(TIỂU LUẬN) REGRESSION MODEL FOR THE DATA SET HI THE HIGH INCOME COUNTRIES

Assessmen t 3A Team Report Team Members  Phan Tan Phuc Cuong - s386416  Le Cong Minh - s3834313  Nguyen Ba Uyen Cat - s3757801  Nguyen Tuan Anh - s3777325  Nguyen Ngoc Anh Thu - s3741263  Chau Ngan Hong- s3813338 Lecturer  Doan Bao Huy Group 12 - Team 02 Fi r s tna me St ude ntI D Par t s Co nt r i but e d Co nt r i but i o n% Cuong s3864161 1, 3, 100% Minh s3834313 5, 6, 100% Cat S3757801 3, 100% Anh s3777325 2, 100% Hong s3813338 5, 100% Thu s3741263 2, 100% Si g nat ur e Table of Contents PART 1: DATA COLLECTION .1 PART 2: DESCRIPTIVE STATISTIC .1 2.1: MEASURE OF CENTRAL TENDENCY 2.2: MEASURE OF VARIATION 2.3: MEASURE OF SHAPE PART 3: MULTIPLE REGRESSION (FROM YOUR COLLECTED DATA) 3.1: REGRESSION MODEL FOR THE DATA SET LI: THE LOW-INCOME COUNTRIES 3.2: REGRESSION MODEL FOR THE DATA SET LMI: THE LOWER-MIDDLE INCOME COUNTRIES 3.3: REGRESSION MODEL FOR THE DATA SET UMI: THE UPPER-MIDDLE INCOME COUNTRIES 3.4: REGRESSION MODEL FOR THE DATA SET HI: THE HIGH-INCOME COUNTRIES 10 PART 4: TEAM REGRESSION CONCLUSION 11 PART 5: TIME SERIES 12 5.1: TIME SERIES TREND MODEL 12 A B C LINEAR TREND: 12 QUADRATIC TREND: 14 EXPONENTIAL TREND 16 5.2: RECOMMENDED TREND MODEL .18 5.3: PREDICTION 19 PART 6: TIME SERIES CONCLUSION .21 6.1: LINE CHART 21 6.2: INTERPRETATION .21 PART 7: OVERALL CONCLUSION 22 REFERENCES: .25 APPENDIX: 27 29 PART 1: DATA COLLECTION All the data collected are conducted as primary data from the World Bank database in the year of 2017; and they are considered quantitative data According to the World Bank, current international $ would equal USD The collecting data process began when we downloaded the excel files of the world’s Gross Net Income (GNI) per capita from the World Bank Database In a separate excel file, we randomly selected 30 countries for each income category (low, lowermiddle, upper-middle, and high income) as classified in the GNI’s file, which also qualified with the requirement for each income category in the assignment After that, we downloaded the excel files for Domestic General Government Health Expenditure Per Capita, PPP (current international $), Immunization, Measles (% of children ages 12-23 months), Compulsory Education Duration (Years); and Child Mortality rate under (per 1,000 live births) respectively on World Bank Afterward, we transferred the data from those categories into the excel file of 120 countries using VLOOKUP function Finally, in order to have a complete data set, we eliminated countries that missed the data for any of those categories PART 2: DESCRIPTIVE STATISTIC The existence of outliers should be considered and analyzed in advance to ensure the accuracy in descriptive statistics and avoid missing correct results or distorting the important findings After checking and analyzing the data, as in Figure 1, it should be noted that there are significant upper outliers existing in the data set Those include upper-middle country and high-income countries which have an extremely high number of child mortality under the age of Panama, a high-income country, has a number of 15.9, which is extremely higher than the number of countries in the same group Min >,, (8.875) 103.2 < 161.325 outliers Lower-Middle Income countries (LMI) 8.9 > (32.58) 122.8 > 116.7 upper outlier Upper-Middle Income countries (UMI) 3.6 > (0.2) 31.2 > 23.8 upper outlier High-Income countries (HI) 2.4 > (0.725) 15.9 > 9.9 upper outliers Figure 1: Test of outliers in each country’s category in 2017 (unit: death per 1,000 live births) 2.1: MEASURE OF CENTRAL TENDENCY Low-Income countries (LI) Lower-Middle Income countries (LMI) Upper-Middle Income countries (UMI) High-Income countries (HI) Mean 72.3 44 12.9 5.1 Median 64.9 31.3 13.7 No mode No mode 14.7 2.7 Mode Figure 2: Central Tendency of each countries category child mortality rate under the age of in 2017 (unit: death per 1,000 live births) Because there are extreme values in the dataset, they will skew the results and the Mean can no longer be the correct representation of the dataset The mode is not an ideal approach, too As it can be seen, the data are numerical, no value repeats in the groups of Low-Income and LowerMiddle income countries, so Mode cannot be found in these groups of the dataset At last, Median, as a central tendency method, seems effective to describe the matter From Figure 2, it should be noted that the Median of Low-Income Countries is the highest with 64.9 points, inferring that 50% of countries of this group has a total of child death per 1000 live births fewer than 64.9 cases Follow this descending pattern, lower-middle-income countries are ranked second with a Median of 31.3 points and upper-middle-income countries are ranked third with 13.7 