(TIỂU LUẬN) measure of central tendency measure of variation box and whisker plot analysis

Group Group Contents Group Members and Contribution Abbreviation Part 1: Data Collection Part 2: Descriptive Analysis a Test of Outliers b Measure of Central Tendency c Measure of Variation d Box-and-Whisker Plot Analysis Part 3: Multiple Regression a LI countries regression model b LMI countries regression model c UMI countries regression model .10 d HI countries regression model 12 Part 4: Team Regression Conclusion .13 a Conclusion for Part .14 b Conclusion for Part and Part 15 Part 5: Time Series 15 Regression Output for Liberia, Lao, Guyana, and Netherlands 15 a Liberia 15 b Lao .16 c Group Guyana 17 d Netherlands 18 Trend Model and Formula for all countries 19 Recommend Trend Model .19 a Liberia 19 b Lao .19 c Guyana 19 d Netherlands 20 Predict crude death rate for Liberia, Lao, Guyana, and Netherlands year 2018-2020 20 a Liberia 2018 to 2020 20 b Lao 2018 to 2020 20 c Guyana 2018 to 2020 20 d Netherlands 2018 to 2020 20 Part 6: Time Series Conclusion 21 a Line chart 21 b Best trend model anticipating the crude death rate all over the world 21 Part 7: Overall Team Conclusion .22 a Main factors that impact the crude death rate 22 b Predicted crude death rate in year 2030 22 c Recommendations 22 References 23 Group Appendices 26 Appendix A: 143 Countries Data sort by GNI (Low to High) 26 Appendix A.1: Low Income 26 Appendix A.2: Low-Middle Income 27 Appendix A.3: Middle-Upper Income 28 Appendix A.4: High Income 29 Appendix B: Backward Elimination process in the regression model 29 Appendix B.1: LI countries 29 Appendix B.2: LMI countries 30 Appendix B.3: UMI countries .31 Appendix B.4: HI countries 31 Appendix C: Time Series 32 Appendix C.1: Significant Trend Models validation process for Liberia, Laos, Guyana, Netherlands 32 Appendix C.2: Crude death rate prediction for Liberia, Lao, Guyana, and Netherlands for year 2018 to 2020 calculations 38 Group Members and Contribution First Name Student ID s3836504 Nguyen, Huynh Thai Dung, Le Thi Thuy s3817818 Group Parts Contributed 1,2,3,4,5,6,7 Contribution % 100 4, 5, 6, 100 My, Huynh Thi Quyen s3817901 1, 2, 3, 4, 100 Thao, Huynh Ngoc Phuong s3870275 4,5,6,7 100 Vy, Pham Thi Thuy s3836232 1,2,3,7 100 Signature Abbreviation  Low Income (LI)  Lower Middle Income (LMI)  Upper Middle Income (UMI)  High Income (HI)  Death rate (DR)  Gross national income (GNI)  Domestic general government health expenditure (GGHE-D)  Immunization, measles (IM)  Prevalence of current tobacco use (PCTU) Part 1: Data Collection The countries divided into four categories based on the income level (Appendix A) The data set is for year 2014 includes variables (Appendix A) The data are collected from World Bank (n.d.a) Initially, it contains 217 countries, however, due to shortage of information of some of the countries so we had to eliminate those and only kept 143 countries that have sufficient information that meet the requirements – variables Besides, the reason we selected all the 143 countries instead of narrowing it down is we want to maintain the original and pure of the data and prevent bias in the data cleaning process, hence, creating a more transparency and accuracy dataset (Šimundić 2013) Part 2: Descriptive Analysis a Test of Outliers Group Figure 2.a: Test of outliers of the total amount of deaths rate in types of studied income With the purpose to evaluating the certainty of descriptive measurement, the table show the test of outliers is displayed Outliers is a tool, which help to observe the data which not stay the same with another data of the rest (Lumenlearning n.d.) Relied on the figure and compared the number of minimums with lower bound and maximum with upper bound, we have outliers occurred in this data b Measure of Central Tendency Figure 2.b: Central Tendency of total amount of deaths rate based on types of studied income Considering the central tendency of this case, some outliers exist in this case, but it was far away from upper bound and lower bound Thus, we could not use the mean to indicate them The median is more useful than others with purpose to calculate the central tendency of types of income levels Moreover, the median is the most suitable dimension because it allows to