ECON1193 Team 06 Assignment 3a Report 1 PDF

Preview

Summary

RMIT International University VietnamASSINGMENT 3 PART ASubject code ECON1193BSubject name Business Statistic 1Location and campus RMIT Vietnam – SouthSaigonTitle of assignment Team assignment reportLecture Greeni MaheshwariAssignment due date 18thSeptember, 2020Team Team 06Number of page 121TABLE O...

Description

RMIT International University Vietnam ASSINGMENT 3 PART A Subject code Subject name

ECON1193B Business Statistic 1

Location and campus Title of assignment

RMIT Vietnam – South Saigon Team assignment report

Lecture

Greeni Maheshwari

Assignment due date

18th September, 2020

Team

Team 06

Number of page

12

1 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

TABLE OF CONTENTS PART 1: DATA COLLECTION

3

PART 2: DESCRIPTIVE STATISTICS

3

PART 3: MULTIPLE REGRESSION

5

PART 4: TEAM REGRESSION CONCLUSION 6 PART 5: TIME SERIES

7

PART 6: TIME SERIES CONCLUSION 11 PART 7: OVERALL TEAM CONCLUSION REFERENCES

12

15

APPENDIX 16

CONTRIBUTION First name

Student ID

Parts contributed Contribution

Khanh

S3811511

1,3,5,7

100%

Kha

S3826384

1,5,6,7

100%

Thinh

S3818172

2,4,6

100%

Lan

S3836374

2,3,7

100%

Hoang

S3826384

1,3,7

100%

Signature

PART 1: DATA COLLECTION The data for the total number of deaths due to COVID 19 between April 01 to July 31, 2020, and five other variables including average temperature (in Celsius) and average rainfall (in mm) based on available data from 1991 to 2016, medical doctors ( per 10,000 people, latest available), hospital beds (per 10,000, latest available) and population of the country (in 2 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

millions, latest available) for 50 countries in Region A: Asia and 23 countries in Region B: North America were collected. After the cleaning process, there are 46 countries remaining in Region A: Asia and 21 countries remaining in Region B: North America. The datasets are presented in the attached Excel file.

PART 2: DESCRIPTIVE STATISTICS 

Central Tendency Measurements Central Tendency Asia

North America

Mean

36.756

91.747

Median

10.031

27.09

Mode

0

0

Figure 1. Measures of Central Tendency of total number of deaths due to COVID-19 between April 01 to July 31, 2020, in Asia and North America. In comparing the total death in Asia and North America by using the Central Tendency measurements, there is nothing worth notice in the mode figure, which will not be considered. Moreover, the mean will not be used to interpret since there is the existence of outliers, based on the calculation in appendix 1.1 and appendix 1.2. Consequently, the Median will be the most suitable measurement for the comparison which illustrates that 50 percent of the values are greater than the median and the remaining 50 percent are lower than the median.At first glance, it can be clearly defined that there is a significant difference between Asia and North America middle number of total deaths relating to the COVID-19. In addition, North America with the figure of 27.09, which is roughly three times higher than Asia with the median of 10.031. Therefore, it can be concluded that North American countries have more deaths relating to the Cocid-19 than the Asian countries.  Box and whisker plot

Figure 2. Box-and-whisker plots of total number of deaths due to COVID 19 in Asia and EU countries.

3 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

As can be seen from the box and whisker plot we drew above, the data distribution of Asia and North America region are both right-skewed. Moreover, the right whiskers of Asia and North America are both longer than the left whiskers shows the presence of outliers in the datasets. The box and whisker plots show that 75% of countries in North America have more than 27 deaths per million population while 75% of countries in Asia have only more than 10 deaths. In addition, 25% of the number of deaths in Asia is around 1 to 10 deaths and 2 to 27 deaths in North America. From which demonstrates that North American countries have a higher death rate than Asian countries.  Measurements of variation Variation Measurements Asia