points Finally, half of the High-Income Countries has fewer than deaths per 1000 child live births This supposes a possible causal relationship between low income and high child mortality 2.2: MEASURE OF VARIATION Low-Income countries (LI) Lower-Middle Income countries (LMI) Upper-Middle Income countries (UMI) High-Income countries (HI) Interquartile Range 42.55 37.33 2.65 Standard Deviation 27.2 30.89 6.2 3.16 Range 70 113.9 27.6 13.5 Coefficient of Variation 38% 70% 48% 61% Figure 3: Measure of variation of each countries category on the child mortality rate under the age of in 2017 (unit: death per 1,000 live births) Due to them endures an aggregate of five upper outliers in the case, Interquartile Range (IQR) can be applied as the best measure Since it partitions the arrangement into four equivalent parts and measures the distance average in the range of first and third quartile, causing it to get unaffected toward outliers Based on the figure 3, the IQR of low-income countries’ group is the highest with 42.55 The following one is a group of lower-middle income countries with 37.33 Meanwhile, and 2.65 are the lower figures of upper-middle and high-income country categories, respectively with the lowest is high-income countries’ group It can be said that the child mortality rate under the age of of low-income and lower-middle income countries differ greatly from the remaining country categories 2.3: MEASURE OF SHAPE Figure 4: Measure of shape of low-income countries group on the child mortality rate under the age of (unit: death per 1,000 live births) Figure 5: Measure of shape of lower-middle income countries group on the child mortality rate under the age of (unit: death per 1,000 live births) It is clearly seen that the range of low-income countries’ group is lower than the one of lower-middle income countries’ group with 103.2, meanwhile, the range of lower-middle income country category is 122.8 Furthermore, there is clear allocation between two groups through figure and figure The child mortality rate under the age of in low-income countries is 97.5 deaths per 1,000 live births Nevertheless, in the lower-middle income country category, the rate is only 60.73 Figure 6: Measure of shape of upper-middle income countries group on the child mortality rate under the age of (unit: death per 1,000 live births) Figure 7: Measure of shape of high-income countries group on the child mortality rate under the age of in 2017 (unit: death per 1,000 live births) Through the box and whisker plots above (figure and 7), it can be easily recognized that the range of upper-middle income country category is twice as high as the group of high-income countries is with 31.2 and 15.9 in turn Similar to figure and 5, both figures and also have distinct division In upper-middle income countries’ group, the rate of child mortality under the age of is 14.8, while 5.9 deaths per 1,000 live births is the child mortality rate under the age of of the high-income country categories From all the box and whisker plots above, it can be said that the rates of child mortality of low-income and lower-middle income country category are much higher than the other two groups It displays how vital income is to mortality in children under years of age LI LMI Factors Left Comparison Right Result Box 9.95 < 32.6 Rightskewed Whisker 21.75 > 5.7 Leftskewed Median to extreme values 31.7 < 38.3 Rightskewed Box 7.9 < 29.43 Rightskewed Whisker 14.5 < 62.08 Rightskewed Median to extreme values 22.4 < 91.51 Rightskewed Conclusio n Rightskewed Rightskewed UMI Box 4.9 > 1.1 Leftskewed Whisker 5.2 < 16.4 Rightskewed Median to extreme values 10.1 < 17.5 Rightskewed Box 0.75 < 1.9 Rightskewed Rightskewed Rightskewed HI Whisker 0.85 < 10 Median to extreme values 1.6 < 11.9 Rightskewed Rightskewed Figure 8: Country categories’ box, whisker, and median comparison in 2017 (unit: death per 1,000 live births) It is obvious that four country categories have right-skewed through comparing the box, whisker, and median The median of low-income countries’ group is the highest rate with 64.9 deaths per 1,000 live births Then it is a group of lower-middle income countries with a median of 31.3 And upper-middle and high-income countries categories are lower with the median are 13.7 and 4, respectively PART 3: MULTIPLE REGRESSION (FROM YOUR COLLECTED DATA) In order to build a multiple regression model for a data set, we must define all variables including the dependent and independent variables In this case, by constructing a regression model with the aim of the mortality rate of children under years old in different income categories for every country Thus, all variables defined below are Y denoted for the dependent variable and X1, X2, X3, X4 are the independent variables  