measure the approximately average of types of income (Investopedia 2020) The median frequently to use in reverse with the mean because when the outliers appear to make value of data skew a bit Furthermore, the median could not be affected by outliers than the mean, so when the outliers exist, the best way to calculate is that we would use median For this reason, expected to measure the central of tendency of income, the median should be applied in this case Based on the figure 2.b, the median of data fluctuated from 6.746 (LMI) to 7.162 (UMI) This number depicts that 50% of UMI countries confront greater than 7.162 of mortality case and another 50% of them had less than 7.162 death case per dollar in community reported survey We would visualize the same picture for LMI dataset, 50% countries in this type of income recorded they had deal with more than 6.7415 of death case and 50% countries had less than 6.7145 mortality case due to the disease In totally, the median of crude death rate based on two types of income upper and lower middle income seems like approximately equal c Measure of Variation Figure 2.c: Measure of Variation of total amount of deaths rate based on types of studied income The movement from the lowest point to the highest point of data is exhibited by Range, then bring a rapid and rough estimation about expansion of value inside the dataset (ChiliMath n.d.) Relied on figure 2.c, the range of HI countries exist is the largest number, which give an information that the amount of deaths’ contribution based on HI is the most scattered in 2014 The Interquartile Range is one of many indicators often used with purpose to calculate how well the data point expands from the mean inside the dataset () The larger the IQR would lead to the more data point is outspreaded () In contrary, the lower the IQR would lead the more data point is gathering close to the median (Stephanie n.d.) According to figure 2.c, the IQR of LI countries is the smallest number in the income group, which give an opinion that the number of death case in LI is gathering around the median, while the number of mortality case of another type of income spread out seriously To be more clearly, the total amount of deaths in LI countries closed to the value in the middle and more stable when compared with the expansion of death case Group in another income level () Because of utilize of IQR, we could claim that the generally picture is Low Income have covered more mortality case than other types of income level The variance exhibits the level of scattering of the data values from the mean () A small variance display that the point of data seems like very close to the mean and other points and vice versa for high variance () Like standard deviation, it also demonstrates how far and closely of the values around the mean Standard deviation is one of the prominent measurements of variability, the reason is that the result is given in original units (Roberts n.d.) Looking at figure 3, it was marked that the pair variance and standard deviation in LI countries is less than the number of other types of income, which could be clarified that the data point of LI countries going to cluster around the mean while the data point of another income separates from the mean Calculating the scatter of data point inside the data set around the mean, the Coefficient of Variation is the statistical estimation is suitable to proceed (Adam 2020) As can be observed from the figure 2.c, a background could be drawn that Low Income has the smallest coefficient of variation when compared with another income area (2364% < 3593% < 3806% < 3810%) This show that the value of data around means of LI countries were more separated than the rest types of income In this situation, it has a paradoxical thing between the analyze in the standard deviation and the coefficient of variation When the standard deviation shows that the recognized values in LI cluster and close to the mean than the rest of type of income, while the coefficient of variation support vice versa This could be defined that standard deviation is usually used to examine one data series and if there are greater than one dataset, coefficient of variation would be considered For this reason, coefficient of variation should