Bstat asignment 3 group orject PDF

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RMIT International University VietnamECON1193 - Business Statistics 1ASSIGNMENT 3Name Student id Part contributed Countribution SignatureNguyen Si Hung S3878216 7,B 100%Le Nguyen Hung S3822922 3 100%Andrew Yit S3881108 1,4 100%Tran Anh Quan S3877058 2 100%Ho Nguyen Phuc S3878433 5,6 100%Subject code...

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RMIT International University Vietnam ECON1193 - Business Statistics 1 ASSIGNMENT 3 Subject code

ECON1193

Subject name

Business Statistics 1

Lecturer

Teck Lee Yap (Stanley)

Name

Student id

Part contributed

Countribution

Nguyen Si Hung

S3878216

7,B

100%

Le Nguyen Hung

S3822922

3

100%

Andrew Yit

S3881108

1,4

100%

Tran Anh Quan

S3877058

2

100%

Ho Nguyen Phuc

S3878433

5,6

100%

Signature

PART 1: For this part of the assignment, our team has to collect nine variables of the dataset from the world bank in the year 2004, which includes GDP per capita growth rate (annual %), Life expectancy at birth, total (years), GNI per capita, Atlas method (current US$), GDP per capita (current US$), Foreign direct investment, net inflow (% of GDP), Exports of goods and services (% of GDP), Imports of goods and services (% of GDP), Trade (% of GDP) and Population (ages 15-64 (total) years). We collected over 55 countries from both regions at first. The cleaning process is straightforward, any countries with missing variables will be void. Below are the following pictures on how the data are cleaned.

Figure 1: How to download data from the worldbank

Figure 2: Worldbank data of GDP (growth annual %)

Once choosing the countries to use, I will go download thee file as an excel as can be seen from the drawing above on the picture. After downloading the excel file from the world bank the raw data looks pretty messy so we transform them into a style where it is much easier to read.

Figure 3: Worldbank missing information Then, any countries with any missing variables as can be seen from the picture above we mark them as red so we could know that these countries should be deleted.

Figure 4: Chosen country data Finally, after successfully voiding all, we finalised the list of chosen countries as can be seen above. PART 2: DESCRIPTIVE STATICS 1. Measures of Central Tendency:



European countries:

Q3 + 1.5*IQR = 11.7666257545 9.28288775 < 11.7666257545 => Max < Q3 + 1.5*IQR => Max is not an outlier in upper values Q1 – 1.5*IQR = -3.7394 1.105911322 > -3.7394 => Min > Q1 – 1.5*IQR => Min is not an outlier in lower values 

African countries:

Q3 + 1.5*IQR = 7.1876624645 6,489599681 < 7.1876624645 => Max < Q3 + 1.5*IQR => Max is not an outlier in upper values Q1 – 1.5*IQR = -2.1719459235 -6,10287512 < -2.1719459235 => Min < Q1 – 1.5*IQR => Min is an outlier in lower values European countries' average GDP per capita growth rate (mean) in 2004 was much higher than that of African countries (4.218861687 % > 1.958022018 %). Due to the exist of outliers, mean is no longer the best measure of central tendency. Meanwhile, the mode has been disabled, as a result of which neither European nor African countries are recognized. Therefore, median is widely recognized as the best measure for analyzing the GDP per capita growth rate (annual %) of European and African countries since it is not affected by outliers. From the table 1, European countries have higher median than African ones, with almost 3.93% compared to mostly 3% and from this comparison, it can be said that European countries have a bigger GDP per capita growth rate (annual %) than countries in Africa.

2. Measures of Variation

Table 2: Measures of Variation of GDP per capita growth rates of 2 country categories in 2004 (annual %)

In terms of range and IQR, European countries’ range is smaller than the range of African countries (8.176976428 < 12.5924748) whereas the IQR of European countries is relatively

bigger than African countries’ one (3.876496621 > 2.339902097). About coefficient of variation, the result in European countries is considerably lower than African countries, specifically almost 59.5% compared to nearly 160%. The coefficient of variation results for countries in Africa and Europe are both fairly high, implying that data dispersion around the mean is enormous in both regions. To put it another way, the GDP per capita growth rates recorded in 2004 for African and European countries varied and ranged by considerable margins.