Y: The child mortality rate under (per 1,000 live births) in 2017  X1: Domestic general government health expenditure per capita, PPP (current international $) in 2017  X2: Immunization, measles (% of children ages 12-23 months) in 2017  X3: Compulsory Education Duration (Years) in 2017  X4: GNI per Capita, Atlas method (US$) in 2017 3.1: REGRESSION MODEL FOR THE DATA SET LI: THE LOW-INCOME COUNTRIES a.1 Final regression output: The approach to backward elimination is used to choose the best regression model that attempts to remove independent variables that are irrelevant at the level of significance of 0.05 and considered adding those variables that are related to the dependent variable indicated in Appendix Although, the final regression output model is found, its p-value is still higher than the significant level of 0.05; Based on that and the fact that all the regression output models before it also does not contain any significant variables, therefore, the regression model for the Low-Income countries is irrelevant Figure 9: Final regression output for the data set of The Low income in 2017 Figure above is the final regression output model with the independent variable of the immunization, measles (% of children ages 12-23 months) a.2 Scatter plot: 31 ^ Y =6.761 ×0.966 31 2020 2.313672341 Figure 37: Predict calculations of Child mortality under the age of in Japan in 2018, 2019 and 2020 PART 6: TIME SERIES CONCLUSION 6.1: LINE CHART Child Mortality rate under (per 1,000 live births) 200 180 160 140 120 100 80 60 40 20 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Afghanistan India China Japan A line chart for child mortality rate under the age of (per 1,000 live births) in four Asia countries: Afghanistan, India, China and Japan from 1990 to 2015 Figure 38: Line chart of child mortality rate under the age of for years 1990 - 2015 of Afghanistan, India, China and Japan 6.2: INTERPRETATION According to the above line chart, it is obvious that every country has had a downward trend in child mortality rate under the age of since 1990, especially Afghanistan, which dropped more than a half during this period time Additionally, its reduction followed the ratio of units per a year Besides, a lower-income country as India, which also decreased dramatically from nearly 130 to 43.5 In China, the rate only dropped slightly in the early time, however since 2000, it continuously followed with a steep fall and reached only 10.7 in 2015 Meanwhile, Japan, which is evaluated as a high-income country, tends to decline steadily with a small drop each year but in the end, its child mortality rate under the age of is still the lowest by jumping down to 2.8 in 2015 25 Country Preferred trend model SSE MAD Afghanistan Exponential 13.78522176 2.624347435 India Quadratic 19.56717 3.087 China Exponential 1.675800671 0.915230088 Japan Exponential 0.011426887 0.062744159 Figure 39: Comparison of SSE, MAD and preferred trend model between countries From the above table, only India is appropriate with the utilization of Quadratic trend for prediction On the other hand, Exponential trend seems to be the most optimal with the rest of countries, hence it is regarded as the best trend model, which should be used to predict the rate of child mortality under the age of More tellingly, by carrying out the comparison of both SSE and MAD for countries preferring Exponential trend, we can recognize that Japan has the smallest values in both SSE (0.011426887 < 1.675800671 < 13.78522176) and MAD (0.062744159 < 0.915230088 < 2.624347435) so that means it will make fewer errors compared with other countries, which will ameliorate the accuracy considerably Consequently, it is summarized that the Exponential trend of Japan is the best method to apply for predicting the child mortality rate under the age of in the world PART 7: OVERALL CONCLUSION Main factors The health status of a country is measured best by data on child mortality (Wang, 2002) The world has made significant progresses in child survival for the past decades, and the risk of children dying in their first years has decreased In order to get further achievement, it is vital to analyze the main determinants of child survival From the above calculations, it is suggested that income, along with other factors, has a significant impact on child mortality and there is a possible causal relationship between these two matters Taking the Median into consideration, we can see that one of low-income countries’ group is the highest rate with 64.9 deaths per 1,000 live births The next ones are of lower-middle income countries, upper-middle and high-income countries categories 26 with 31.3, 13.7 and 4, respectively In addition, with the coefficient of determination 75.89%, it means that 