Life Expectancy at Births - Case Study Example

DATA ANALYSIS Name Goes Here: Name of University Here: Introduction Life expectancy at births can be defined as the average number of years that a newly child would live given that the current mortality patterns are kept constant. Life expectancy is basically a qualitative reflection of a country’s quality of life, because individuals have the potential of living longer and fuller lives. Thus, life expectancy is an estimation of an individual's life span calculated from average ages of all individuals who die in a particular year. Also, life expectancy takes a further step in measuring the physical wellness of a country’s citizenry; it supposes measures such as per capita GNP, literacy rates and even education attainment. The manner in which life expectancy is affected on a national level is important for economic planners. Inasmuch as various factors are essential for living longer, in solitary, they cannot be the only influencing factors. Undoubtedly, the social and economic conditions of a particular country will affect its citizens, their standards of living, decisions, lifestyles and culture. In essence, ccitizens of wealthier nations have quality access to modern health facilities, technologies, entertainment, leisure and exercise, and meticulous maintained water and sanitation systems. It is expected that their life expectancies should naturally be higher than those of struggling economies. However, this is not always true as the analysis will show. It behooves researcher then to investigate the particular social and economic factors that contribute most in determining life expectancy at birth. In this study, the average life expectancy at birth is chosen, because individuals who have live on past childhood are more likely to enjoy an extended life span compared to the average member of their birth cohort, an approach that easily presents a selection bias. Thus, this study selected economic and social variables that are comprehensive over across varied social and economic conditions from over 62 countries, hoping that the selected variables would cover more important facets and thus assist in the building of an accurate model of life expectancy. This research uses data to examine how Life Expectancy differs between groups of countries by economy type (industrialised and oil producing). The research also examines the relationship between Life expectancy and other variables in the data set other than economy type. In addition, the study also examines the extent to which Life Expectancy can be predicted using the variables other than economy type. Measures used in the study The following methods are appropriately used in the analysis: a. Comparisons of variable distributions (using the mean, median, standard deviation, skew etc.) with appropriate comments on what your findings show and how these findings relate to the report aims b. Basic probability calculated from the data, with appropriate explanations of how calculated in the appendix, and what the probability values found imply in relation to the aims c. Confidence intervals and appropriate explanations of why they are being used and what they show in relation to the aims. d. T-test hypothesis test of means or proportions with appropriate explanations of why the tests have been used and what the tests show in relation to the aims e. Chi squared tests with appropriate explanations of why the tests are being used and what the results shows in relation to the aims f. Correlation with appropriate explanations of why the techniques are being used and what the results show in relation to the aims. It is noted that correlations do not show causal links instead they only show how the causation works both ways. g. Regression with appropriate explanations of why the techniques are being used and what the results show in relation to the aims. Research Variables The variables below were chosen to measure some of the most important distinct components of the quality of life. The list is in no way exhaustive. Some of the data points are missing (unemployment rate data for Iraq, India, Iceland, Qatar, Saudi Arabia and UAE). Because missing data points would result in lack of contiguity in the different analyses used, we are left with no other choice but to make compromises—the missing categories are eliminated. In the analysis, Life Expectancy at Birth was regressed with the following economic and social variables: a) GDP per capita: The wealthier a nation is, the more income its citizens will have to spend on life-sustaining things including healthcare, and in the same way, the more likely they are to access quality leisure and exercise. b) Literacy Levels: The more knowledgeable an individual is, the more he or she is able to make informed life decisions, and live a quality of life. c) No. of mobile phones: Access to information gives people a chance to be aware of their surroundings--from medical developments, economic performance, weather updates and job openings, to outbreaks of disease and political skirmishes. d) Unemployment rate: It is assumed that access to employment enables people to earn income and other benefits which in turn allow them to access important services such as healthcare. e) Percentage over 65 years: As a people continue to age, their bodies become more susceptible to various diseases and ailment which increases their likelihood of dying. Assumptions on the Regression Model 1. It is assumed that the chosen economic and social variables exert a clear and noteworthy effect on life expectancy at birth of all nations. Thus, the relationship between life expectancy and the selected variables is assumed to be linear and subject to random error. 