be organized with purpose to compare the scatter of income areas In a nutshell, having a smallest standard deviation and variance, LI data is more consistent than another income, demonstrate that the reported survey staying the same d Box-and-Whisker Plot Analysis Figure 2.d: Box and whisker plots represent the crude deaths rate based on types of income level Based on figure 2.d., it is can be seen that the only data distributions of HI countries are slight left skewed For the other income levels, the length of the right whiskers is much longer than that of the left Group whiskers, reflecting on the of outliers in the data distribution Furthermore, and max of the amount of death cases in LI because of disease was higher than these measurement in other areas of income For this reason, we could assume that the countries in the LI area suffered more mortality case than another types of income In additional, the median of LMI was slower than the median of Upper Middle Income (6.7415 < 7.162), which mean that 50% of Lower Income confirmed that the number of death case no more than 6.7415 cases, while, in UMI half of them suffered fewer than 7.162 cases Because of the application of box and whisker plot, we could visualize to draw a generally picture that LI have a huge number of deaths than another area before the reported research Part 3: Multiple Regression Regardless of the income level of the selected country category, it is all initially comprised of the same dependent and independent variables, which are: Basically, the backward elimination method is employed to eliminate irrelevant, redundant, or not statistically significant at a 5% level of significance variables from many variables hence, it can enhance the accuracy and the quality of regression models (Ruan et.al 2020) a LI countries regression model Based on the result of Figure B.1.4 of Appendix B.1, because all variables’ p-value are much higher than the given level of significant, so we must eliminate all (Narin, Isler & Ozer 2013) Hence, no final regression output is constructed for the LI countries dataset which means there is no relationship between DR and the fourth variables and the variation of that will not affect the DR so it might depends on different factors (Hannerz et al 2019) In other words, those predictor variables are not statistically significant, we not reject H0 and there is insufficient evidence in our sample to conclude that a non-zero correlation exists and as the results, there is no scatter plot to illustrate for LI countries (Hannerz et al 2019) b LMI countries regression model Regression output: Group Figure 3.b.1: Final model of LMI countries Final model of LMI countries Based on the result of Figure B.2.2 of Appendix B.2 and figure 3.b.1., after eliminating least significant variable, the remaining- Immunization - measles, GGHE-D, and GNI are the most significant variables because its p-value = 0.0003; 0.006; 0.044 < α = 0.05 In other words, the remaining predictor variables are statistically significant, our sample data provide enough evidence to reject the H0 so changes in the independent variables are associated with changes in the response at the DR (Fauzi 2017) Scatter plot: Group Figure 3.b.2: Scatter plots of final output of LMI countries Regression Equation: Y = 18.8623 -0.0011X + 0.0183X2 - 0.1264X3 (where Y is the estimated DR and X1 X2 X3 are the independent variables - the GNI, GGHE-D, and IM) Interpret the regression coefficient of the significant independent variable: b1 = -0.0011 shows that for every increase of unit of current US$ of the GNI per capita by using Atlas method, the DR per 1000 live births will decrease by 0.001 deaths, considering the two remaining factors as constant b2 = 0.0183 shows that for every increase of unit of international US$ of the domestic general government expenditure on health per capita, the DR per 1000 live births will increase by 0.018 deaths, considering the two remaining factors as constant b3 = -0.1264 shows that for every increase of 1% of children ages 12-23 months who received the measles vaccination before 12 months or at any time before the survey, the DR per 1000 live births will decrease by 0.126 deaths, considering the two remaining factors as constant Interpret the coefficient