75.89% variation in the child mortality rate under the age of of lower-middle income countries will be explained by variations in the Gross Net Income per capita (US$) and the percentage of children ages 12-23 months has taken the immunization for measles Moreover, the slope value is 1.4195 shows that the number of child mortality rate under the age of will decrease by 1.4195 per 1,000 live births when the percentage of children ages 12-23 months has taken the immunization for measles increase From these findings, we can perceive the importance of income, along with other factors heavily affected by it, in the relationship with child mortality It is suggested that wealthier people are healthier people (Pritchett & Summers, 1996), better health outcomes correlates closely with higher income of a population (Preston, 1975), and income has a remarkable impact on ways to prevent several causes of death (such as immunization), which are sensitive to the level of technology and nutrition (Birchenall, 2007) However, some researchers argue that when income increases, it is not compulsory to spend it on projects helping to develop the health care system Although the true nature of this relationship has not been discovered and analyzed thoroughly yet, it is still noted that income is one of the main determinants of health status of a country This report confirms the importance of income in developing child health, especially in developing countries, and gives policymakers vital ideas about this matter What will be the predicted child mortality rate under the age of in year 2030? As mentioned above, Exponential trend of Japan is recognized as the most optimal predictor in the world for measuring the rate of child mortality under the age of from Part Therefore, applying T= 41, which is the time period of year 2030 in order to calculate the child mortality rate under in 2030 based the aforementioned formula: ^ Y =6.761 ×0.966 T = 6.761 x (0.96641) = 1.637 (deaths per 1000 births) In 2030, with each 1000 births under the age of 5, the world mortality rate will be 1.637 deaths, which will continuously follow the same downward trend as previous years but it can suffer an intensive slump In conclusion, it is likely that the world rate mortality of child under will keep going down gradually in 2030 That sayings, it must be one of the most glorious success of world healthcare as well as pharmacy industry in the process of achieving SDG However, some limitations by using available data as a method to predict the future numbers need to be concerned For instance, extrapolation, which occurs due to exceeding the existing observation range (Uddin & Ullah, 2013) More tellingly, it can likely lead to the outcomes of unintelligible approach as well as inaccurate results in case of a far distance between the current dataset and the forecasted time period In this circumstance, because of the further spread of the predicted time period to the right from the available data, it can result in the imprecise calculation in the future child mortality rate under the age of Besides that, Japan seems to be unable to represent and reflect the world’s change in child mortality because of its inappropriate features compared with the world’s pattern For example, as a high-income country with the enormous development in technology and facilities in the past as well as at the present, Japan has had a smaller rate in child mortality than other countries in the world so its modification in child mortality rate is marginally not much The method, which is based on Japan to foresee the world’s future trend, is called generalization According to Watt 27 & Berg (1995), it is said that if the sample (Japan) and the world have inconsistence traits, the utilization of generalization will lead to erroneous assumptions Based on your research what kind of recommendations can you provide Under-five mortality rates have large disparities across regions and countries, especially income (UNICEF, 2020) It can be clearly seen from the measure of shape in part To be more specific, the child mortality rates under the age of of low-income and lower-middle income country categories are much higher than the other two gatherings with the numbers are 97.5 and 60.73 deaths per 1,000 live births, respectively Meantime, upper-middle and high-income country categories’ rates are 14.8 and 5.9 deaths per 1,000 live births, in turn Nevertheless, according to World Health Organization (WHO), generous worldwide advancement has been made in lessening child deaths since 1990 The absolute number of under-five passing’s worldwide has declined from 12.6 million out of 1990 to 5.2 million out of 2019 Contagious illnesses, including pneumonia, loose bowels and pre-term birth remain the main