Report on the Relationship between Infant Mortality, Income and Public Expenditures in Sri Lanka 1951 to 1981

In the present analysis, the collected data is used to define the infant mortality rates that have been fallen after half of the twentieth century. The hypothesis proposed in the project explains the unprecedented trend that is observed for the broad sweep of history. In the present analysis, information is related to the infant mortality rates (IMR), real gross domestic product per capita in rupees (GDPPC), educational and health expenditures per capita in rupees (EDUCPC and HEXPPC) for Sri Lanka, covering the period 1951 to 1981. The summary of quantitative analysis of data includes measured mean, standard deviation, skewness, and range of the data collected. In the case of infant mortality rates (IMR) mean, standard deviation, skewness, and range are 53.75, 12.8, 4, and 29.5 to 82 respectively. In real gross domestic product per capita in rupees (GDPPC) mean, standard deviation, skewness, and range are 742.13, 123.3, 0.87, and 617 to 1023 respectively. When comparing educational and health expenditures per capita in rupees (EDUCPC and HEXPPC) mean, standard deviation, skewness, and range for HEXPPC are 13.70, 2.01, -0.68, and 8.8 to 16.54 respectively. While for the EDUCPC the values of mean, standard deviation, skewness, and range are 26.6, 6.3, -0.6, and 14.6 to 35.53 respectively. The statistical summary of all the analysis is formulated below in table 1, 2, 3, and 4. When comparing all the analysis, the maximum mean values are observed for real gross domestic product per capita (statisticshowto, 2019).

Table 1: Statistical summary of IMR

Table 2: Statistical summary of GDPPC

Table 3: Statistical summary of HEXPPC

Table 4: Statistical summary of EDUCPC

2). Calculate the pair-wise correlation coefficients between IMR and each of the other variables. Test the statistical significance of each correlation coefficient.

The pairwise correlation coefficient is a linear correlation between two factors, and it is used to measure the correlation factor of IMR with GDPPC, HEXPPC, and EDUCPC. The correlation factor of IMR and GDPPC is 0.86. The pair-wise correlation coefficients between IMR and HEXPPC is 0.78. In the case of IMR and EDUCPC, the value of pair-wise correlation coefficient is 0.77. The maximum value of pair-wise correlation coefficient is observed for GDPPC. The maximum to minimum correlation factor is as EDUCPC < GDPPC < IMR. The values of pair-wise correlation coefficients for all the factors are mentioned below in table 5 (sciencedirect, 2019) and (djsresearch, 2019).

Table for Correlation coefficient between IMR and GDPPC

Table for Correlation coefficient between IMR and HEXPPC

Table for Correlation coefficient between IMR and EDUCPC

3). Estimate a regression model of the form:

I_'m =α + β₁GDPPC_t + β₂HEXPPC_t +u_t

where the t subscript corresponds to year t, Interpret the coefficients that you obtain, and comment on their economic and statistical significance.

The regression model is calculated for two data sets separately including regression analysis of IMR with GDPPC and IMR with HEXPPC. The multiple regression analysis is conducted to measure the regression coefficients and other variables. The regression model corresponds to the time in the year and interprets the economic and statistically significant values. The number of observations in the analysis is 31. The value of R-Square for the regression of IMR and GDPPC is observed as 0.744 with adjusted R Square value as 0.73. The t-value of the analysis is -9.19 that is smaller than standard t-value of 0.001. The value of correlation coefficient is between -1 and 1 that demonstrate for validation of hypothesis. The p-value  is smaller than the standard value of 1. Another regression analysis is carried out to identify the statistical correlation between IMR and HEXPPC. The multiple R and R squared values of regression statistics are 0.78 and 0.61 respectively. The value of adjusted R square is 0.61 with the standard error of 8.15. The significant factor is . The t-value for IMR and HEXPPC is less than the standard value of t-value as . The p-value measured  is less significant because of less value from the standard statistical value. The significance value of multiple regression is less than the standard value of the regression. The coefficient of intercept is 145 with different t value and p-value. The regression summary of IMR v/s GDPPC, IMR V/S HEXPPC and multiple regression are tabulated below in table 6, 7, and 8 (stat, 2019) and (statsoft, 2019).

