Demographical Variables from the World Bank Dataset - Statistics Project Example

Quantitative Report Introduction This paper focuses on three demographical variables from the World Bank Dataset; life expectancy at birth, infant mortality rate and under-5 mortality rate. Life expectancy is deemed as a dependent variable which is explained by infant mortality rate and under-5 mortality rate; where the mortality rates are explanatory variables. Life expectancy at birth tends to compare, averagely, the years that can be lived by individuals born within the same year only if the future rate of mortality will remain constant at each age (Pollard, 1982). In addition, it measures the general life quality of a given population and provides a summary of deaths at every age. Infant mortality rate tends to compare the total deaths of infants below the age of one year per one thousand (1000) live births within the same year. Thus, it measures the level of health of the given population. Under -5 mortality rate compares the total deaths of children below the age of five per one thousand (1000) live births in a year (India National Commission on Population, 1999). Additionally, it can be described as the probability that a newly born baby can die before attaining the age of five, only if it is subject to the age-specific death rates in a given year. Thus, the research uses a dataset sampled from one hundred and fifty (150) countries whereby these three variables are considered. This study hypothesizes that infant mortality rate and under -5 mortality of a population affect life expectancy at birth. Thus, it seeks to answer the following question: Can changes in infant mortality rate and under-5 mortality rate determine life expectancy of a population? The main objective of this study is to find out if the two mortality rates affect life expectancy at birth. To validate the hypothesis, this paper uses descriptive statistics, histograms, correlation, regression and scatterplots to analyze the data of the three variables. Histograms are used to represent distributions of data; whether skewed or not. Correlation, regression and scatterplots represent the relationship between the depended and each of the explanatory variables. Analysis Life Expectancy at Birth Fig 1 is a histogram representing life expectancy at birth. From the diagram, it is clear that the data is negatively skewed; skewed to the left. This implies that there is a low life expectancy between the age of 70 and high above the age 70. This data has a minimum life expectancy of 45 years and a maximum of 83, with an average of 70.68. Moreover, from table 1, the standard deviation is relatively low (9.10605) implying that the data points are closer to the mean. As described above (from the histogram), the skewness statistic is -0.774; which is negatively skewed. The data has a flatter distribution as depicted by the kurtosis statistic. Fig 1: Histogram Table 1: Descriptive Statistics Descriptive Statistics N Minimum Maximum Sum Mean Statistic Statistic Statistic Statistic Statistic Std. Error Life expectancy at birth, total (years) 149 45.00 83.00 10532.00 70.6846 .74600 Valid N (listwise) 149 Descriptive Statistics N Range Std. Deviation Variance Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error Life expectancy at birth, total (years) 149 38.00 9.10605 82.920 -.774 .199 -.122 .395 Valid N (listwise) 149 Under -5 Mortality Rate Fig 2 is a histogram representing Under-5 Mortality Rate. From the diagram, it is clear that the data is positively skewed; skewed to the right. This implies that the under-5 mortality rate of many countries lies between zero and 40 per 1000 live births. This data has a minimum under-5 mortality rate of 2 and a maximum of 161, with an average of 32.08. Moreover, from table 2, the standard deviation is relatively high (32.516) implying that the data points are far away from the mean. The data has a skewness statistic of 1.359; which confirms its positivity. A positive kurtosis of .394 shows that this data has a peaked distribution; it is not normal. Fig 2: Histogram Table 2: Descriptive Statistics N Range Std. Deviation Variance Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error Mortality rate, under-5 (per 1,000 live births) 150 159.00 32.51567 1057.269 1.359 .198 1.342 .394 Valid N (listwise) 150 Descriptive Statistics N Minimum Maximum Sum Mean Statistic Statistic Statistic Statistic Statistic Std. Error Mortality rate, under-5 (per 1,000 live births) 150 2.00 161.00 4812.00 32.0800 2.65489 Valid N (listwise) 150 Infant Mortality Rate Fig 3 is a histogram representing Infant Mortality Rate. From the diagram, it is clear that the data is positively skewed; skewed to the right. This implies that the infant mortality rate of many countries lies between zero and 30 per 1000 live births. This data has a minimum infant mortality rate of 2 and a maximum of 107, with an average of 23.85. Moreover, from table 3, the standard deviation is relatively high (21.723) implying that the data points are far away from the mean. The data has a skewness statistic of 1.141; which confirms its positivity. A positive kurtosis of .394 shows that this data has a peaked distribution; it is not normal. Fig 3: Histogram Table 3: Descriptive Statistics Descriptive Statistics N Minimum Maximum Sum Mean Statistic Statistic Statistic Statistic Statistic Std. Error