This lab focuses on hypothesis testing. You will estimate models of life expecta

Question

This lab focuses on hypothesis testing. You will estimate models of life expectancy at birth across the 50 states and the District of Columbia using economic and demographic variables.

Variable    Description

Lifeexpecti    Life expectantcy at birth, in years, in state i

medinci The median household income in state i ( thousands of dollars)

uninsuredi    The % of the population in that i that was without health insurance

smokei    The % of adults in state i that smoked

obesityi The % of adults in state i who were overweight

teenbirthi    The number of births to teenaged mothers in state i per 1,000 females aged 15-19

gunlawi    Dummy variable = 1 if state i has a firearm law pretoecting children, 0 otherwise

metroi    The % of the population in state i that lived in a metropolitan area

1.) Specify (write out) a linear regression equation for lifeexpecti with all 7 independant variables included. Use proper subscripts and greek letters where appropriate.

2.) For all 7 variables, hypothesize the sign of each coefficient.

state lifeexpect medinc uninsured smoke obesity teenbirth gunlaw metro Alabama 75.4 40.933 14.4 21.9 33 43.6 0 71.46 Alaska 78.3 57.848 18.3 20.8 27 38.3 0 67.36 Arizona 79.6 46.896 19.1 16.6 26 41.9 0 92.53 Arkansas 76 38.587 18.5 22.4 31 52.5 0 60.27 California 80.8 54.283 18.9 12.9 25 31.5 1 97.73 Colorado 80 60.233 14.3 16.9 21 33.4 0 86.33 Connecticut 80.8 65.998 10.5 14.9 22 18.7 1 91.37 Delaware 78.4 55.214 11.7 18 28 30.5 1 78.04 D.C. 76.5 56.928 11.4 15.7 22 45.4 0 100 Florida 79.4 44.066 20.7 18 26 32 1 94.09 Georgia 77.2 44.117 19 18.1 29 41.4 0 81.01 Hawaii 81.3 59.539 7.5 15.3 23 32.5 1 70.07 Idaho 79.5 47.05 16.6 16.5 27 33 0 65.59 Illinois 79 50.728 13.8 18.3 27 33 1 86.97 Indiana 77.6 46.139 12.8 22.8 30 37.3 0 78.33 Iowa 79.7 49.016 10.7 17.5 29 28.6 1 56.52 Kansas 78.7 46.054 12.5 17.5 29 39.3 0 68.32 Kentucky 76 41.104 15.5 25.6 31 46.2 0 58.16 Louisiana 75.7 39.3 18 21.7 33 47.7 0 74.57 Maine 79.2 47.931 9.9 18.6 27 21.4 0 58.4 Maryland 78.8 64.201 12.6 15.4 28 27.3 1 94.62 Massachusetts 80.5 60.934 5 15.2 23 17.2 1 99.59 Michigan 78.2 46.276 12.5 19.7 31 30.1 1 81.28 Minnesota 81.1 52.321 8.7 16.2 26 22.5 1 74.88 Mississippi 75 38.16 18.7 23.2 35 55 0 44.86 Missouri 77.5 45.817 13.7 22.6 31 37.1 0 74.53 Montana 78.5 41.28 16.3 18.1 24 35 0 35.24 Nebraska 79.8 52.504 11.8 17.6 29 31.1 0 58.66 Nevada 78.1 51.2 20 20.8 26 38.6 1 90.05 New Hampshire 80.3 66.633 10.1 16.7 26 15.7 1 62.22 New Jersey 80.3 62.968 14.4 15.6 24 20.1 1 100 New Mexico 78.4 45.134 21.8 18.7 26 53 0 66.56 New York 80.5 49.781 14.2 16.6 25 22.7 1 91.93 North Carolina 77.8 43.83 16.7 20.2 29 38.3 1 70.31 North Dakota 79.5 51.006 11.7 18.1 29 28.8 0 48.38 Ohio 77.8 45.886 12.9 21.2 30 34.1 0 80.61 Oklahoma 75.9 43.103 16.3 24.1 32 50.4 0 64.17 Oregon 79.5 50.602 16.5 16.2 27 28.2 0 77.75 Pennsylvania 78.5 48.314 10.5 19.9 28 27 1 84.12 Rhode Island 79.9 51.623 11.5 16.4 24 22.3 1 100 South Carolina 77 41.698 17.6 20.3 31 42.6 0 76.45 South Dakota 79.5 45.352 12.8 18.1 28 34.9 0 45.33 Tennessee 76.3 38.591 14.7 22.6 32 43.2 0 73.43 Texas 78.5 47.266 24.8 16.7 30 52.2 1 87.83 Utah 80.2 56.701 13.2 9.4 25 27.9 0 88.61 Vermont 80.5 55.928 9.4 16.1 24 17.9 0 33.76 Virginia 79 60.367 12.9 17.5 27 27.4 1 86.08 Washington 79.9 56.163 12.8 15.5 27 26.7 0 87.74 West Virginia 75.4 42.777 13.9 26 33 44.8 0 55.73 Wisconsin 80 50.351 9.2 18.3 28 26.2 1 72.83 Wyoming 78.3 52.201 15.3 19.8 26 39 0 29.66