Figure 1: Box and Whisker graph of GDP per capita growth rates of 2 country categories in 2004 (annual %)

According to figure 1, the most obvious factor is that African countries had the lowest GDP per capita growth rate, whereas countries in Europe dominated the growth rate of GDP per capita. European countries’ box plot is right-skewed whereas the box plot of African countries is leftskewed. None of European countries has negative GDP per capita growth rate whereas the minium GDP per capita growth value of countries in Africa records a number of -6.10287512

(Table 3). All the values of European countries ( min, Q1, median, Q3 and max ) is higher than in African countries

PART 3: MULTIPLE REGRESSION (2004) In this case, we are going to utilize backward elimination to analyze the regression of Region A (Europe). The final regression modle after applying backward elimination will include only variable(s) that are significant at the level of 5%.

1. Regression Output and Scatter Plots 

Region A: Europe

Figure X: Final regression model of Europe

GDP per capita growth rate (annual %)

Life expectancy at birth, total (years) Line Fit Plot GDP per capita growth rate (annual %) Predicted GDP per capita growth rate (annual %)

Linear (GDP per capita growth rate (annual %))

14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 60.00

65.00

70.00

75.00

80.00

85.00

90.00

Life expectancy at birth, total (years)

Fig ure Y: The scatter plot of GDP per capita growth rate (annual %) and Life expectancy at birth, total (years) of Europe countries

As data shown in Figure Y, it is considerable that: 

The Life expectancy at birth, total (years) results in 2004 of Europe countries in the dataset were all higher than 60 years. The points were quite near to one other, showing that the variations in life expectancy at birth amongst Asian nations were not very significant.



The trendline had a decreasing slope, indicating that there was a negative relationship between GDP per capita growth rate and life expectancy at birth.

Figure Z: The scatter plot of GDP per capita growth rate (annual %) and Population (age 1564 (total) years) of Europe countries

As data shown in Figure Z, it is considerable that: 

Most Europe countries recorded the Population (age 15-64 (total) years) results lower than 60 millions, whereas two of them were outliers of more than 100 millions.



The trendline had a increasing slope, indicating that there was a positive relationship between GDP per capita growth rate and Population.

From both Figure Y and Z, we can see that there is no Europe countries received negative GDP per capita growth rate when the points are all greater than 0. They were also quite far away from each other, especially there was existence of two outliers of almost 11% - 12% GDP per capita growth.



Region B: Africa

Figure 1: Final regression model of Africa

Foreign direct investment, net inflow (% of GDP) Line Fit Plot

GDP per capita growth rate (annual %)

GDP per capita growth rate (annual %) Predicted GDP per capita growth rate (annual %)

Linear (GDP per capita growth rate (annual %))

35.00 30.00 25.00 20.00 15.00 10.00 5.00 -2.00

0.00 0.00 -5.00

2.00

4.00

6.00

8.00

10.00

12.00

-10.00 Foreign direct investment, net inflow (% of GDP)

Figure 2: The scatter plot of GDP per capita growth rate (annual %) and Foreign direct investment, net inflow (% of GDP) of Africa countries As data shown in Figure 2, it is considerable that: 

The majority of African countries had positive net inflows of Foreign direct investment, net inflows of (% of GDP), while one had a negative outcome. The points were likewise distributed between 0 and 6 percent of GDP which means that there are some voids in the Foreign direct investment, net inflow among African nations.



Same as the Foreign direct investment, net inflows of (% of GDP), GDP per capita growth rate reecorded by Africa countries are positive, where as one of them had a negative result.

The values are quite close to each other, indicating that the differnces between GDP per capita growth rate of countries in this region were not too significant.  The trendline was going upward and this means that the relationship between between GDP per capita growth rate and Foreign direct investment, net inflow (% of GDP) was positive.

2. Regression Equation The equation for regression is going to be built as below: Region A: Europe

Region B: Africa





Whereas:

Whereas:

: GDP per capita growth (annual %)

: GDP per capita growth (annual %)

: Life expectancy at birth, total (years)

: Foreign direct investment, net inflow (%

Population (age 15-64 (total) years)

of GDP)

a) Regression Coefficient 

Region A: Europe indicates that the expected GDP per capita growth rate will decline by 0.694 percent for every one year rise in life expectancy at birth. indicates that the expected GDP per capita growth rate will decrease by 4,055E-08 percent for every one year rise in Population (age 15-64 (total) years)



Region B: Africa indicates that the expected GDP per capita growth rate will increase by 1,548 percent for every one year rise in Foreign direct investment, net inflow (% of GDP)

b) Coefficient of Determination 

Region A: Europe

means that 66,8% of the variation in Europe countries’ GDP per capita growth rate can be explained by the variation of their Life expectancy at birth and Population (1564) every single year. 