Mortality rate, infant (per 1,000 live births) 150 2.00 107.00 3578.00 23.8533 1.77367 Valid N (listwise) 150 Descriptive Statistics N Range Std. Deviation Variance Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error Mortality rate, infant (per 1,000 live births) 150 105.00 21.72290 471.884 1.141 .198 .794 .394 Valid N (listwise) 150 Relationship between dependent and explanatory variables Fig 4 and 5 are scatterplots representing the relationship between life expectancy at birth and infant mortality rate and life expectancy at birth and under-5 mortality rate respectively. The plots are concentrated on the upper left region and scatter sparsely towards the lower right region. Additionally, the best fit lines have negative slopes implying that when the infant and under -5 mortality rates are low, the life expectancy at birth is high and decreases with the increase in mortality rates. Fig 4: Scatterplot for Life Expectancy against Infant Mortality Rate Fig 5: Scatterplot for Life Expectancy against Under-5 Mortality Rate Correlation Table 4 and 5 represents the correlation of the dependent variable with each of the explanatory variable. From table 4, the correlation coefficient is -0.918, implying that life expectancy at birth and under-5 mortality rate have a strong negative relationship. From table 5, the correlation coefficient is -0.924, depicting a strong negative relationship between life expectancy at birth and the infant mortality rate. This justifies the scatterplots above; as the explanatory variables increases, the depended variable decreases (Archdeacon, 1994). Table 4: Correlation Mortality rate, under-5 (per 1,000 live births) Life expectancy at birth, total (years) Mortality rate, under-5 (per 1,000 live births) Pearson Correlation 1 -.918** Sig. (2-tailed) .000 Sum of Squares and Cross-products 157533.040 -40263.067 Covariance 1057.269 -272.048 N 150 149 **. Correlation is significant at the 0.01 level (2-tailed). Table 5 Correlations Life expectancy at birth, total (years) Mortality rate, infant (per 1,000 live births) Life expectancy at birth, total (years) Pearson Correlation 1 -.924** Sig. (2-tailed) .000 Sum of Squares and Cross-products 12272.174 -27050.000 Covariance 82.920 -182.770 N 149 149 **. Correlation is significant at the 0.01 level (2-tailed). Regression Table 6 represents a linear regression model summary of life expectancy at birth (dependent) and Infant Mortality rate (explanatory). The model has a coefficient of determination, R2=0.845. This implies that 84.5% of life expectancy at birth is explained by the infant mortality rate. Thus, this model is significant or appropriate. The model can be summarized as: Life Expectancy= -.387 Infant Mortality Rate + 79.981 (Chatterjee & Hadi, 2006). Table 6: Model Summary Model Summary Model R R2 Adj R2 Std. Error of the Estimate Change Statistics R2 Change F Change df1 df2 Sig. F Change 1 .924a .854 .853 3.49327 .854 858.672 1 147 .000 a. Predictors: (Constant), Mortality rate, infant (per 1,000 live births) Coefficientsa Model Unstandardized Coefficients Standardized Coefficients T Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) 79.981 .427 187.193 .000 79.137 80.826 Mortality rate, infant (per 1,000 live births) -.387 .013 -.924 -29.303 .000 -.413 -.361 a. Dependent Variable: Life expectancy at birth, total (years) Conclusion Life expectancy for a given population depends on early mortality rate. From the above analysis, the regression model, Life Expectancy= -.387 Infant Mortality Rate + 79.981, fully describes how infant mortality rate affects. When mortality rate is at zero, life expectancy at birth is equal to 79.981 years. Additionally, when a unit of mortality rate is increased by one, the life expectancy at birth reduces by 0.387. References Archdeacon, T. J. (1994). Correlation and Regression Analysis: A Historian Guide . Wisconsin: University of Wisconsin Press. Carver, R. & Nash, J. (2011). Doing Data Analysis with SPSS. Boston: Cengage Learning Inc. Chatterjee, S. & Hadi, A. S. (2006). Regression Analysis by Example. New York: John Wiley and Sons. Demetrius, L. (1979). Relations between Demographic Parameters. Journal of Demography, vol.2, p.329-338. India National Commission on Population. (1999). Birth Rate, Death Rate, Infant Mortality Rate and Total Fertility Rate. India: National Commission on Population. Keyfitz, N. (1972). Applied Mathematical Demography. New York: John Wiley and Sons. Myrskylia, M. (2010). The Effects of shocks in Early Life Mortality on Later Life Expectancy and Mortality Compression: A Cohort Analysis. Journal of Demographic Research, vol.22, p.289-320. Print Oakes, M. (1986). Statistical Inference: A Commentary for the Social and Behavioral Sciences. Chichester, John Wiley & Sons Pollard, J. H. (1982). The Expectation of Life and its Relationship to Mortality. Journal of Institute of Actuaries, vol. 109, p.225-240. Print Riley, J.C. (2001). Rising Life Expectancy: A Global History. Cambridge: Cambridge University Press. Vaupel, J. W. (1986). How Change in Age- Specific Mortality Affects Life Expectancy. Journal of population Studies, vol.40, p.147-157. Print Vaupel, J. W. (1982). Statistical Insinuation. Journal of Policy Analysis and Management, vol.1, p.261- 263. Print Xie, Y. (2000). Demography: Past, Present and Future. Journal of the American Statistical Association, vol.95, p. 670-673. Read More