sources of death for youngsters under five Moreover, Plecher’s research (2020) reveals that gender is also the reason which influences the rate of child mortality, notably in India There have many solutions that may help to cut down the child mortality rate under the age of Having a solid handle of knowledge about nutrition just as perils to the health of youngsters is essential in each family (Huber, 2016) When families have a firm grasp of that knowledge, taking care of the child will not only be less complex but also easy to recognize when the child is sick so that they can be treated promptly Furthermore, enhancement in the soundness of pregnant ladies and new mothers will assume a significant job in producing further decreases in child mortality Poor sustenance in women can prompt preterm births and infants with low-birth weight (Veneman, n.d) Last but not least, education plays a necessary role in life because it may subsidize to the healthiness and well-being of women, children and their nations as well Mainly, changing the mindset of favoring men and women in some countries to avoid abortion or be killed right after birth 28 REFERENCES: Birchenall, J 2007, ‘Economic Development and the Escape from High Mortality’, World Development, vol 35, no 4, pp 543-568 Frost, J 2015, Introduction to Statistics: An Intuitive Guide An Intuitive Guide for Analyzing Data and Unlocking Discoveries, 2nd edn, Statistics by Jim Publishing Huber, C 2016, “Child mortality: Top causes, best solutions”, 13 January, viewed 16 January 2021, Plecher, H 2020, ‘Countries with the highest infant mortality rate 2017’, 30 March, viewed 16 January, 2021, Pr e s t o n , S, 19 , ‘ Th eCh a n g i n gRe l a t i o nbe t we e nMor t a l i t ya n dLe v e lo fEc o n o mi c De v e l o p me n t ’ ,Po pu l a t i o nSt u di e s ,v o l 29 , n o 2, p p 1– , v i e we d1 6J a n u a r y2 02 , h t t p s : / / www j s t o r o r g / s t a b l e / p d f / 21 p d f ? r e f r e qi d =e x c e l s i or %3 Af 6b e 22 c 63 2c a f b e d d f Pr i t c h e t t , L& Su mme r s , L1 9 , ‘ We a l t h i e ri sHe a l t h i e r ’ ,J o ur n a lo fHuma nRe s o u r c e s ,v o l , t p s : / / i or g/ 23 / 46 9> n o , p p 84 8 , v i e we d16J a n u a r y2 , The World Bank, n.d., GNI per Capita, Atlas method (US$), World Bank Group, viewed January 2021, The World Bank, n.d., Immunization, measles (% of children ages 12-23 months), World Bank Group, viewed January 2021, < https://data.worldbank.org/indicator/SH.IMM.MEAS> The World Bank, n.d., Mortality rate, under-5 (per 1,000 live births), World Bank Group, viewed January 2021, < https://data.worldbank.org/indicator/SH.DYN.MORT > The World Bank, n.d., What is an “international dollar”?, World Bank Group, viewed 13 January 2021, 29 Uddin, M & Ullah, M 2013, ‘An approach to generalized extrapolation formula based on rate of changes (derivatives)’, American International Journal of Research in Science, Technology, Engineering & Mathematics, vol 3, pp 169-175, viewed 16 January 2021, < https://www.researchgate.net/publication/285511862_An_approach_to_generalized_extrap olation_formula_based_on_rate_of_changes_derivatives> UNICEF 2020, Under-five mortality, UNICEF, September, viewed 16 January 2021, Veneman, A n.d, ‘Education Is Key to Reducing Child Mortality: The Link Between Maternal Health and Education’, United Nations, viewed 16 January 2021, Wa n g , L2 0 , ‘ He a l t hOu t c o me si nPo o rCo u n t r i e sa ndPo l i c yOp t i o ns :Emp i r i c a lFi n d i n g sf r o m De mo g r a p hi ca n dHe a l t hSu r v e y s ’ ,Wor l dBa n kGr o u p ,2 1J un e , vi e we d1 4J a nu a r y2 02 , < h t t p s : / / d o i o r g / 10 59 / 39 1> Watt, J & Berg, S 1995, Research Methods for Communication Science, Al l y na n dBa c o n , USA WHO 2020, Children: improving survival and well-being, WHO, September, viewed 16 January 2021, < https://www.who.int/news-room/fact-sheets/detail/children-reducingmortality#:~:text=Children%20under%20the%20age%20of%205&text=The%20total %20number%20of%20under,1990%20to%2038%20in%202019> WHO n.d., Hospital beds (per 10 000 population), World Health Organization, viewed 16 January 2021, < https://www.who.int/data/gho/data/indicators/indicatordetails/GHO/hospital-beds-(per-10-000-population)> 30 APPENDIX: APPENDIX 1: Backward elimination process in the regression model for the Low-Income Countries Since we use multiple regression with significance level at 5%, we will determine if the coefficients in each independent variable have an effect on the dependent variable (Y) - the total number of the child mortality rate under the age of (per 1,000 live births) by testing the null hypothesis below: The null hypothesis � �; �� = � (no independent variable explains the change in Y) The alternative hypothesis � �; �� ≠ � (at least one of the independent variables X1, X2, X3, X4 contributes to the variation in Y) where j = 1,2,3,4 To achieve that, we test whether these independent variables are (1) significant or (2) insignificant compare to the p-value with the significance level � = � ��: (1) � − ����� < � = 0.05 => we reject the null hypothesis (�0) => the independent variable is significant (2) � − ����� > � = 0.05 => we not reject the null hypothesis (�0) => the independent variable is insignificant Figure I: Part of the regression outputs for the full data set of Low-Income countries According to that figure I, there are no independent variables that is significant All of their P-value are greater than the significance level of 0.05 To search for the significant, independent variable, we will have to remove the one variable with the highest p-value Hence, the GNI per capita, Atlas method (US$) variable is eliminated Figure II: Part of the regression outputs when GNI per capita, Atlas method (US$) is eliminated In figure II, there are still no sign of independent variables with p-value less than 0.05, thus we continue with the backward elimination method and eliminate the one with the highest p-value, Compulsory Education Duration (years) Figure III: Part of new regression outputs when Compulsory Education Duration is eliminated Since there are still no significant independent variables found in figure III, domestic general government health expenditure, PPP (current international $) with the highest level of pvalue (0.5848) will be eliminate 31 Figure IV: Final regression output for the data set of The Low-Income countries Coming to an end with figure IV, the significant independent variables are still unseen, thus, the regression model for the Low-Income Countries will be rejected; and it is considered irrelevant APPENDIX 2: Backward elimination process in the regression model for The LowerMiddle Income Countries Figure V: Part of the regression outputs for the full data set of the Lower-Middle Income countries According to that figure V, there is one independent variable, which is important at a significance level of 0.05, and three other variables are insignificant since the p-values (0.0575, 0.00472, 0.80847) are higher than the significance level (0.05) The highest p-value, but is eliminated first (0.92193) from the Compulsory Education Duration variable The figure will remove the Compulsory Education Duration first Figure VI: Part of the regression when Compulsory Education Duration is eliminated At the 0.05 significance level, there are three variables here, but the variable in Domestic general government level health expenditure will first be excluded because of the highest p-value, which is 0.8131 Therefore, the new regression output after domestic general government level health expenditure is eliminated is shown on the figure below Figure VII: Part of the regression outputs when Domestic General Government Health Expenditure, PPP is eliminated 32 Based on figure VII, the Immunization, measles (% of children ages 12-23 months) and GNI per Capita, Atlas method (US$) are significant independent variables, since its p-value is smaller than the significance level (0.05) In turn make figure VII the final regression output model for the LowerMiddle Income countries APPENDIX 3: Backward elimination process in the regression model for The Upper-Middle Income Countries Figure VIII: Part of the regression outputs for the full data set of the Upper-Middle Income countries Based on figure VIII, there is only one independent variable that is significant; the other three independent variables are insignificant since its p-value is higher than the significant level α =0.05 However, the variable for compulsory education duration (0.93) highlights the highest p-value, thus, compulsory education duration is eliminated Figure IX: Part of the new regression outputs when Compulsory Education Duration is eliminated In figure IX, there are still two independent variables that are insignificant Hence, we have to continue eliminate the category with the highest p-value In this case, immunization, measles contains the highest p-value at 0.83 Figure X: Part of the new regression outputs when Immunization, Measles is eliminated Next in figure X, GNI’s p-value is 0.28 which is higher than the significant level of 0.05, therefore, GNI is an independent variable that is insignificant Thus, it is eliminated Figure XI: Final regression output for the Upper-Middle Income countries 33 In the last output, figure XI contains only one independent variable and its p-value is less than the significant level at 0.05, thus, domestic general government health expenditure is significant Consequently, figure X is the final regression output model for