North America

Range

248.04

447.099

IQR

50.501

99.125

Variance

3170.34

17621.706

Standard Deviation

56.306

132.747

Coefficient of Variation

86.253

192.068

Figure 3. Measures of Variation of total deaths in Asia and EU (Unit: number of deaths except for the Coefficient of Variation). In this scenario, the best measure of variation is the Interquartile Range (IQR) due to the existence of outliers. In addition, standard deviation is not suitable to measure because it can be heavily influenced by the outliers, the coefficient of variation is also not a good choice as we can notice that the distribution of the datasets above is highly right-skewed. The Interquartile Range of Asia region (50.501) is smaller than the Interquartile Range of North America (99.125), indicating that the dispersion of data of Asia region around the median is smaller. In other words, the total number of deaths by Covid-19 in Asia are more consistent than in North America, or the Covid-19 pandemic has less impact on the Asia region than on North America.

PART 3: MULTIPLE REGRESSION 1. Region A: Asian countries (FINAL) After applying backward elimination, we find that one variable which is the average rainfall is significant at a 5% level of significance. The FINAL regression model for Asian countries is given below. a. Regression output

4 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

Figure 4: FINAL regression model of Region A: Asia b. Regression Equation : = b0 + b1 * = 61.01 - 0.286* c. Regression coefficient of the significant independent variable The slope b1= - 0.286 indicates that the total number of deaths due to COVID 19 between April 01 to July 31, 2020, decreased by 0.286 deaths with every mm increase in the amount of rainfall. In this case, for no rainfall, b0 = 61.01, which makes sense as it is possible to have deaths regardless there is rain or not. Also, the intercept indicates that over the sample size selected, the portion of the total number of deaths due to COVID 19 between April 01 and July 31, 2020, is not explained by the average rainfall (in mm) of a country is 61.01 deaths. Therefore, the total number of deaths is 61.01 when there is no rainfall. d. The coefficient of determination The coefficient of determination (R square = 16.3%) shows that 16.3% of the total variation in the total number of deaths due to COVID 19 from April 01 to July 31, 2020, can be explained by the variation in the amount of rainfall, while 83,7% of the total variation in the total number of deaths due to COVID 19 between April 01 and July 31, 2020, is due to non included factors in the observation. 2. Region B: North American Countries (FINAL) After applying backward elimination, we find that only one variable named Population (in millions) is significant at a 5% level of significance. The Final regression for North American countries is given below.

5 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

a. Regression Output

Figure 5: FINAL regression model of Region B: North America. b. Regression Equation: = b0 + b1* = 52.98 +1.399* c. The regression coefficient of the significant independent variables The slope b1= 1.399 indicates that the total number of deaths due to COVID 19 between April 01 to July 31, 2020, increased by 1.399 deaths with every million people increasing in the population of the country. In this case, for no population, b0= 52.98, which makes no sense. However, the intercept simply indicates that over the sample size selected, the portion of the total number of deaths due to COVID 19 between April 01 and July 31, 2020, not explained by the number of the population of the country is 52.98 deaths. Also, when X1 = 0, that means it is impossible to have deaths when there is no population. d. The coefficient of determination The coefficient of determination (R Square = 61.1 %) shows that 61.1 % of the total variation in the total number of deaths due to COVID 19 from April 1 to July 31, 2020, can be explained by the variation in the population of the country, while 38.9% of the total variation in the total number of deaths due to COVID 19 between April 1 and July 31, 2020, is due to non included factors in this observation.

PART 4: TEAM REGRESSION CONCLUSION According to the study in Part 3, the final claim is that the two regions have the same amount of significant independent variables but in different types including average rainfall (in mm), hospital beds (per 10,000 population), medical doctors (per 10,000 population), average temperature (in Celsius) and population (in millions). In the Asia final regression model, the significant independent variable is the average rainfall (in mm). In the North America data set, the significant independent variable in the final regression model is Population (in millions) among the five listed above variables. In comparison, the North America region has remarkably more total deaths according to the findings in part 2, which means the region has 6 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

