GDP Per Capita and Life Expectancy Order Instructions:
Question 2 A
GDP Per Capita and Life Expectancy Sample Answer
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 years 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 a 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 years 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 a variation of 98.8% GDP per Capita due to the 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.