the Upper-Middle Income countries, where only significant variables remain APPENDIX 4: Backward elimination process in the regression model for The High-Income Countries Figure XII: Part of the regression outputs for the full data set of the High-Income countries According to figure XII, out of the four-independent variable, there is only one variable that is significant since its p-value is less than 0.05 The other three are insignificant because 0.77, 0.20, 0.71 is higher than the significant level at 0.05 Thus, the one with the highest p-value at 0.77 (immunization, measles) is eliminated Figure XIII: Part of the new regression outputs when Immunization, Measles is eliminated In figure XIII, there are still two independent variables that are insignificant because their p-value are higher than 0.05 Therefore, we continued with the elimination of the variable with the highest p-value In this case, GNI with the p-value at 0.73 is removed Figure XIV: Part of the new regression outputs when GNI per Capita is eliminated Based on figure XIV, compulsory education duration with its p-value at 0.18 is higher than 0.05, thus, it is considered insignificant On the other hand, the p-value of domestic general government health expenditure is significant is lower than 0.05, hence, it is considered significant Since not all variables are significant, we continued with the eliminating process This time, compulsory education duration is eliminated Figure XV: Final regression output for the High-Income countries Lastly in figure XV, the p-value at 0.007 is lower than the significant level at 0.07, thus, makes domestic general government health expenditure significant In consequence, figure XIV is the final regression output for the High-Income countries APPENDIX 5: Linear Trend Calculation – Hypotheses Testing for Typical Asia Countries in each Level of Income a Low-income country: Afghanistan Null hypothesis H0; b1 = (No existence of linear trend) Alternative hypothesis H1; b1 ¹ (Existence of Linear trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no linear trend In case p-value > α=0.05 => we accept the null hypothesis => There is linear trend Since the p-value = 0.0000000000000000000000000000005724429 < α=0.05 , we reject H0 Consequently, with 95% of confidence, we conclude that there is linear trend in lowincome country data set b Lower-middle income country: India Null hypothesis H0; b1 = (No existence of linear trend) Alternative hypothesis H1; b1 ¹ (Existence of Linear trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no linear trend In case p-value > α=0.05 => we accept the null hypothesis => There is linear trend Since the p-value = 0.000000000000000000000000000000000000002192 < α=0.05 , H0 must be rejected, therefore we assume that there is linear trend in lower-middle income country data set with 95% of confidence c Upper-middle income country: China Null hypothesis H0; b1 = (No existence of linear trend) Alternative hypothesis H1; b1 ¹ (Existence of Linear trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no linear trend 35 In case p-value > α=0.05 => we accept the null hypothesis => There is linear trend Due to the smaller value of p compared with α (0.00000000000000000000000525 < 0.05), we are 95% of confidence to jump into the conclusion that there is certainly linear trend in uppermiddle income country data set by rejecting H0 d High-income country: Japan Null hypothesis H0; b1 = (No existence of linear trend) Alternative hypothesis H1; b1 ¹ (Existence of Linear trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no linear trend In case p-value > α=0.05 => we accept the null hypothesis => There is linear trend As the p-value = 0.000000000000000000000000000000000000002192 < α=0.05 , the rejection of H0 will be carried out, thus we can claim that linear trend exists in high-income country data set with 95% of confidence APPENDIX 6: Quadratic Trend Calculation – Hypotheses Testing for Typical Asia Countries in each Level of Income a Low-income country: Afghanistan Null hypothesis H0; b2 = (There is no quadratic trend) Alternative hypothesis H1; b2 ¹ (There is quadratic trend) So as to test the null hypothesis, the comparison between the p-value and level of significance α=0.05 need to be clarified In case p-value < α=0.05 => we reject the null hypothesis => There is no quadratic trend In case p-value > α=0.05 => we accept the null hypothesis => There is quadratic trend 36 As p-value (T-squared) = 0.0000000000026072658461822 < α=0.05 , the confirmation about the existence of quadratic trend in low-income country data set will be supported by the rejection of H0 with 95% of confidence b Lower-middle income country: India Null hypothesis H0; b2 = (There is no quadratic trend) Alternative