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.

1. Test the slope coefficients of gunlaw, metro, and obesity at the 5 level of significance using p-values. List the p-value used for each test. Which which coefficients can you reject the null hypothesis?

2. Use the overall F-statistic to test whther the regression is significant at the 5% level. Show your null and alternative hypotheses and your decesion rule, and use the f-table

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

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

Here below is the Excel results of regression between dependent variable (life expectancy) and independent variable(s)

Here as we can see that p - value for obesity is 0.0157 < 0.05 so it is significant here.

P - value for gunlaw is 0.0594 > 0.05, so gunlaw is not significant here

P - value for metro is 0.02275 < 0.05, so Metro is a significant variable here.

(b) Here

Null hypothesis : H0 : 1 = 2 = .....7 = 0

Alternative Hypothesis: Ha : at least one coefficient is not zero.

Here F = 37.808

and p -value = 2.32 x 10-16

Here Fcritical = 2.188

so we reject the null hypothesis and can conclude that the regression is significant here.

SUMMARY OUTPUT Regression Statistics Multiple R 0.927488 R Square 0.860233 Adjusted R Square 0.837481 Standard Error 0.672164 Observations 51 ANOVA df SS MS F Significance F Regression 7 119.5728 17.08183 37.808 2.32E-16 Residual 43 19.4276 0.451805 Total 50 139.0004 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 89.73553 2.251922 39.84842 1.38E-35 85.19409 94.27696 85.19409 94.27696 medinc -0.01085 0.022245 -0.48791 0.62809 -0.05572 0.034008 -0.05572 0.034008 uninsured 0.045937 0.036861 1.246242 0.219422 -0.0284 0.120274 -0.0284 0.120274 smoke -0.222 0.050253 -4.4176 6.64E-05 -0.32335 -0.12065 -0.32335 -0.12065 obesity -0.12659 0.050311 -2.51611 0.015679 -0.22805 -0.02513 -0.22805 -0.02513 teenbirth -0.07818 0.018433 -4.24119 0.000116 -0.11535 -0.041 -0.11535 -0.041 gunlaw 0.484511 0.250156 1.936839 0.059353 -0.01998 0.988998 -0.01998 0.988998 metro -0.01551 0.006564 -2.3625 0.022747 -0.02874 -0.00227 -0.02874 -0.00227

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