2. In order to maintain consistency and contiguity, when performing a multiple regression analysis, any missing data point is left out of the data set. As a result, data on unemployment from Iraq, India, Iceland, Qatar, Saudi Arabia and UAE could not be gathered and therefore were excluded from the regression. We assume that the data set consisting of 56 countries is a good reflection of the overall world population, and that variables used in our model are applicable to all nations of the world. 3. Analysis of the Gauss-Markov assumptions is performed so as to examine whether the Gauss-Markov model is applicable. Before the performing our regressions, the Gauss-Markov model was initially assumed to be applicable. Data Analysis Descriptive Statistics From the table below, the mean life expectancy of the data is 73.58 years, while the standard error is 0.8. Table-1: Descriptive Statistics is a summary of comparisons of variable distributions (mean, median, mode, standard deviation, sample variance, kurtosis, skewness, range and confidence interval at 95.0%). Table-1: Descriptive Statistics Descriptive Statistics   Overall sample Non-IndustrialisedG20 Industrialized G20 No oil as a natural resource Has oil as a resource Has oil and member of OPEC Mean 73.58096774 74.15860465 72.27368421 74.91741935 73.658 69.67454545 Standard Error 0.795118559 0.798971417 1.866403053 1.094283088 1.228456798 2.090211544 Median 75.455 75.94 74.65 76.58 75.73 69.95 Mode 69.95 69.95 0 0 0 69.95 Standard Deviation 6.260769792 5.239205947 8.135462297 6.092710381 5.493825817 6.932447423 Sample Variance 39.19723839 27.44927896 66.18574678 37.12111978 30.18212211 48.05882727 Kurtosis 5.522480 7.92671794 3.095665 12.38832515 -0.528342 5.65557846 Skewness -2.02800 -2.2909324 -1.55407 -3.092566 -0.824960 -2.1256564 Range 32.71 28.66 32.71 32.71 17.19 25.2 Minimum 48.09 51.07 48.09 48.09 62.68 51.07 Maximum 80.8 79.73 80.8 80.8 79.87 76.27 Count 62 43 19 31 20 11 Largest(1) 80.8 79.73 80.8 80.8 79.87 76.27 Smallest(1) 48.09 51.07 48.09 48.09 62.68 51.07 Confidence Level(95.0%) 1.589938 1.6123896 3.921167 2.2348242 2.5711896 4.65728152 From Table-1, it is clear that Basic probability calculated from the data, with appropriate explanations of how calculated in the appendix, and what the probability values found imply in relation to the aims Figure-1: Descriptive Statistics Mean The Figure-below shows mean of Countries in the category of countries without oil resources as a natural resource and those that are non-industrialized G20 have a relatively higher life expectancy than the average life expectancy of the overall data. Standard Deviation The standard deviation of Industrialised G20 countries have the highest standard deviation from the mean compared to the overall sample. This is consistent with the result above, as indicated by comparison of the means. Comparison of variances is similar to the comparison of standard deviation since variance= s2 Skewness and Kurtosis In general, if skewness is less than −1 or greater than +1, the distribution is considered to be highly skewed, negatively or positively. On the other hand, if skewness is between −1 and -0.5 or between +0.5 and +1, the distribution is said to be moderately skewed. And finally, if the skewness is between -0.5 and +0.5, the distribution is said to be approximately symmetric. In fig-6, the overall distribution is highly negatively skewed (lies between +0.5 and +1). The same case applies to the distribution of Non-Industrialized G20, Industrialised G20, countries that have no oil as a natural resource, and those that have oil as a natural resource and are OPEC members. It is important to note that the skewness varies; the sample skewness is not necessarily applicable to the whole population. Kurtosis This data uses a two-tailed test of excess kurtosis ≠ 0 at approximately the 0.05 level of significance. In general, whenever kurtosis is less than -2, the population is very likely to have a negative excess kurtosis, though one cannot determine its magnitude. If it lies between −2 and +2, no conclusion about the kurtosis, whether excess, positive, negative, or zero can be made. If it is greater than +2, the population is very likely to have positive excess kurtosis (kurtosis >3, leptokurtic), again we cannot determine by how much. In fig-6 above, the overall sample shows that the population has positive excess kurtosis, as it is greater than +2. This is common for all categories except for the countries with oil resources. Confidence Interval