Assignment 3A-Team-6-G8 SGN business statistic PDF

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RMIT International University VietnamASSIGNMENT COVER PAGEYour assessment will not be accepted unless all fields below are completedSubject code ECON Subject name Business Statistics 1 Class time Thursday 11: Location and campus RMIT Vietnam – SGS Title of Assignment Team Assignment Report 3A Studen...

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RMIT International University Vietnam ASSIGNMENT COVER PAGE

Subject code Subject name Class time Location and campus Title of Assignment Student name - Student number

ECON1193 Business Statistics 1 Thursday 11:30 RMIT Vietnam – SGS Team Assignment Report 3A Ho Trong Dat - S3804678 Do Hoai Viet - S3750310 Phan Minh Dang Khoa - S3818139 Tu Huu Phuc - S3812120 Greeni Maheshwari 22rd May 2020 24th May 2020 12

Lecturer Group number Assignment due date Date of submission Number of pages

Name Khoa Phan

Student ID S3818139

Part Contributed Part 1 (Find 1 dataset) Part 2 (All) Part 3 (All)

Contribution % 100%

Signature Khoa

2

Part 6 (Half) Viet Do

S3750310

Part 7 (2 questions) Part 1 (Find 1 dataset)

100%

Viet

100%

Phuc

85%

Dat

Part 5 (All) Assignment 3B (Powerpoint + Phuc Tu

S3812120

Edit) Part 1 (Find 3 datasets + content) Part 4 (All) Part 7 (2 questions) Assignment 3B (Question 1, 3 +

Dat Ho

S3804678

Presentation) Part 1 (Find 1 dataset) Part 6 (Half) Assignment 3B (Question 2 + Presentation)

PART 1: DATA COLLECTION: In collecting-data process, by enquiring various reliable sources, such as WHO or World Bank, our team successfully collected a wide range of secondary data in the majority of countries in two regions, Asia and Europe & European Union in terms of for six variables: -

Numbers of COVID-19 deaths (between January 22 and April 23, 2020) (Our World In Data 2020).

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-

Average temperature (in mm) that is calculated by data from 1991 to 2016 (World Bank Group 2020). Average rainfall (in Celsius) that is calculated by data from 1991 to 2016 (World Bank Group 2020). Population (in 1,000s) by using data in 2018 (The World Bank 2019). Hospitals beds (per 10,000 people) by using latest available data (WHO 2020). Medical doctors (per 10,000) by using latest available data (WHO 2020).

However, due to the many national issues, mostly relating to sovereignty recognition of few countries, there is still a lack of data in those nations. And solving this problem, we implemented the data-cleansing method, which adjusts and rejects the missing or poor-quality data, hence enhancing the reliability of final result in testing (Gschwandtner et al. 2014), especially building regression model as in this research. As a result of this cleansing progress, we finally have new well-qualified datasets without any missing data, which ensures more reliable output for final regression model: -

Asia: 32 countries (cleaning 3 countries: Hong Kong, Macao, Taiwan). Europe & European Union: 42 countries (cleaning 11 countries: Faroe Islands, Gibraltar, Guerney and Aderney, Jersey, Kosovo, Liechtenstein, Vatican City, Svalbard and Jan Mayen Islands, San Marino, The Isle of Man, Moldova).

PART 2: DECRIPTIVE MEASURE: From the collected and cleaned data about deaths due to COVID-19 pandemic in the first part, we are able to analyze the descriptive measure in two those regions. Generally, the death cases due to Covid-19 in European region is higher than that in Asia but the difference between mortality cases in Asian countries is overall greater than this measure in Europe & European Unions. a. Measure of Central Tendency: Measures Mean (Cases of death) Mode (Cases of death) Median (Cases of death)

Asia 215.37 0 7

Europe & European Union 2329.08 0 79.5

Table 1: Measures of Central Tendancy of COVID-19 deaths in Asia and Europe & European Union

Except for mode that cannot be utilized for assessing due to the variability of data in countries having death cases, two other statistics both can be ideal representative for Central Tendency. And by the way of evaluation, despite the impact from outliers (7 in Asia and 9 in Europe & European Union), mean still seems to be a better statistic for assessing Central Tendency because median witnesses a stronger detrimental effect from the unusual distribution, especially when there are 12 Asian countries having no deaths from COVID-19 (accounted for over one-third of all data in set). With this selection, the number of mortality case in Europe and European Union countries is considerably greater than that in Asia (2329.08 deaths vs 215.37 deaths). In other words, the average COVID-19 deaths in Asian countries is nearly 10 times lower than that number in Europe & European Union countries. b. Measure of Variance: Measures

