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 Metropolitan Area (in $1,000s) Unemployment et Washington, D.C. Seattle Baltimore Boston S1,285 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 $103.5 6.3% 82.2 89.5 75.9 93.4 75.5 73.1 68.2 75.1 78.3 84.0 78.3 San Francisco San Diego Sacramento Los Angeles Chicago Philadelphia Minneapolis New York Atlanta Dallas Phoenix Portland Cincinnat Houston Columbus St. Louis Miami Detroit Cleveland Tampa 12.4 12.9 68.3 66.6 71.2 69.5 65.1 68.6 68.3 60.2 69.8 64.8 59.4 10.2 920 889 886 867 832 791 763 12.6 SOURCE: eFannieMae.com; bls.com; and Experian.com. for the a-1. Estimate the model Debt cB2Unemp+. (Round your answers to 4 decimal places.) Debt 198.99510.5122 In+0.6186 Une mp a-2. Is unemployment significant at the 5% level? c-1. Estimate Debt Bo +BInc B2Unemp +BaUnemp2 (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) ebt-264.62311.4821 Inc73.9527 Unemp + c-2. Determine if Unemp and Unemp? are jointly significant at the 5% level With the t-tests, we conclude that Unemp and Unemp are jointly significant. With the t-tests, we cannot conclude that Unemp and Unemp are jointly significant. With the partial Ftest, we conclude that Unemp and Unemp are jointly significant. With the partial F-test, we cannot conclude that Unemp and Unemp2 are jointly significant.

Answer 1

a-1)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.867561816
R Square	0.752663505
Adjusted R Square	0.731155983
Standard Error	64.60976155
Observations	26
ANOVA
	df	SS	MS	F	Significance F
Regression	2	292170.7719	146085.386	34.99536244	1.05394E-07
Residual	23	96011.68963	4174.421288
Total	25	388182.4615
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	198.9955611	156.3619079	1.272660099	0.215853972	-124.4636877	522.4548099
Income	10.51215911	1.47652528	7.119525312	2.98439E-07	7.457733866	13.56658435
Unemployment	0.618572208	6.867902274	0.090067124	0.929013632	-13.58876602	14.82591043

a-2) No, because p-value of t-test statistic is not significant(>0.05)

c-1)

Regression Statistics
Multiple R	0.879258984
R Square	0.77309636
Adjusted R Square	0.742154955
Standard Error	63.27429948
Observations	26
ANOVA
	df	SS	MS	F	Significance F
Regression	3	300102.4481	100034.1494	24.98581914	2.82564E-07
Residual	22	88080.01345	4003.636975
Total	25	388182.4615
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-264.6230355	363.2412507	-0.728504912	0.473988523	-1017.939279	488.6932081
Income	11.48205201	1.601799738	7.168219437	3.47378E-07	8.160122693	14.80398133
Unemployment	73.95267632	52.5339168	1.407712975	0.173189616	-34.99599838	182.901351
Uemploy^2	-3.239278119	2.301405229	-1.407521839	0.173245547	-8.01210042	1.533544181

c-2) Hypothesis test:

$H_0:\beta =0$ , $H_a:\beta \neq 0$

$\alpha =0.05$

Test statistic: Unemp= 1.4077 and p-value= 0.17319

Unemp^2= -1.4075 and p-value= 0.1732455

Both are not significant to significant value 0.05 and reject H0. So, we cannot conclude that Unemp and Unemp^2 are jointly significant to dept.

Answer: B