been impacted more than the Asia Region due to the pandemic. Moreover, from the study in part 3, 61.1% of the total variation in the total total deaths in North America due to COVID 19 can be explained by the population of the country (in millions) which illustrates that the variation of population contributes a major impact to the variation of the total number of deaths in the NA region. Meanwhile, in Asia, only 16.3% of the variations in the total number of deaths can be explained by the variation of the average rainfall (in mm), which means that the average rainfall influence on the total deaths is not too great and a large amount of other considerable factors that are not included in the study leading to a lower reliable result compared to that of the North America region. To conclude, by building the regression models and comparing the descriptive statistics of two regions, this study indicates that the average rainfall can be used to forecast the total number of deaths due to COVID 19 in Asia while in North America, the population of the country is the independent variable that can be utilized to predict the total number of deaths. Also, the North American countries have suffered a higher impact due to the greater number of deaths due to the pandemic in comparison to Asian countries.

PART 5. TIME SERIES In part 5, our group collected data for the total number of deaths per day in two regions Asia and North America from April 01 to July 31, 2020. In the collected datasets, if there are no deaths on a particular day and hence to build the exponential trend model, we will take 0.00005 instead of 0 to build the exponential trend model as log(0) cannot be calculated. The datasets are presented in the attached Excel file. 1. Build Linear, Quadratic and Exponential trend models. 1.1 Region A: Asia After testing the Hypothesis for trend models in the Asia region (appendix 3.1), the findings indicate that linear, quadratic and exponential trend models are significant for this region. 

a.

Linear Trend Model Regression output

Figure 6. Time Series outputs for Region A: Asia linear trend. b. Formula: = 88.199 + 10.366* 7 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

  

a.

The slope b1= 10.366 indicates that the total number of deaths due to COVID 19 between April 01 to July 31, 2020, increased by 10.366 deaths every day. b0 = 88.199 when T = 0, which illustrates that there were 88.199 deaths on 31 March, 2020. Quadratic Trend Model Regression output

Figure 7. Time Series outputs for Region A: Asia quadratic trend. b. Formula: =338.607–1.75*+ 0.0985*  The slope b2= 0.0985 indicates that the total number of deaths due to COVID 19 between April 01 to July 31, 2020, increased by 0.0985 deaths every .  b0 = 338.607 when T = 0, which illustrates that there were 338.607 deaths on 31 March, 2020.  Exponential Trend Model a. Regression output

Figure 8. Time Series outputs for Region A: Asia exponential trend. b. Formula: in linear format: log() = 2.383 + 0.00653* In non-linear format: = 241.546 *

8 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

Interpretation: ( b1 - 1) * 100% = 1.5% is the estimated daily compound growth rate in percentage for the total number of deaths due to COVID 19 from April 01 to July 31, 2020 in Asia. 1.2 Region B: North America After testing the Hypothesis for trend models in the North America region (appendix 3.2), the findings indicate that linear and exponential trend models are significant. Linear Trend Model a. Regression output



Figure 9. Time Series outputs for Region B: North America linear trend. b. Formula: = 2056.42 - 5.37*  The slope b1= - 5.37 indicates that the total number of deaths due to COVID 19 between April 01 to July 31, 2020, decreased by 5.37 deaths every day.  b0 = 2056.42 when T = 0, which illustrates that there were 2056.42 deaths on 31 March, 2020.  Exponential Trend Model a. Regression output

Figure 10. Time Series outputs for Region A: Asia exponential trend.

9 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

b. Formula: In linear format: log() = 3.2840 - 0.00127* In non-linear format: = 1923.43 * Interpretation: ( b1 - 1) x 100% = 0.3% is the estimated daily compound decrease rate in percentage for the total number of deaths due to COVID 19 from April 01 to July 31, 2020 in North America. 2. Recommended Trend Models The Coefficient of Determination (R Square) will be used to determine the most suitable trend model for the regression outputs. Higher the coefficient of determination, the more of the total variation in the number of deaths can be explained, which is better for the estimating the number of deaths due to COVID 19. a. Region A: Asia

R Square

Linear

Quadratic

Exponential

67.62%

73.68%

80.60%

Figure 11. Coefficient of determination of linear , quadratic and exponential trend models of NA (%). For region A, it can be seen in the figure that the exponential trend had the highest coefficient of determination, which means the exponential trend model will be the most suitable in region A's situation to predict the total number of deaths due to Covid-19 as it will produce fewer errors. b. Region B: North America

R Square

Linear

Exponential

7.90%

7.26%

Figure 12. Coefficient of determination of linear and exponential trend models of NA (%). For region B, with a slightly higher coefficient of determination; hence, the linear trend model will be the most suitable in region B's situation to predict the total number of deaths due to Covid-19 as it will produce fewer errors compared to the exponential trend model. 3. Predict the number of deaths on September 28, September 29, and September 30.