of determination: R2= 0.381 interprets that only 38.1% of the variation of the DR is explained by the variation of GNI, GGHE-D, and Immunization, measles, the remaining 61.9% of the DR is explained by different factors (Glen n.d) c UMI countries regression model Regression output: 10 Group Appendices Appendix A: 143 Countries Data sort by GNI (Low to High) Appendix A.1: Low Income Appendix A.2: Low-Middle Income 26 Group 27 Group Appendix A.3: Middle-Upper Income 28 Group Appendix A.4: High Income Appendix B: Backward Elimination process in the regression model Appendix B.1: LI countries The hypothesis testing (applied onward for all other backward eliminations) 29 Group The Null hypothesis H0 : β j = (The chosen independent variable(s) has no relationship with the Death rate, crude - dependent variable)  The Alternative hypothesis H1 : βj ≠ (at least one of the X1, X2, X3, X4, X5 - the chosen independent variable(s) has a relationship with the DR- dependent variable) P-value test  If p-value < α = 0.05 => Reject the Null hypothesis and accept the Alternative hypothesis, there is at least variable influences DR  If p-value > α = 0.05 => Accept the Null hypothesis and reject the Alternative hypothesis, there is no relationship between chosen independent variable(s) and DR Step 2: Backward Elimination  Includes of rounds of running to identify variable(s) which are significant at 5% (0.05) level of significant  Figure B.1.1: The initial regression model before applying backward elimination method of LI countries  From the first regression output, Prevalence of current tobacco use is the least significant variable because its p-value = 0.586 > α = 0.05 Hence, we eliminate PTU Figure B.1.2: The second regression output after eliminating least significant variable of LI countries  From the second regression output, Domestic general government health expenditure per capital is the least significant variables because its p-value = 0.539 > α = 0.05 Hence, we eliminate PPP Figure B.1.3: The third regression output after eliminating least significant variable of LI countries  From the third regression output, GNI per capita is the least significant variables because its p-value = 0.393 > α = 0.05 Hence, we eliminate GNI Figure B.1.4: The final regression output after eliminating least significant variable of LI countries Lastly, from the fourth regression output, Immunization, measles is the least significant variables because its p-value = 0.148 > α = 0.05 Hence, we eliminate IM Appendix B.2: LMI countries The hypothesis testing & P-value test can be done same as LI countries Step 2: Backward Elimination  Includes of rounds of running to identify variable(s) which are significant at 5% (0.05) level of significant  Figure B.2.1: The initial regression model before applying backward elimination method of LMI countries 30  Group From the first regression output, Prevalence of current tobacco use is the least significant variable because its p-value = 0.476 > α = 0.05 Hence, we eliminate PCTU Figure B.2.2: The second regression output after eliminating least significant variable of LMI countries From the second regression output after eliminating PCTU, the three remaining variables are significant variables because their p-value < α = 0.05 Hence, the backward elimination process stops here Appendix B.3: UMI countries The hypothesis testing & P-value test can be done same as LI countries Step 2: Backward Elimination  Figure B.3.1: The initial regression model before applying backward elimination method of UMI countries  From the first regression output, Domestic general government health expenditure per capita is the least significant variable because its p-value = 0.689 > α = 0.05 Hence, we eliminate GGHE-D Figure B.3.2: The second regression output after eliminating least significant variable of UMI countries  From the second regression output, Immunization, measles is the least significant variable because its pvalue = 0.639 > α = 0.05 Hence, we eliminate IM Figure B.3.3: The third regression output after eliminating least significant variable of UMI countries  From the third regression output, GNI per capita is the least significant variables because its p-value = 0.403 > α = 0.05 Hence, we eliminate GNI Figure B.3.4: The