IntroductionThe United Nations developed a tool known as Human Development Index (HDI) to measure and rank countries levels of economic and social development based on several criteria such as mean years of schooling, expected years of schooling, gross national income per capita and life expectancy at birth. It is possible to track changes with HDI in developmental levels over time and be able to compare developmental levels for several countries.
The question to ask ourselves is that; is there any significant relationship between Human Development Index and life expectancy at birth? To answer this question, data of HDI and life expectancy at birth for the year 2011 was collected from UN Human Development Report Statistical Annex. The null hypothesis of the research is; there is no significant relationship between HDI and life expectancy at birth.
Data analysis and discussion
The data collected was for 187 countries whose variables the HDI and the life expectancy at birth for the year 2011 was computed. The dependent variable is HDI and the independent variable is the life expectancy at birth. The data was analyzed using excel and then results discussed. To describe the data, the descriptive statistics for the data was done and the output was as follows.
HDI life expectancy at birth
Mean 0.66297861 69.63582888
Standard Error 0.012578411 0.703046059
Median 0.698 73
Mode 0.908 74
Standard Deviation 0.172007188 9.614010259
Sample Variance 0.029586473 92.42919326
Kurtosis -0.850868183 -0.392592475
Skewness -0.417195299 -0.809098553
Range 0.657 35.6
Minimum 0.286 47.8
Maximum 0.943 83.4
Sum 123.977 13021.9
Count 187 187
The above table shows that the average HDI for the countries is 0.6629 with a standard error of 0.0125 and the average life expectancy at birth is approximately 70 years with a standard error of 0.703. The standard deviation showcases how far the data is from the mean for instance the life expectancy at birth of the countries is 9.614 years far apart from the mean. The data for the two variables is normally distributed since their kurtosis (measure of asymmetry) is -0.417 for HDI and -0.809 for life expectancy at births which both are close to zero implying a perfect asymmetry (normal distribution).
To showcase the relationship between the human development index and life expectancy at birth then a regression analysis was done and the results were as follows.
Multiple R 0.90147
R Square 0.812647
Adjusted R Square 0.811635
Standard Error 0.074653
From the above table of the regression statistics, it can be seen from the R square that the regression model accounts for 81.26% of the dependent variable and the remaining 18.74% is due to error.
ANOVA df SS MS F Significance F
Regression 1 4.472066 4.472066 802.4424 3.41E-69
Residual 185 1.031018 0.005573 Total 186 5.503084
The Anova table tells us how significant our model is. The p-value (3.41E-69) of the model is less than the default alpha (0.05) thus we reject the null hypothesis that there is no significant relationship between the variables and accept the alternative that there is significant relationship between HDI and life expectancy at birth. The equation of the model can be established from the table below.
Coefficients Standard Error t Stat P-value
Intercept -0.46014 0.040022 -11.4972 1.98E-23
life expectancy at birth 0.016128 0.000569 28.32741 3.41E-69
Therefore the regression model is given by;.To showcase the direction of the relationship then the following scatter plot was developed.
The graph shows a very strong positive relationship between HDI and life expectancy at birth meaning as the life expectancy at birth increase, also HDI increases.
Since the p-value of the model is less than the default alpha and we accept the alternative hypothesis that there is significant relationship between HDI and the life expectancy at birth then we can conclude that life expectancy at birth is a good determinant of the HDI. The developed countries in the Arab empire, in Europe and many others experience a high HDI since they have excellent health services, infrastructure, and education among many other factors.
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