For data DEMOG, fit three simple linear regression models of the per capita income on each...

For data DEMOG, fit three simple linear regression models of the per capita income on each of the three predictor variables. Does a linear regression model appear to provide a good fit for each of the three predictor variables? Use all appropriate tests, descriptive measures, and plots to conclude your findings here. Which predictor variable leads to significant effect on the per capita income?

usborn cap.income home pop
Alabama 0.98656 21442 75.9 4040587
Alaska 0.93914 25675 34.0 550043
Arizona 0.90918 23060 34.2 3665228
Arkansas 0.98688 20346 67.1 2350725
California 0.74541 27503 46.4 29760021
Colorado 0.94688 28657 43.3 3294394
Connecticut 0.89761 37598 57.0 3287116
Delaware 0.95850 29814 50.2 666168
DC 0.88972 37278 39.3 606900
Florida 0.84932 25852 30.5 12937926
Georgia 0.96751 25020 64.5 6478216
Hawaii 0.81911 26137 56.1 1108229
Idaho 0.96322 21081 50.6 1006749
Illinois 0.89801 28873 69.1 11430602
Indiana 0.97848 24219 71.1 5544159
Iowa 0.98089 23925 77.6 2776755
Kansas 0.96944 24981 61.3 2477574
Kentucky 0.98856 21506 77.4 3685296
Louisiana 0.97371 21346 79.0 4219973
Maine 0.96208 22952 68.5 1227928
Maryland 0.92187 29943 49.8 4781468
Massachusetts 0.88732 32797 68.7 6016425
Michigan 0.95113 25857 74.9 9295297
Minnesota 0.96928 27510 73.6 4375099
Mississippi 0.98987 18958 77.3 2573216
Missouri 0.97952 24427 69.6 5117073
Montana 0.97708 20172 58.9 799065
Nebraska 0.97743 24754 70.2 1578385
Nevada 0.89650 27200 21.8 1201833
New.Hampshire 0.95268 29022 44.1 1109252
New.Jersey 0.85111 33937 54.8 7730188
New.Mexico 0.93406 19936 51.7 1515069
New.York 0.81116 31734 67.5 17990455
North.Carolina 0.97908 24036 70.4 6628637
North.Dakota 0.98026 21675 73.2 638800
Ohio 0.96953 25134 74.1 10847115
Oklahoma 0.97432 21072 63.5 3145585
Oregon 0.94060 24766 46.6 2842321
Pennsylvania 0.96227 26792 80.2 11881643
Rhode.Island 0.89000 26797 63.4 1003464
South.Carolina 0.98197 21309 68.4 3486703
South.Dakota 0.98541 22114 70.2 696004
Tennessee 0.98544 23559 69.2 4877185
Texas 0.89072 24957 64.7 16986510
Utah 0.95172 21019 67.2 1722850
Vermont 0.95951 24175 57.2 562758
Virginia 0.94037 27385 54.2 6187358
Washington 0.91964 27961 48.2 4866692
West.Virginia 0.98895 19362 77.3 1793477
Wisconsin 0.96958 25079 76.4 4891769
Wyoming 0.97770 23167 42.6 453588

Solutions

Expert Solution

using usborn as independent variable and cap.income as dependent variable following simple regression analysis information has been generated and usborn is significant as p-value is less than typical level of significance alpha=0.05

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.578098
R Square	0.334198
Adjusted R Square	0.32061
Standard Error	3489.541
Observations	51

ANOVA
	df	SS	MS	F	Significance F
Regression	1	299496027.8	299496027.8	24.59543	8.89146E-06
Residual	49	596668053.2	12176899.04
Total	50	896164081

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	68642.24	8739.004004	7.854698187	3.19E-10	51080.55319	86203.92
USborn	-46018.6	9279.115638	-4.959377652	8.89E-06	-64665.71938	-27371.6

using home as independent variable and cap.income as dependent variable following simple regression analysis information has been generated and home is significant

Regression Statistics
Multiple R	0.335561
R Square	0.112601
Adjusted R Square	0.094491
Standard Error	4028.609
Observations	51

ANOVA
	df	SS	MS	F	Significance F
Regression	1	100909370.3	100909370.3	6.217579	0.016073972
Residual	49	795254710.7	16229687.97
Total	50	896164081

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	31398.51	2482.61579	12.64734964	4.77E-17	26409.50679	36387.51
X Variable 1	-99.0825	39.73619742	-2.493507408	0.016074	-178.9353795	-19.2296

using pop as independent variable and cap.income as dependent variable following simple regression analysis information has been generated and pop is not significant as p-value is greater than typical level of significance alpha=0.05

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.240744
R Square	0.057958
Adjusted R Square	0.038733
Standard Error	4150.791
Observations	51

ANOVA
	df	SS	MS	F	Significance F
Regression	1	51939787.66	51939787.66	3.01466	0.0887991
Residual	49	844224293.3	17229067.21
Total	50	896164081

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	24456.22	784.1029691	31.19005546	5.56E-34	22880.50121	26031.93	22880.5	26031.93
X Variable 1	0.000187	0.000107922	1.73627776	0.088799	-2.94949E-05	0.000404	-2.9E-05	0.000404

orchestra answered 1 year ago

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