final regression output after eliminating least significant variable of UMI countries After eliminating GNI, the PCTU is the significant variable because its p-value = 0.0015 < α = 0.05 Hence, the backward elimination process stops here Appendix B.4: HI countries The hypothesis testing & P-value test can be done same as LI countries Step 2: Backward Elimination  Figure B.4.1: The initial regression model before applying backward elimination method of HI countries 31  Group From the first regression output, Immunization, measles is the least significant variable because its pvalue = 0.156 > α = 0.05 Hence, we eliminate IM Figure B.4.2: The second regression output after eliminating least significant variable of LMI countries From the second regression output after eliminating IM, the three remaining variables are significant variables because their p-value < α = 0.05 Hence, the backward elimination process stops here Appendix C: Time SeriesX  Appendix C.1: Significant Trend Models validation process for Liberia, Laos, Guyana, Netherlands Appendix C.1.1: Liberia Linear Trend Model Hypothesis testing at 5% significance level for Linear Trend in Liberia: Ho: �1 = (There is no linear trend) Ha: �1 ≠ (There is a linear trend) 32 Group According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is a linear trend for crude death rate in Liberia Quadratic Trend Model Hypothesis testing at 5% significance level for Quadratic Trend in Liberia: Ho: �1 = (There is no quadratic trend) Ha: �1 ≠ (There is a quadratic trend) According to the regression output, p-value = 0.09 > � (0.05), therefore we accept Ho We have enough evidence at 95% level of confidence to conclude that there is no quadratic trend for crude death rate in Liberia Exponential Trend Model Hypothesis testing at 5% significance level for Exponential Trend in Liberia: Ho: �1 = (There is no exponential trend) Ha: �1 ≠ (There is an exponential trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is an exponential trend for crude death rate in Liberia Appendix C.1.2: Laos Linear Trend Model 33 Group Hypothesis testing at 5% significance level for Linear Trend in Laos: Ho: �1 = (There is no linear trend) Ha: �1 ≠ (There is a linear trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is a linear trend for crude death rate in Laos Quadratic Trend Model Hypothesis testing at 5% significance level for Quadratic Trend in Laos: Ho: �1 = (There is no quadratic trend) Ha: �1 ≠ (There is a quadratic trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is a quadratic trend for crude death rate in Laos Exponential Trend Model 34 Group Hypothesis testing at 5% significance level for Exponential Trend in Laos: Ho: �1 = (There is no exponential trend) Ha: �1 ≠ (There is an exponential trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is an exponential trend for crude death rate in Laos Appendix C.1.3: Guyana Linear Trend Model Hypothesis testing at 5% significance level for Linear Trend in Guyana: Ho: �1 = (There is no linear trend) Ha: �1 ≠ (There is a linear trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is a linear trend for crude death rate in Guyana 35 Group Quadratic Trend Model Hypothesis testing at 5% significance level for Quadratic Trend in Guyana: Ho: �1 = (There is no quadratic trend) Ha: �1 ≠ (There is a quadratic trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is a quadratic trend for crude death rate in Guyana Exponential Trend Model Hypothesis testing at 5% significance level for Exponential Trend in Guyana: Ho: �1 = (There is no exponential trend) Ha: �1 ≠ (There is an exponential trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is an exponential trend for crude death rate in Guyana Appendix C.1.4: Netherlands Linear Trend Model 36 Group Hypothesis testing at 5% significance level for Linear Trend in Netherlands: Ho: �1 = (There is no linear trend) Ha: �1 ≠ (There is a linear trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is a linear trend in the crude death rate in Netherlands Quadratic Trend Model Hypothesis testing at 5% significance level for Quadratic Trend in Netherlands: Ho: �1 = (There is no quadratic trend) Ha: �1 ≠ (There is a quadratic trend) According to the regression output, p-value = 0.814 > � (0.05), therefore we