hypothesis H1; b2 ¹ (There is quadratic trend) So as to test the null hypothesis, the comparison between the p-value and level of significance α=0.05 need to be clarified In case p-value < α=0.05 => we reject the null hypothesis => There is no quadratic trend In case p-value > α=0.05 => we accept the null hypothesis => There is quadratic trend Since p-value (T-squared) = 0.0000000000026072658461822 < α=0.05 , H0 must be rejected Hence, the existence of quadratic trend in lower-middle income country data set will be confirmed with 95% of confidence c Upper-middle income country: China Null hypothesis H0; b2 = (There is no quadratic trend) Alternative hypothesis H1; b2 ¹ (There is quadratic trend) So as to test the null hypothesis, the comparison between the p-value and level of significance α=0.05 need to be clarified In case p-value < α=0.05 => we reject the null hypothesis => There is no quadratic trend In case p-value > α=0.05 => we accept the null hypothesis => There is quadratic trend Due to the larger value of α ( 0.05 ) compared with p-value (T-squared) (0.022079224), it leads to the rejection of H0, which results in the attestation of the existence of quadratic trend in upper-middle income country data set with 95% of confidence d High-income country: Japan Null hypothesis H0; b2 = (There is no quadratic trend) Alternative hypothesis H1; b2 ¹ (There is quadratic trend) So as to test the null hypothesis, the comparison between the p-value and level of significance α =0.05 need to be clarified 37 In case p-value < α=0.05 => we reject the null hypothesis => There is no quadratic trend In case p-value > α=0.05 => we accept the null hypothesis => There is quadratic trend As p-value (T-squared) = 0.0000000000026072658461822 < α=0.05 , with 95% of confidence, H0 must be rejected as well as there is quadratic trend in high-income country data set APPENDIX 7: Exponential Trend Calculation – Hypotheses Testing for Typical Asia Countries in each Level of Income a Low-income country: Afghanistan Null hypothesis H0; b1 = (There is no exponential trend) Alternative hypothesis H1; b1 ¹ (There is exponential trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no exponential trend In case p-value > α=0.05 => we not reject the null hypothesis => There is exponential trend As p-value (trend) = 0.0000000000000000000000000000348934494560064 < α=0.05 , H0 must be rejected Hence, the existence of exponential trend in low-income country data set will be confirmed with 95% of confidence b Lower-middle country: India Null hypothesis H0; b1 = (There is no exponential trend) Alternative hypothesis H1; b1 ¹ (There is exponential trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no exponential trend In case p-value > α=0.05 => we not reject the null hypothesis => There is exponential trend Since p-value (trend) = 0.00000000000000000000000599200091244421 < α=0.05 , H0 must be rejected Thus, the existence of exponential trend in lower-middle income country data set will be confirmed with 95% of confidence 38 c Upper-income country: China Null hypothesis H0; b1 = (There is no exponential trend) Alternative hypothesis H1; b1 ¹ (There is exponential trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no exponential trend In case p-value > α=0.05 => we not reject the null hypothesis => There is exponential trend Since p-value (trend) = 0.00000000000000000000363 < α=0.05 , H0 must be rejected Therefore, the existence of exponential trend in upper-middle income country data set will be confirmed with 95% of confidence d High-income country: Japan Null hypothesis H0; b1 = (There is no exponential trend) Alternative hypothesis H1; b1 ¹ (There is exponential trend) Null hypothesis needs to be tested by performing the comparison between the p-value and level of significant α=0.05 In case p-value < α=0.05 => we reject the null hypothesis => There is no exponential trend In case p-value > α=0.05 => we not reject the null hypothesis => There is exponential trend As p-value (trend) = 0.000000000000000000000000055 < α=0.05 , H0 must be rejected Consequently, the existence of exponential trend in high-income country data set will be confirmed with 95% of confidence 39 ... 3.3: REGRESSION MODEL FOR THE DATA SET UMI: THE UPPER-MIDDLE INCOME COUNTRIES 3.4: REGRESSION MODEL FOR THE DATA SET HI: THE HIGH- INCOME COUNTRIES 10 PART 4: TEAM REGRESSION. .. REGRESSION MODEL FOR THE DATA SET HI: THE HIGH- INCOME COUNTRIES a.1 Final regression output: The backward elimination was applied to reach to the final regression output model for HighIncome countries, ... MULTIPLE REGRESSION (FROM YOUR COLLECTED DATA) 3.1: REGRESSION MODEL FOR THE DATA SET LI: THE LOW -INCOME COUNTRIES 3.2: REGRESSION MODEL FOR THE DATA SET LMI: THE LOWER-MIDDLE INCOME COUNTRIES