Explanation / Answer

Solution:

1)

Here, we have to find out regression model or equation for the prediction of life expectancy at birth in years. Required regression output is given as below:

Regression Statistics

Multiple R

0.927487736

R Square

0.8602335

Adjusted R Square

0.837480814

Standard Error

0.672164126

Observations

51

ANOVA

df

SS

MS

F

Significance F

Regression

7

119.5727938

17.08183

37.808

2.31526E-16

Residual

43

19.42759832

0.451805

Total

50

139.0003922

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

89.73552764

2.251921749

39.84842

1.38E-35

85.19409467

94.2769606

medinc

-0.010853762

0.022245294

-0.48791

0.62809

-0.05571567

0.034008148

uninsured

0.045937467

0.036860781

1.246242

0.219422

-0.02839938

0.120274317

smoke

-0.221999449

0.050253439

-4.4176

6.64E-05

-0.32334517

-0.120653731

obesity

-0.12658827

0.050311004

-2.51611

0.015679

-0.22805008

-0.025126462

teenbirth

-0.078176585

0.018432703

-4.24119

0.000116

-0.11534967

-0.041003498

gunlaw

0.484511305

0.250155641

1.936839

0.059353

-0.01997562

0.988998229

metro

-0.015507343

0.006563952

-2.3625

0.022747

-0.02874481

-0.002269873

Value of R square or coefficient of determination is given as 0.86, which means about 86% of the variation in the dependent variable life expectancy at birth is explained by the independent variables in the given regression model.

Required regression equation is given as below:

Lifeexpecti = 89.73552764 -0.010853762*medinc + 0.045937467*uninsured -0.221999449*smoke -0.12658827*obesity -0.078176585*teenbirth + 0.484511305*gunlaw -0.015507343*metro

2)

For two independent variables uninsured and gunlaw, the sign of coefficients or slopes are positive. All remaining independent variables have negative signs. The variables medinc, uninsured, and gunlaw are not statistically significant at 5% level of significance as the corresponding p-values are greater than 0.05 alpha level of significance.

Regression Statistics

Multiple R

0.927487736

R Square

0.8602335

Adjusted R Square

0.837480814

Standard Error

0.672164126

Observations

51

ANOVA

df

SS

MS

F

Significance F

Regression

7

119.5727938

17.08183

37.808

2.31526E-16

Residual

43

19.42759832

0.451805

Total

50

139.0003922

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

89.73552764

2.251921749

39.84842

1.38E-35

85.19409467

94.2769606

medinc

-0.010853762

0.022245294

-0.48791

0.62809

-0.05571567

0.034008148

uninsured

0.045937467

0.036860781

1.246242

0.219422

-0.02839938

0.120274317

smoke

-0.221999449

0.050253439

-4.4176

6.64E-05

-0.32334517

-0.120653731

obesity

-0.12658827

0.050311004

-2.51611

0.015679

-0.22805008

-0.025126462

teenbirth

-0.078176585

0.018432703

-4.24119

0.000116

-0.11534967

-0.041003498

gunlaw

0.484511305

0.250155641

1.936839

0.059353

-0.01997562

0.988998229

metro

-0.015507343

0.006563952

-2.3625

0.022747

-0.02874481

-0.002269873

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