Asia

Europe & European Union

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IQR (Cases of death) Range (Cases of death) Variance ((Cases of death)2) Standard Deviation (Cases of death) Coefficient of Variance (%)

71.5 4,619 617,357.01 785.72 364.82

491.5 25,085 37,610,339.91 6,132.73 263.31

Table 2: Measures of Variance of COVID-19 deaths in Asia and Europe & European Union

Statistically, IQR and Range are not ideal statistics for reflecting the Variance because they do not demonstrate the distribution. Although Standard Deviation is usually used as representation for Variance due to the relation of all data in set, it seems not to be this case because the absolute value in this statistic is not suitable when the means of Asia and Europe & European Union are vastly different (about 10 times in comparison). As a consequence, Coefficient of Variance is the best selection for representing Variance since this measure shows the relative value, which allows the accurate comparison, no matter how different the means of objectives are. With this choice, we conclude that the variability of numbers of deaths between Asian countries is much greater than that in European nations (364.82% vs 263.31%). Specifically, there is a further dispersion of mortality cases around its average deaths in Asian nations than those in Europe & European Union. c. Measure of Shape:

44619

Graph 1: Box-and-Whisker plot of Asia and Europe & European Union

Even though box-and-whisker plot and mean-and-median comparison always demonstrate the same result of skewness, graph-illustrating solution is still better for analysis as it not only explains the detail of skewness but also reveals exactly the distribution of data in four quarters, which provides the viewers with a deep understanding about features of different sets. For example, in this case, in spite of the same right-skew distribution, box of Europe & European Union is much longer, which describes the vaster spread of middle 50% of data in this region than that in Asian nations. And as a result of this choice, we generally infer that two regions has right skewness, which means that more than 50% of total Asian countries have the COVID-19 deaths below 215.37 mortality cases while lower than 50% of total countries in Europe and European Union have the deaths over 2329.08 cases due to pandemic.

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PART 3: MULTIPLE REGRESSION: As mentioned in part 1, through the collecting and cleansing step, we have two sets with the data from 32 Asian and 41 European countries for building regression model. And with this model, we are able to estimate the change in number of COVID-19 deaths when tested predictors change. Specifically, our purpose in Multiple Regression part is finding out: - Whether there are significant influences from 5 independent variables (average temperature, average rainfall, populations, hospital beds and medical doctors) on dependent variable (COVID-19 deaths). - How those independent variables impacts dependent variable (Negative/Positive, Strong/Weak). Most remarkably, to fulfil those purposes, elimination backward procedure is used for removing all insignificant variables in this case. The reason behind using this method is that the variability of error is impacted by the number of predictors, which can be explained by the mutual interactions between those independent variables that results in the inaccuracy of regression model (Cai & Hayes 2007). Consequently, by eliminating variables one-by-one, elimination backward can effectively remove those interactions, which enhances the veracity of final regression model. After applying this method, our team successfully eliminate insignificant predictors to reach to the final model that contains only variable that are significant at 5% level of significance in two regions: 1. Asia: a. Regression output:

b. Equation: COVID19 deaths (y-hat) = -19.551 + 0.002(Population) -

In which Units are:  Estimated COVID19 deaths (cases).  Population (1000s).

c. Regression coefficients:

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

b1 = 0.002 indicates that the number of deaths increases by 0.002 cases for every 1000 people increase in population.  b0 = -19.551 shows that when the population is zero, the estimated deaths due to COVID19 is -19.5512 cases. However, this interpretation makes no sense in this case because the deaths cannot be a negative value and it is impossible for having deaths when there are no people in a country. * As a consequence of this equation, we implicate that: - There is a significant influence from population on the COVID-19 deaths in each country (p-value = 0.000 < 0.05 = Level of significance). - There is a positive (0.002 is positive) relation between COVID-19 deaths and population. d. Coefficients of determination: R square = 0.631 indicates that about 63.1% of the variation in COVID19 deaths may due to variation in population of a country, the remaining 36.9% of variation of COVID19 deaths are influenced by other factors. 2. Europe & European Union: a. Regression output:

b. Equation: COVID19 deaths (y-hat) = -11669.702 + 0.142(Population) + rainfall) + 579.428(Average temperature) -



90.87(Average

In which Units are:  Estimated COVID19 deaths (cases).  Average Rainfall (mm).  Average Temperature (Celsius).  Population (1000s).

c. Regression coefficients: b1 = 0.142 shows that the COVID 19 deaths will increase, on average, by 0.142 death for every 1000 people increase in population, holding average rainfall and average temperature as constant.