Therefore, we can assume that for the normal curve, 95% of the area lies between-1.96 and +1.96 Standard deviations. Confidence interval (95.0%) T-test hypothesis test of means or proportions with appropriate explanations of why the tests have been used and what the tests show in relation to the aims. Regression Regressions are performed and appropriate explanations of why the technique is used are given and what the results shown in relation to the aims. 1. Single Regression Models of Life Expectancy against Economic and Social Variables To begin our analysis, single regression models of life expectancy at birth were run against each of the selected economic and social indicator so as to obtain individual models representing how well each variable could explain variances in life expectancy. These regression results are displayed in the appendices below. These regressions, together with the various tests found throughout this analysis, were done using the statistical analysis package MS Excel 2007. On their own, the variables did not hold a significant (R2= 0.60) linear relationship with life expectancy at birth. For GDP/capita, R2 = 0.45 and for literacy rate, R2= 0.38). Unemployment rate had an R2= 0.31, while for those with mobile phones, R2= 0.03, and for percentage over 65, R2=35. Therefore, the regression models did not show significance in single regressions, individually, the chosen variables do not significantly influence life expectancy. Therefore, it we decided to perform a multiple regressions of life expectancy with the independent variables. Multiple Regressions Single regressions take into account the effect of one variable at a time, but multiple regressions simultaneously take into consideration the effects of many variables. The analysis performed standard least square multiple regressions: firstly, of Life expectancy and GDP/capita and Literacy rate. In this model, R2 = 0.533. This means that 53.3% of the variance was accounted for in our model. For the model of Life expectancy and all the variables, R2=0.513, implying that 51.3% of variance was accounted for in this model. Therefore, it was inferred that the data set consisting of GDP/capita and Literacy rate is best for creating a regression model for life expectancy at birth for all countries. Inasmuch as the goodness of fit is high, the two variables exert great significance with respect to life expectancy at birth. Also the model consisting of all variables (GDP/capita, literacy rate, number of mobile phones, unemployment rate and percentage over 65 years) is also significant in creating a regression model to predict life expectancy for all nations. The use of individual regressions has some discrepancies, for instance the insignificance of number of mobile phones is unexpected, since access to information is important for prolonging one’s life. It can be assumed that those with mobile phones have a higher standard of living. It seems counterintuitive that number of mobile phones does not influence life expectancy and the negative coefficient indicates a negative relationship of technology with life expectancy. Test for Multicollinearity The assumption of the absence of multicollinearity is fundamental to any multiple regression models. In a regression, it is assumed that the X-variables are independent, but with multicollinearity, these variables are actually correlated with one another. For instance, if X1 and X2 are highly correlated, then it is mostly reasonable to add X1 to the model, one can also add a bit of X2. This dilutes the significance of both X1 and X2, resulting to a higher standard error. As a result, so as to refine the model, a correlation plot between life expectancy and the chosen indicators was performed. Correlation Correlation with appropriate explanations of why the techniques are being used and what the results show in relation to the aims were performed in excel 2007. It is noted that correlations do not show causal links instead they only show how the causation works both ways. This plot identifies the variables are highly correlated. The results of the test for multicollinearity are shown below. It can be observed that the correlation coefficient of GDP/capita and Literacy rate is 0.60. This shows a strong positive relationship supporting the multiple regression model of life expectancy with GDP/capita and Literacy rate. Correlation analysis of all variables*   Life Expectancy GDP/capita Literacy Rate(%) No. of Mobile Phones Unemployment rate(%) No. over 65years Life Expectancy 1           GDP/capita 0.65235 1         Literacy Rate (%) 0.60783 0.599 1       No. of Mobile phones 0.15948 0.230 0.066724 1     Unemployment Rate (%) -0.55657 -0.5645 -0.660488 -0.189310385 1   No. over 65years 0.580627 0.7358 0.71694 0.1325454 -0.448881841 1 *(Note: This data excludes Iraq, India, Iceland, Qatar, Saudi Arabia and UAE for lack of data on unemployment rates) Conclusion It can be concluded that, the selected economic and social variables that are comprehensive over across varied social and economic conditions from over 62 countries, they cover more important facets of