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 $103.5 $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 63% 82.2 89.5 75.9 93.4 75.5 73.1 68.2 75.1 78.3 84.0 78.3 9.3 10.6 12.4 12.9 9.7 9.2 7.0 9.3 10.3 68.3 66.6 10.2 69.5 65.1 68.6 68.3 60.2 69.8 64.8 59.4 63.0 8.7 14.5 15.7 9.6 12.6 886 867 832 812 791 763 SOURCE: eFannieMae.com; bls.com; and Experian.com Click here for the Excel Data File a-1. Estimate the model Debt-Ao + Anc + 2Unemp + . (Round your answers to 4 decimal places.) Debt= 198.9956 + 10.5122 Inc + 0.6186 Unemp

Explanation / Answer

### By using R command

> Inc=c(103.5,81.7,82.2,89.5,75.9,93.4,75.5,73.1,68.2,75.1,78.3,84,78.3,71.8,68.3,66.6,71.2,69.5,65.1,68.6,68.3,60.2,69.8,64.8,59.4,63)
> Inc
[1] 103.5 81.7 82.2 89.5 75.9 93.4 75.5 73.1 68.2 75.1 78.3 84.0
[13] 78.3 71.8 68.3 66.6 71.2 69.5 65.1 68.6 68.3 60.2 69.8 64.8
[25] 59.4 63.0
> Une=c(6.3,8.5,8.1,7.6,8.1,9.3,10.6,12.4,12.9,9.7,9.2,7,9.3,10.3,8.4,9.1,10.2,9.3,8.7,8.3,9.9,14.5,15.7,9.6,12.6,8.3)
> Une
[1] 6.3 8.5 8.1 7.6 8.1 9.3 10.6 12.4 12.9 9.7 9.2 7.0 9.3 10.3 8.4
[16] 9.1 10.2 9.3 8.7 8.3 9.9 14.5 15.7 9.6 12.6 8.3
> Debt=c(1285,1135,1133,1133,1104,1098,1076,1045,1024,1017,1011,1011,989,986,970,957,948,920,889,888,886,867,832,812,791,763)
> Debt
[1] 1285 1135 1133 1133 1104 1098 1076 1045 1024 1017 1011 1011 989 986 970
[16] 957 948 920 889 888 886 867 832 812 791 763
> fit=lm(Debt~Inc+Une)
> fit

Call:
lm(formula = Debt ~ Inc + Une)

Coefficients:
(Intercept) Inc Une  
198.9956 10.5122 0.6186  

> summary(fit)

Call:
lm(formula = Debt ~ Inc + Une)

Residuals:
Min 1Q Median 3Q Max
-110.456 -38.454 -5.836 51.156 102.121

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 198.9956 156.3619 1.273 0.216   
Inc 10.5122 1.4765 7.120 2.98e-07 ***
Une 0.6186 6.8679 0.090 0.929   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 64.61 on 23 degrees of freedom
Multiple R-squared: 0.7527, Adjusted R-squared: 0.7312
F-statistic: 35 on 2 and 23 DF, p-value: 1.054e-07

a1) Debt= 198.9956 + 10.5122 *Inc+ 0.6186*Une

a2) The Coefficient of slope of Unemployment is 0.929 which indicates that Unemploymen is not significant at 5% level of significance.

### Using r command

> fit1=lm(Debt~Inc+Une+I(Une^2))
> fit1

Call:
lm(formula = Debt ~ Inc + Une + I(Une^2))

Coefficients:
(Intercept) Inc Une I(Une^2)  
-264.623 11.482 73.953 -3.239  

> summary(fit1)

Call:
lm(formula = Debt ~ Inc + Une + I(Une^2))

Residuals:
Min 1Q Median 3Q Max
-117.395 -46.847 0.902 51.981 110.648

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) -264.623 363.241 -0.729 0.474   
Inc 11.482 1.602 7.168 3.47e-07 ***
Une 73.953 52.534 1.408 0.173   
I(Une^2) -3.239 2.301 -1.408 0.173   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 63.27 on 22 degrees of freedom
Multiple R-squared: 0.7731, Adjusted R-squared: 0.7422
F-statistic: 24.99 on 3 and 22 DF, p-value: 2.826e-07

c1) Debt = -264.623 + 11.482 *inc+73.953*Une -3.239*Une2

c2) With partial F test we conclude that Unemployment and Unemployment^2 are jointly significant.

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