and the unemployment rate. The data are shown in the accompanying table. Use Table 4 Income (in $1,000s) Unemployment Metropolitan Area Washington, D.C. Seattle Baltimore Boston Denver San Francisco San Diego Sacramento Los Angeles Chicago Philadelphia Minneapolis New York Atlanta Dallas Phoenix Portland Cincinnati Houston Columbus St. Louis Miami Detroit Cleveland Tampa Pittsburgh Debt 63% $103.5 81.7 82.2 89.5 75.9 93.4 75.5 73.1 68.2 75.1 78.3 84.0 78.3 71.8 68.3 66.6 71.2 69.5 65.1 68.6 68.3 60.2 69.8 64.8 59.4 63.0 $1,285 1,135 1,133 1,133 1,104 1,098 1,076 1,045 1,024 1,017 1,011 1,011 989 986 970 957 948 920 889 8.1 10.6 12.4 12.9 7.0 10.3 10.2 886 867 832 812 791 763 14.5 15.7 12.6 SOURCE: eFannieMae.com; bls.com; and Experian.com Click here for the Excel Data File

Explanation / Answer

Linear Model:-

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.8676

R Square

0.7527

Adjusted R Square

0.7312

Standard Error

64.6098

Observations

26

ANOVA

df

SS

MS

F

Significance F

Regression

2

292170.7719

146085.3860

34.9954

0.0000

Residual

23

96011.6896

4174.4213

Total

25

388182.4615

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

198.9956

156.3619

1.2727

0.2159

-124.4637

522.4548

Income
(in $1,000s)

10.5122

1.4765

7.1195

0.0000

7.4577

13.5666

Unemployment

0.6186

6.8679

0.0901

0.9290

-13.5888

14.8259

Quadratic Model: -

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.8793

R Square

0.7731

Adjusted R Square

0.7422

Standard Error

63.2743

Observations

26

ANOVA

df

SS

MS

F

Significance F

Regression

3

300102.448

100034.149

24.986

0.000

Residual

22

88080.013

4003.637

Total

25

388182.462

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-264.6230

363.2413

-0.7285

0.4740

-1017.9393

488.6932

Income
(in $1,000s)

11.4821

1.6018

7.1682

0.0000

8.1601

14.8040

Unemployment

73.9527

52.5339

1.4077

0.1732

-34.9960

182.9014

Unemployment^2

-3.2393

2.3014

-1.4075

0.1732

-8.0121

1.5335

a-1)

Debt=198.9956+10.5122*Inc+0.6186*Unemp

a-2)

No

c-1)

Debt=-264.6230+11.4821*Inc+73.9527*Unemp-3.239*Unemp^2

c-2)

With the t-tests, we cannot conclude that Unemp and Unemp^2 are jointly significant

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.8676

R Square

0.7527

Adjusted R Square

0.7312

Standard Error

64.6098

Observations

26

ANOVA

df

SS

MS

F

Significance F

Regression

2

292170.7719

146085.3860

34.9954

0.0000

Residual

23

96011.6896

4174.4213

Total

25

388182.4615

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

198.9956

156.3619

1.2727

0.2159

-124.4637

522.4548

Income
(in $1,000s)

10.5122

1.4765

7.1195

0.0000

7.4577

13.5666

Unemployment

0.6186

6.8679

0.0901

0.9290

-13.5888

14.8259

Quadratic Model: -

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.8793

R Square

0.7731

Adjusted R Square

0.7422

Standard Error

63.2743

Observations

26

ANOVA

df

SS

MS

F

Significance F

Regression

3

300102.448

100034.149

24.986

0.000

Residual

22

88080.013

4003.637

Total

25

388182.462

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-264.6230

363.2413

-0.7285

0.4740

-1017.9393

488.6932

Income
(in $1,000s)

11.4821

1.6018

7.1682

0.0000

8.1601

14.8040

Unemployment

73.9527

52.5339

1.4077

0.1732

-34.9960

182.9014

Unemployment^2

-3.2393

2.3014

-1.4075

0.1732

-8.0121

1.5335

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