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

b2 = 90.87 shows that the COVID 19 deaths will increase, on average, by 90.87 death for every mm increase in average rainfall, holding the average temperature and the population as constant.  b3 = 579.428 shows that the COVID 19 deaths will increase, on average, by 579.428 death for every Celsius increase in average temperature, holding average rainfall and population as constant.  b0 = -11669.702 shows that when the Average rainfall, the Average temperature and Population are zero, the approximated deaths due to COVID19 calculated as – 11669.702 deaths. However, it is meaningless if there is no population in a single country and number of deaths remain negative; hence there is no significant interpretation for this intercept. * From equation, we infer that: - There are significant influences from population, average rainfall and average temperature on the COVID-19 deaths in each country (p-value (population) = 0.000 < 0.05; p-value (average rainfall) = 0.028 < 0.05; p-value (average temperature) = 0.005 < 0.05). - There are positive (0.142; 90.87 and 579.428 are positive) relation between COVID deaths and population. d. Coefficients of determination: R square equals 0.417 indicates that about 41.7% of the variation in COVID19 deaths may due to variation in the average rainfall, the average temperature and the population of a country, the remaining 58.3% of variation of COVID19 deaths are influenced by other factors.

PART 4: TEAM REGRESSION CONCLUSION: 1. Do both the models have the same significant independent variable/s? Based on the final regression model in two regions, it is obvious that there are dissimilarity in significant variables between two regions. Particularly, by applying Elimination Backward method (see more from 5 models and hypothesis tests in appendix), we eliminated 4 insignificant variables in Asia and 2 insignificant variables in Europe & European Union. Consequently, we have the final models in two regions, in which Asia has only one significant variable: population, Europe & European Union has 3 significant independent variables: average temperature, average rainfall and population. Thus, two models have different significant variables. Explaining by scientific evidences, population appears in both models showing the close positive relation between population and number of deaths, which can be interpreted by many intermediate elements, especially the number of cases. Specifically, the crowded population would encourage the invasion of infectious diseases as the pathogens rises (Dobson & Carper 1996). As a result, as Donaldson and his colleagues (2009) proved, the more crowed area likely has the higher number of infectious cases, hence possibly having higher deaths if the death rate is the same internationally. Another explanation is that larger population size may result in lower individual care and overwhelming situation. Considering Wuhan three months ago as a typical example, all hospitals at there were overcrowded and the mortality cases accelerated exponentially (Li et al. 2020). So, most of scientific evidence support our final regression model. Regarding remained variables, the European model implicates the positive correlation between numbers of deaths and average temperature. However, it is widely acknowledged that the viability of Coronavirus is lower with the higher temperature (Chan et al. 2011). In other words, this finding shows the negative relation between average temperature and the

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numbers of COVID-19 deaths since the higher temperature discourages the development of this virus. Similarly, in this study, Chan and his colleagues (2011) stated the negative relationship between the stability of Coronavirus and the humidity. As a consequence, they also denied the positive correlation between number of mortality cases and average rainfall, which is result of our final model. Therefore, the positive relations of two variables with deaths are not supported by scientific evidences. 2. Which region is more impacted due to this pandemic? Based on equation of our final regression model, we conclude that Covid-19 has more impact on Europe & European Union than Asia by checking out the slopes, which summarizes the change in death cases resulting from the change in variables. By the way of illustration, in the ‘population’ variable, b1 value in Asia is 0.002 that is extremely small in a comparison with the slope of 0.142 in Europe & European Union, which is nearly 70 times. As a result of this exponential difference, despite the population in Asia is 5 times greater than that in Europe & European Union (The World Bank 2019), the European nations are more impacted by population due to its massive slope comparing with Asia. (1) In addition, while Asia is not significant influenced by average rainfall and average temperature due to the disappearance of two variables in equation but they strongly affect the number of death in European countries (b2 = 90.87, b3 = 579.428). Once again, Europe & European Union is more impacted by average rainfall and average temperature. (2) From (1) and (2), we infer the more influence from pandemic on Europe & European Union than Asia. Impressively, this finding is strongly supported by the result of the descriptive measure when the number of death in European is nearly 10 times higher than Asia (Central Tendency). * Non-technical conclusion: To sum up, from the regression output, we imply that the number of Covid-19 death in European nations are affected by average temperature, average rainfall and population while mortality cases in Asia are influenced by only population. Moreover, from regression equation and descriptive measure, we generally conclude that European countries are more impacted by pandemic that the Asian partner.