factors influencing life expectancy and thus assist in the building of an accurate model of life expectancy. The research identifies that Life Expectancy differs between groups of countries by economy type (industrialised and oil producing). The research also observes the relationship between Life expectancy and other variables in the data set other than economy type. Also the model consisting of all variables (GDP/capita, literacy rate, number of mobile phones, unemployment rate and percentage over 65 years) is also significant in creating a regression model to predict life expectancy for all nations. APPENDIX-A APPENDIX-B Regression Results: Summary Output LIFE EXPECTANCY WITH No. of Mobile pho Regression Statistics Multiple R 0.17455567 R Square 0.03046968 Adjusted R Square 0.01431084 Standard Error 6.21581 Observations 62 ANOVA   df SS MS F Significance F Regression 1 72.85397309 72.85397309 1.885635701 0.174805077 Residual 60 2318.177569 38.63629281 Total 61 2391.031542         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 73.0842908 0.8683 84.16684 5.48301E-64 71.3474 74.8 71.3 74.8 Number with Phones 0.0758861 0.0552 1.3732 0.1748 -0.03465 0.18 -0.03 0.18 Life expectancy with GDP and literacy rate Regression Statistics Multiple R 0.730600792 R Square 0.533777517 Adjusted R Square 0.517973365 Standard Error 4.346735894 Observations 62 ANOVA   df SS MS F Significance F Regression 2 1276.278879 638.1394395 33.77451176 1.67301E-10 Residual 59 1114.752663 18.89411293 Total 61 2391.031542         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 52.1718171 4.51961319 11.54342527 9.06164E-17 43.12809207 61.21554213 43.12809207 61.21554213 GDP/capita 0.327022885 0.075404454 4.336917381 5.72423E-05 0.176138924 0.477906847 0.176138924 0.477906847 Literacy Rate (%) 0.181822824 0.055342772 3.285394256 0.001716884 0.071082195 0.292563454 0.071082195 0.292563454 % over 65 Regression Statistics Multiple R 0.589141149 R Square 0.347087293 Adjusted R Square 0.336205415 Standard Error 5.100873905 Observations 62 ANOVA   df SS MS F Significance F Regression 1 829.8966665 829.8966665 31.89589879 4.72239E-07 Residual 60 1561.134875 26.01891459 Total 61 2391.031542         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 66.36415522 1.43267108 46.32197588 1.1346E-48 63.49838641 69.22992404 63.49838641 69.22992404 % over 65 0.70250954 0.12438981 5.64764542 4.72239E-07 0.453692876 0.951326203 0.453692876 0.951326203 GDP Regression Statistics Multiple R 0.669689456 R Square 0.448483967 Adjusted R Square 0.439292033 Standard Error 4.688091706 Observations 62 ANOVA   df SS MS F Significance F Regression 1 1072.339311 1072.339311 48.79103494 2.65271E-09 Residual 60 1318.69223 21.97820384 Total 61 2391.031542         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 66.59061109 1.164476226 57.18503273 4.84824E-54 64.26131185 68.91991 64.26131185 68.91991033 GDP/capita 0.467658066 0.066951207 6.985057977 2.65271E-09 0.333735713 0.60158 0.333735713 0.601580419 Literacy rate Regression Statistics Multiple R 0.620603365 R Square 0.385148536 Adjusted R Square 0.374901012 Standard Error 4.949965057 Observations 62 ANOVA   df SS MS F Significance F Regression 1 920.9022981 920.9022981 37.58454443 7.42655E-08 Residual 60 1470.129244 24.50215406 Total 61 2391.031542         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 44.67951909 4.75600571 9.394336721 2.15493E-13 35.16609131 54.19294687 35.16609131 54.19294687 Literacy Rate 0.318077539 0.051883392 6.130623494 7.42655E-08 0.214295305 0.421859773 0.214295305 0.421859773 Unemployment Regression Statistics Multiple R 0.556570399 R Square 0.309770609 Adjusted R Square 0.297220984 Standard Error 5.239075549 Observations 57 ANOVA   df SS MS F Significance F Regression 1 677.5147786 677.5147786 24.68365403 6.93377E-06 Residual 55 1509.635193 27.44791261 Total 56 2187.149972         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% INTERCEPT 78.9688911 1.219060184 64.77850077 1.28312E-53 76.52583991 81.41194228 76.52583991 81.41194228 Unemployment Rate VAR -0.50112428 0.100865053 -4.96826469 6.93377E-06 -0.703262362 -0.298986199 -0.703262362 -0.298986199 LIFE EXPECTANCY WITH ALL VARIABLES Regression Statistics Multiple R 0.716357582 R Square 0.513168185 Adjusted R Square 0.465439576 Standard Error 4.569236839 Observations 57 ANOVA   df SS MS F Significance F Regression 5 1122.375 224.475 10.75 4.30474E-07 Residual 51 1064.77 20.8529 Total 56 2187.15         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Life Expectancy 56.75609702 10.01679558 5.666093168 6.81E-07 36.6465412 76.86565284 36.6465412 76.86565284 GDP/Capita 0.256197839 0.110933577 2.309470647 0.025002 0.033489396 0.478906282 0.033489396 0.478906282 Literacy rate 0.147823392 0.10982439 1.345997839 0.184256 -0.072658267 0.36830505 -0.072658267 0.36830505 Mobile Phones 0.008180975 0.042617877 0.191961103 0.848535 -0.077377981 0.09373993 -0.077377981 0.09373993 Unemployment rate -0.147191648 0.127331116 -1.155975477 0.253078 -0.402819525 0.108436229 -0.402819525 0.108436229 % Over 65 0.090177 0.21689 0.41577 0.679 -0.3452 0.52556 -0.34525 0.5256 Read More