Region B: Africa Same as Europe, states that 40,7% of the variation in GDP per capita growth rate in Africa can be observed by the changes in Foreign direct investment, net inflow (% of GDP).

PART 4: TEAM REGRESSION CONCLUSION 

Looking at both regression model for Africa and Europe we can conclude that for Europe the most significant independent variables would be the Life expectancy and population while for Africa it would be the Foreign direct investment.



Based on our scatter plots and some academic research it is safe to say that African countries experience a higher economic growth compared to European countries, due to the fact that over the past decades, Africa has increased the trade with the rest of the world by 200% (Ighobor 2012).



The models for Europe in 2004, showed that there was a positive relationship between the GDP per capita growth rate and Population while on the other hand, the scatter plot for life expectancy at birth and GDP per capita growth rate shows a negative relationship. On the other hand, for African countries the Foreign direct investment, net inflows of (% of GDP), GDP per capita growth rate are positive.



The regression model for Europe show that there a high coefficient of determination. By implementing the backward elimination process, we can observe that only variables that are significant at level of 5% will be include.



For the regression model of Africa, we have found that we didn’t include variables such as Life expectancy at birth, total (years), GNI per capita, Atlas method (current US$), GDP per capita (current US$),), Exports of goods and services (% of GDP), Imports of goods and services (% of GDP), Trade (% of GDP) and Population (ages 15-64 (total) years). Will record a p-values smaller but close to 5% significance level.

PART 5: TIME SERIES LIN,QUA,EXP trend of four countries ( South Africa, Congo, Netherland and Moldova) Region B: Africa

Low income country: Congo (1990-2015)  Regression trend 1. Linear regression trend (LIN) A. regression output

B. Formula & Coefficient explanation: Formula: Y^= 120,62 +10,7368*T Coefficient explanation: b0 =120,628743 is the estimated and expected GDP of Congo when T =0. But it does not make sense because the range not included T=0 b1= 10,7386 is the estimate increase of GDP of Congo each year 2. Quadratic regression trend (QUA) A. Regression output

B. Formula & Coefficient explanation: Formula: Y^= 282,79 –24,01*T+1,28*(T^2) Coefficient explanation b1= -24,01 is the estimate of GDP when T=0. But in this case T=0 is not in the range so it canot be identified b2= -1,28*2=-2,56 is the estimate rate GDP decrease annually of Congo

3. Exponential trend (EXP) A. Regression output:

B. Formula & Coefficient explanation: Formula: Linear format: log(Y^)=2,154+0,016*T Non linear format: Y^= 142,56* 1,03^T

b1=1,03=> annual compuand growth rate =(1,03-1)*100=3% This is the estimation of GDP growth of Congo evey year.

Middle Income country: South Africa (1990-2015)  Regression moodel: 1. Linear regression (LIN) A. Regression output

B. Formula & Coefficient explanation: Formula: Y^=2184,9 +183,1*T Coefficient explanation b0= 183,16 is the estimation of GDP of South Africa when T=0. =>Does not make sense because T=0 not included in the range b1=183,166 is the estimate average of evey one year the GDP of South africa(1990-2015) will decrease 183,166$ 2.Quadratic regression trend (QUA) A. Regression output:

B.Formula & Coefficient explanation: Formula:Y^= 3093,18-11,46*T +7,028*T^2 Coefficient explanation: b1=-11,46 is the estimate decrease annually of GDP of South Africa when T=0. But in this case T=0 is not in the range so that it can not be identified b2: annually rate 7,028*2=14,056 is the increase of GDP rate annually of South Africa

3.Exponential regresion trend ( EXP) A. Regression output:

B. Formula & Coefficient explanation: Formula: Linear format: log(Y^)=3,418+0,0165*T Non-linear format:Y^= 2618*1,03^T Annual growrth rate: (1,03-1)*100=3% Annualy, South Africa GDP each year will increase 3%

Region A: Europe

High income country: Netherland  Regression model: 1. Linear regression trend(LIN) A. Regression Output:

B. Formula & Coefficient explanation: Formula: Y^=17168+1486,59*T Coefficient explanation: b0=17168 is the estimate of GDP when T=0. But does not make sense because the range not included T=0 b1:=1486,5 the decrease of GDP in the time period T