10 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

a. Region A: Asia As the above conclusion, the exponential trend is the best model for predicting the number of deaths due to COVID 19 in Asia, with the formula: = 241.546 *

Date (T)

Forecasted number of deaths

September 28 (181)

3575.64

September 29 (182)

3629.27

September 30 (183)

3683.71

Figure 13. Forecasted number of deaths on September 28,29,30 in Asia. b. Region B: North America As the above conclusion, the linear trend is the best model to predict the number of deaths due to COVID 19 in North America, with the formula: = 2056.42 - 5.37*

Date (T)

Forecasted number of deaths

September 28 (181)

1084.45

September 29 (182)

1079.08

September 30 (183)

1073.71

Figure 14. Forecasted number of deaths on September 28, 29, 30 in North America.

PART 6: TIME SERIES CONCLUSION a. Line chart 11 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

Figure 15. . Line graph of Daily total number of deaths due to COVID 19 in Asia and North America from April 01 to July 31,2020. b. Explanation The line graph above presents the daily total number of Deaths in Asia and North America due to Covid 19 from April 01 to July 31, 2020. It can be concioused that the number of Deaths in Asia is more stable and significantly less (in number of deaths) compared to North America, although this is the region where the pandemic was spread. There is an existence of irregular components in 2 periods, once occurred in 15-April and once in 17-June, and started to increase steadily from 24-June to 29-June. On the other hand, in North America was a chaos of fluctuation, the number of deaths reached the peak in 15-April, then started to move downward with the cyclical component of a 7 days period until the end of the observation. Also, the region has the irregular component of 24-June, which the number of deaths got higher than any other nearby period. Relating to Part 5.3, Asia and North America do not follow the same trend model in order to predict the numbers of death due to the Covid-19, which is the exponential trend model in Asia and the linear trend model in North America. To come up with the conclusion, our team has compared the Coefficient of Determination (R Square), because the higher the Coefficient of Determination, the lesser error, the more total variation in the number of deaths can be explained. The R Square of exponential trend mode of Asia is the highest (80.6%), similarity, the linear trend model of North America is higher than the other (7.9%). In conclusion, we want to use exponential trend model to predict the total number of death in the world since its R square is larger than the Linear trend model in North America (80.6% > 7.9%), presenting that 80.6% of the independent variable (number of deaths by the Covid 19) can be explained by exponential trend model.

PART 7 : OVERALL TEAM CONCLUSION 7.1 Main factors impacting the total number of deaths Based on part 3, Multiple Regression analysis of Asia region, it indicates that there is only one significant independent variable that may affect the total number of deaths due to COVID 19 which is the average rainfall (in mm) at 95% level of confidence. Based on the regression 12 SGS RMIT – Business Statistic 1 – ECON1193B – TEAM 06

equation in part 3 (Total number of deaths= 61.01 - 0.286 *average rainfall), we can easily see that the coefficient of rainfall is negative, hence, the amount of rainfall has an inverse relationship with the total number of deaths due to COVID 19 which means that with every mm increasing in rainfall, the total number of deaths will decrease by 0.286 deaths. However, the findings in Part 3 show that the coefficient of determination of the average rainfall is only 16.3%, which could be inferred that the influence of rainfall on COVID 19 pandemic is not too great but still be considered. Similarly with the Multiple Regression analysis of the North America region, the significant variable that may affect the total number of deaths due to COVID 19 is population (in millions) at 95% level of confidence. By observing the regression equation for North Am...