IMR V/S GDPPC

Table 6: Regression statistics of IMR V/S GDPPC

IMR V/S HEXPPC

Table 7: Regression statistics of IMR v/s HEXPPC

 Multiple Regression

Table 8: Multiple regression statistics

4). Interpret the R² statistic from the regression and test whether it is statistically significant.

The R square statistics define the significance of the regression test and how significantly the statistical analysis is. The equation used for the regression analysis is as follow

_s,

_I'm =α + β₁GDPPC_t + β₂HEXPPC_t +u_t

In the analysis, the value of IMR is considered equivalent to the sum of GDPPC and HEXPPC with some additional parameters. The interpretation of these variables is based on the t-value and p-value of the regression.  The regression analysis is further subdivided into three combinations including regression analysis of IMR v/s GDPPC, IMR v/s HEXPPC and multiple regression analysis. The significance factor and adjusted R square of IMR v/s GDPPC is  and 0.73 respectively. When considering the IMR v/s HEXPPC the significant factor and adjusted R square is  and 0.59 respectively. The results of multiple regression show significance factors and adjusted R square is  and 0.92 respectively. The maximum to the minimum value of the adjusted R square is as follows IMR v/s HEXPPC < IMR v/s GDPPC < multiple regression.

5). Predict the IMR for Sri Lanka at a GDP per capita level of 750 rupees, assuming HEXPPC is at its mean value.

The R square in the statistical analysis is used to measure the closeness of data that is fitted to the regression line. The models are used to explain the variability of the response data around the mean conditions. The results indicate model conditions along with with the variability to response the data conditions. The mean value of HEXPPC is 13.70 and based on HEXPPC, the IMR value will be 13.70 at GDP per capita level of 750 rupees.

6). Re-estimate the model including the EDUCPC variable and comment on any changes to the results and goodness of fit:

IMR_t =α + β₁GDPPC_t + β₂HEXPPC_t + β₃EDUCPC_t +u_t

Explain how the omission of EDUCPC in part 3 may have biased the results. (Note: it is sufficient to discuss the changes, without explicitly showing the testing procedure).

The linear regression is used to re-estimate the model that include the EDUCPC variables. The significant impact is measured on the results and it fit the values of the variables. The results demonstrate the explicit conditions based on procedures used in the model. The results of linear regression for IMR and EDUCPC shows R square value and adjusted R square values as 0.57 and 0.59 respectively. In the analysis, the number of observations considered to take the outcomes is 31.  The t value of multiple regression value for variable 1, variable 2, and variable 3 are measured as -11.11, -3.03, and -2.08. The p-value for variable 1, variable 2, and variable 3 are measured as , , and . The t value and p-value are less than the significant value of the regression values.

Linear Regression

IMR v/s EDUCPC

Multiple Regression

7). What conclusions do you draw from your analysis?

The present report aimed to measure infant mortality rates that have been decreasing in Sri Lanka. The report is established to measure the GDP, health and educational expenditures per Capita based on regression analysis and linear regression of all the variables in the analysis.  The comparison of R square values is used to highlight the limitations and to determine the estimated coefficients. These coefficients are used to measure the mean changes in the values. The regression measurement indicates changes in the dependent and independent variables with the correlation to measure the shift in the dependent and independent variables. The coefficient relations are used to consider the assumptions and relationship between the variables and coefficients.

Appendix 1: Data for analysis

where:

Year                = the year of observation;

IMR                = Infant Mortality Rate per 1000 live births

GDPPC          = Real GDP per capita in rupees

EDUCPC       = Real Educational Expenditures per capita in rupees

HEXPPC       = Real Health Expenditures per capita in rupees

 References of The Relationship between Infant Mortality, Income and Public Expenditures in Sri Lanka 1951 to 1981

djsresearch. (2019). Correlation analysis: market research. Retrieved from https://www.djsresearch.co.uk/glossary/item/correlation-analysis-market-research

sciencedirect. (2019). Correlation analysis. Retrieved from https://www.sciencedirect.com/topics/medicine-and-dentistry/correlation-analysis

stat. (2019). Linear Regression. Retrieved from http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm

statisticshowto. (2019). Descriptive Statistics: Definition & charts and graphs. Retrieved from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/descriptive-statistics/

statsoft. (2019). Multiple Regression. Retrieved from http://www.statsoft.com/Textbook/Multiple-Regression