accept Ho We have enough evidence at 95% level of confidence to conclude that there is no quadratic trend for crude death rate in Netherlands Exponential Trend Model 37 Group Hypothesis testing at 5% significance level for Exponential Trend in Netherlands: Ho: �1 = (There is no exponential trend) Ha: �1 ≠ (There is an exponential trend) According to the regression output, p-value = < � (0.05), therefore we reject Ho We have enough evidence at 95% level of confidence to conclude that there is an exponential trend for crude death rate in Netherlands Appendix C.2: Crude death rate prediction for Liberia, Lao, Guyana, and Netherlands for year 2018 to 2020 calculations ❑ Liberia: log ( Ŷ )= b0 + b1 X = 1.339-0.016*T In 2018 correlative with T=29, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 1.339-0.016*29 = 0.868 → Ŷ ❑ = 7.380 In 2019 correlative with T=30, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 1.339-0.016*30 = 0.852 ❑ → Ŷ = 7.109 In 2020 correlative with T=31, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 1.339-0.016*31 = 0.836 ❑ → Ŷ = 6.848 Error : |e| = |Actual - Prediction| We calculate the error in 2018: |e| = |7.5 – 7.380| = 0.120 We calculate the error in 2019: |e| = |7.4 – 7.109| = 0.291 We calculate the error in 2020: |e| = |7.3 – 6.848|= 0.452 ❑ ❑∨e∨ ¿ ∑ MAD : MAD = n ❑ ¿ We predict years hence n=3 ❑ ❑∨e∨ ¿ = = 0.288 ∑ We have the formula for MAD = n ❑ ¿ SSE: The formula for SSE = Σ e = 0.745 Lao: log ( Ŷ ❑ )= b0 + b1 X = 1.148-0.013*T In 2018 correlative with T=29, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 1.148-0.013*29 = 0.764 38 Group ❑ → Ŷ = 5.808 In 2019 correlative with T=30, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 1.148-0.013*30 = 0.751 → Ŷ ❑ = 5.633 In 2020 correlative with T=31, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 1.148-0.013*31 = 0.738 → Ŷ ❑ = 5.464 Error : |e| = |Actual - Prediction| We calculate the error in 2018: |e| = |6.4 – 5.808| = 0.592 We calculate the error in 2019: |e| = |6.3 – 5.633| = 0.667 We calculate the error in 2020: |e| = |6.3 – 5.464|= 0.836 ❑ ❑∨e∨ ¿ ∑ MAD : MAD = n ❑ ¿ We predict years hence n=3 ❑ ❑∨e∨ ¿ We have the formula for MAD = ∑ n = = 0.698 ❑ ¿ SSE: The formula for SSE = Σ e = 4.389 ❑ Guyana: log ( Ŷ )= b0 + b1 X = 0.918-0.003*T In 2018 correlative with T=29, we have the result: log ( Ŷ ❑ )= b0 + b1 X = 0.918-0.003*29 = 0.832 ❑ → Ŷ = 6.797 In 2019 correlative with T=30, we have the result: log ( Ŷ ❑ )= b0 + b1 X = 0.918-0.003*30 = 0.829 ❑ → Ŷ = 6.751 In 2020 correlative with T=31, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 0.918-0.003*31 = 0.826 ❑ → Ŷ = 6.705 Error : |e| = |Actual - Prediction| We calculate the error in 2018: |e| = |7.5 – 6.797| = 0.703 We calculate the error in 2019: |e| = |7.6 – 6.751| = 0.849 We calculate the error in 2020: |e| = |7.7 – 6.705|= 0.995 ❑ ❑∨e∨ ¿ ∑ MAD : MAD = n ❑ ¿ We predict years hence n=3 ❑ ❑∨e∨ ¿ = = 0.849 We have the formula for MAD = ∑ n ❑ ¿ SSE: The formula for SSE = Σ e = 6.490 ❑ Netherlands: log ( Ŷ )= b0 + b1 X = 0.948-0.001*T In 2018 correlative with T=29, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 0.948-0.001*29 = 0.913 ❑ → Ŷ = 8.184 In 2019 correlative with T=30, we have the result: 39 Group ❑ log ( Ŷ )= b0 + b1 X = 0.948-0.001*30 = 0.912 ❑ → Ŷ = 8.162 In 2020 correlative with T=31, we have the result: ❑ log ( Ŷ )= b0 + b1 X = 0.948-0.001*31 = 0.911 ❑ → Ŷ = 8.139 Error : |e| = |Actual - Prediction| We calculate the error in 2018: |e| = |8.7 – 8.184| = 0.516 We calculate the error in 2019: |e| = |8.8 – 8.162| = 0.638 We calculate the error in 2020: |e| = |8.9 – 8.139|= 0.761 ❑ ❑∨e∨ ¿ ∑ MAD : MAD = n ❑ ¿ We predict years hence n=3 ❑ ❑∨e∨ ¿ ∑ We have the formula for MAD = n = = 0.638 ❑ ¿ SSE: The formula for SSE = Σ e = 3.664 40 ... a Test of Outliers b Measure of Central Tendency c Measure of Variation d Box- and- Whisker Plot Analysis Part 3: Multiple Regression... two types of income upper and lower middle income seems like approximately equal c Measure of Variation Figure 2.c: Measure of Variation of total amount of deaths rate based on types of studied... the number of minimums with lower bound and maximum with upper bound, we have outliers occurred in this data b Measure of Central Tendency Figure 2.b: Central Tendency of total amount of deaths