2. Quadratic regression trend (QUA): A. Regression Output:

B. Formula & Coefficient explanation: Formula:Y^= 17328,75-1452,26*T +1,27*(T^2) Coefficient explanation: b1=-1452,26 is the estimate decrease annually of GDP of Netherland when T=0. But in this case T=0 is not in the range so that it can not be identified b2: annually rate 1,27*2=2,54% is the increase of GDP rate annually of Netherland

3. Exponential regression trend (EXP) A. Regression Output:

B. Formula & Coefficient explanation: Formula: Linear format: log(Y^)=4,305+0,0179*T Non-linear format:Y^= 20183*1,039^T Annual growrth rate: (1,039-1)*100=3.9% Annualy, Netherland’s GDP each year will increase 3%

Low-Middle Imcome country: Moldova 1. Linear regression trend(LIN) A. Regression trend output

B. Formula& Coefficient explanation: Formula: Y^=-246,4711+158,653*T Coefficient explanation: B0=-246,4711 is the estimate of GDP when T=0. But does not make sense because the range not included T=0. So it is not related to the trend B1:=158,653 the decrease of GDP in the time period T 2. Quadratic regression trend(QUA) A. Regression output

B. Formula & Coefficient explanation: Formula:Y^= 479,038-30,609*T +8,6*(T^2) Coefficient explanation: B1:=-30,609 is the estimate decrease annually of GDP of Moldova when T=0. But in this case T=0 is not in the range so that it can not be identified B2: annually rate 8,6*2=17,2% is the increase of GDP rate annually of Moldova

3. Exponential regression trend (EXP) A. Regression output

B. Formula & Coefficient explanation: Formula: Linear format: log(Y^)=2,5206+0,049*T Non-linear format:Y^= 331,5*1,119^T Annual growrth rate: (1,119-1)*100=11.9% Annualy, Moldova’s GDP each year will increase 11.9% Time series forecast: after calculating both SSE and MAD of all three trend types. The smallest SSE and MAD of Congo :

 Quadratic regression trend Congo GDP Prediction:

South Africa:

 Quadratic regression trend South Africa GDP Prediction:

Moldova:

 Quadratic regression trend Moldova GDP Prediction:

Netherland:

 Linear regression trend Netherland GDP Prediction:

PART 6: Time series Conclusion:

Figure 1: Three low-middle countries: South Africa,Moldova and Cong,DEM.REP Description: As you can see in the graph, The above three countries have different income level: Low Income: Congo,dem.rep: is a country with a low GDP below 1000. Since the years 2002 to 2015, there has been an upward trend and according to the above prediction, it will continue to increase by 8% in each of 2017, 2018 and 2019

Low-midlle income: Moldova: grew rapidly from 2004 to 2014. Based on calculated projections, it will continue to grow at 7% per year in 2017,2018 and 2019 Middle Income: South Africa: has an upward trend since the early 1990s but gradually decreased and reached the lowest value in 2002(1990-2015). But then it gradually increased until 2012 and tended to decrease again. But with the above prediction, from 2017-2019 there will be an upward trend in GDP with a growth rate of about 5%.

Figure 2:High income country: Netherland

High income country (Netherland): had a rapid growth from 2000-2007 and as predicted calculated above. GDP will continue to grow by 3% in 2018 and 2% in 2019 Conclusion: Both region A and B follow the same trend line: The similarity is that they all grew rapidly from 2000 onwards Pridict world trend: After comparison and analysis, the SSE and MAD of the Quadratic regression trend of Congo are the lowest

 World’s quadratic model: Y^= 282,79-24,01*T+1,28*(T^2) PART 7: TEAM CONCLUSION: 1&2. Predicted GDP Per Capita Growth Rate In 2030: Applying the formula derived from the quadratic regression trend model of low-income country, Congo, 2030 will have the T value of 41, which shows a rate of -0.154 lower than the previous years. The main factors are possibly the urban concentration level and the takeover of technology. 3. Recommendations: Our datasets only include gathering information from African and European countries,but there are 195 countries in the world, which means still many places not evaluated in this research. If expanding the sample size, the data will be more reliable. Our data has worked on 8 aspects for the GDP per capita growth rate evaluation, but studies illustrate some other factors:  Tuğba & Yılmaz (Intechopen, 2020) demonstrate the importance of inflation rate and unemployment rate in economic growth and how their influences over GDP per capita  Vernon Henderson (Worldbank) suggests the contribution of urban concentration...