PART 5: TIME SERIES: In this part, we will collect data of COVID-19 deaths in Asia and Europe & European Union between February 15, 2020 and April 30, 2020. Based on this dataset, we will build the trend models and choose the best one for predicting the number of COVID-19 deaths in future by using time series:

1. Asia: After using the hypothesis tests (see more in Appendix), we infer that Quadratic (QUA) does not exist and only two significant models exist in Asia with regression outputs and formulas below: a. Regression output: - Linear (LIN) trend model:

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-

Exponential (EXP) trend model:

b. Formula: Model

Formula ^ Y

LIN EXP (in non-linear format) EXP (in linear format)

= 2.425 + 5.706T

Log ( ^ Y ) = 1.761 + 0.012T ^ Y = 57.677 × 1.028T

Table 3. Formula of significant models in Asia Based on regression output, we are able to compare the R-square for choosing the best model to predict the number of COVID-19 deaths in Asia. Specifically, R-square of Exponential trend model is 67.3%, which is higher than the other significant trend model (38.6%). Thus, we strongly recommend the exponential (EXP) trend model for estimating the further mortality cases in Asia due to the least fault among numerous models. And so, we also choose this model for forecasting the number of deaths due to COVID-19 in Asia on May 29, May 30 and May 31 as table below: EXP ^ Y

= 57.677

May 29 ×

≈ 1048

May 30 ≈ 1077

May 31 ≈ 1107

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1.028T Table 4. Predicted deaths on May 29, May 30, May 31 in Asia 2. Europe & European Union: After using the hypothesis tests (see more in Appendix), we infer that Quadratic (QUA) does not exist and only two significant models exist in Europe & European Union with regression outputs and formulas below: a. Regression output: - Linear (LIN) trend model:

-

Exponential (EXP) trend model:

b. Formula: Model LIN

Formula ^ Y

= -730.218 + 64.340T

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EXP (in non-linear format)

Log ( ^ Y ) = -2.717 + 0.112T ^ Y

EXP (in linear format)

= 0.002 × 1.294T

Table 5. Formula of significant models in Europe & European Union With this regression output, in the similar way, we use R-square as a tool for evaluating the best model. And once again, Linear (LIN) trend model still has the highest Rsquare at 71.5% (comparing with 50.1% of Linear trend model). Consequently, we recommend using the Linear trend model for predicting the number of deaths due to COVID19 in Europe & European Union. Based on this model, we also estimate the number of COVID-19 deaths in Europe & European Union on May 29, May 30 and May 31 as table below: LIN

May 29

May 30

May 31

^ Y

= -730.218 + ≈ 6025 ≈ 6089 ≈ 6154 64.340T Table 6. Predicted deaths on May 29, May 30, May 31 in Europe & European Union

PART 6: TEAM SERIES CONCLUSION: 1. Line charts of number of deaths in two regions:

Graph 2. A line chart of number of deaths in Europe & European Union

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Graph 3. A line chart of number of deaths in Asia 2. Comment on trend models and line charts: Based on our analysis in part 5 above, we conclude that both regions have the same significant trend models: Linear (LIN) trend model and Exponential (EXP) trend model. However, the best model for predicting deaths in Asia is the Exponential trend model while the Europe & European Union chooses the Linear trend model as the best one. Anyway, both suitable models show the increasing trend when β 1 (= 1.028) in Asian Exponential trend model and b1 (= 64.340) in European Linear trend model are all positive. Moreover, the line graphs above demonstrate the complicated fluctuations. By the way ...