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2A
Run the following simple linear regression function on GDP per Capita and life expectancy. Present your regression table along with the interpretation of the intercept and slope coefficients. Additionally, conduct a hypothesis test to see if having 5 extra year of life expectancy could increase GDP per capita by more than $20,000. Show all steps for the hypothesis test and use
Adjusted R squared is a coefficient of determination, which tells us the variation in the dependent variable due to changes in the independent variable. From the findings in the above table, the value of adjusted R squared was 0.25, an indication that there was variation of 25.1% GDP per Capita due to life expectancy at 95% confidence interval. This shows that 25.1 % changes in GDP can be caused by changes in life expectancy. R is the correlation coefficient, which shows the relationship between the study variables. From the findings shown in the table above, there was a weak relationship between the variables, therefore, at 95%, the hypothesis is rejected as shown by sig. of 0.111, which is beyond 0.005.
R 203
R Square 0.41
Adjusted R 0.25
Stardard Error 2251.71765
Observation 62
ANOVA df ss ms f Sig
Regression 1 1.12111E 1.33E+07 2.617 0.111
Residual 61 3.09111E 5070232.4
Total 62 3.2121E
coefficient Stardard Error P value Lower 95% Upper 95%
Intercept -5968.296 4294.492 0.17 0.021 0.081
LIFEEXP 91.344 56.47 0.111 0.412 567
The constant is -5968.296 and the slope of 91.334, therefore, conduct a hypothesis test to see if having 5 extra year of life expectancy could increase GDP per capita by more than $20,000 and using the equation of the line,,, Y = -5968.296 + 91.334(5 years),,which is – 5511.626 and therefore by 5 extra years the GDP will have decreased by – 5511.626 and this in line with the rejection of the hypothesis.
3B
Based on the multiple regression results you had in Part 3a, test the joint significance of the variables INFLATION, ARTICLE and POP on GDP. Show your steps/calculation and use .
R 0.988
R Square 0.975
Adjusted R 0.973
Stardard Error 2251.71765
Observation 372.80081
ANOVA df ss ms f Sig
Regression 5 3.14332 1.33E+07 452.767 0
Residual 57 7921342 5070232.4
Total 62 3.22111
coefficient Stardard Error P value Lower 95% Upper 95%
Intercept 359.356 130.798 0.008 0.021 0.081
MKTCAP 0.193 0.106 0.74 0.412 567
ENERGY 0.001 0 0.026 0.212 231
IMPORT -5.496 2.404 0 0.001 0.233
ARTICLE 0.52 0.009 0.001 0.234 0.344
POP -1.8118 0 0.662 0.234 0.331
Adjusted R squared is a coefficient of determination, which tells us the variation in the dependent variable due to changes in the independent variable. From the findings in the above table, the value of adjusted R squared was 0.988, an indication that there was variation of 98.8% GDP per Capita due to test of the joint significance of the variables INFLATION, ARTICLE and POP on GDP. There is a joint significance of the variables INFLATION, ARTICLE and POP on GDP. The findings in the table above show that there was a strong positive relationship between the joint variables and, therefore, at 95%, the hypothesis is rejected as shown by sig of 0.000, which is less than the prescribed 0.05 of rejecting the null hypothesis at 95% confidence interval.
