fileCUsersBinhBIenDownloadsTIỂU%20LUWe collected over 55 countries from both regions at first the cleaning process is straightforward, any countries with missing variables will be void below a

PART 1:For this part of the assignment, our team has to collect nine variables of the dataset from theworld bank in the year 2004, which includes GDP per capita growth rate annual %, Lif

RMIT International University Vietnam

ECON1193 - Business Statistics 1

ASSIGNMENT 3

PART 1:

For this part of the assignment, our team has to collect nine variables of the dataset from theworld bank in the year 2004, which includes GDP per capita growth rate (annual %), Lifeexpectancy 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 andservices (% of GDP), Imports of goods and services (% of GDP), Trade (% of GDP) andPopulation (ages 15-64 (total) years)

We collected over 55 countries from both regions at first The cleaning process isstraightforward, any countries with missing variables will be void Below are the followingpictures 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:

Q3 + 1.5*IQR = 7.1876624645

6,489599681 < 7.1876624645 => Max < Q3 + 1.5*IQR => Max is not an outlier in upper valuesQ1 – 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 left- skewed 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 onlyvariable(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

Life expectancy at birth, total (years) Line Fit Plot

GDP per capita growth rate (annual %)

Predicted GDP per capita growth rate (annual %)

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, showingthat 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 15-64 (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 negativeGDP per capita growth rate when the points are all greater than 0 They were also quite faraway 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 %)

Predicted GDP per capita growth rate (annual %)

-2.00

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

:GDP per capita growth (annual %)

:Life expectancy at birth, total (years)

Population (age 15-64 (total) years)

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 ratecan be explained by the variation of their Life expectancy at birth and Population (15-

64)every single year

Region B: Africa

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

PART 4: TEAM REGRESSION CONCLUSION

Looking at both regression model for Africa and Europe we can conclude that for Europethe 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 plotfor 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 Byimplementing 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)

b1= 10,7386 is the estimate increase of GDP of Congo each year

2 Quadratic regression trend (QUA)

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)

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%

b1:=1486,5 the decrease of GDP in the time period T

2.Quadratic regression trend (QUA):

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)

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 andunemployment rate in economic growth and how their influences over GDP per capita Vernon Henderson (Worldbank) suggests the contribution of urban concentration level in

the GDP growth rate and this also relative to level of technology

References:

Dayıoğlu, Tuğba, and Yılmaz Aydın, September 2020, Relationship between Economic Growth, Unemployment, Inflation and Current Account Balance: Theory and Case of Turkey, IntechOpen, IntechOpen, viewed on 30 May 2021,

<and-practice/relationship-between-economic-growth-unemployment-inflation-and-current-account-balance-theory-and-c.>

www.intechopen.com/books/linear-and-non-linear-financial-econometrics-theory-Worldbank, How Urban Concentration Affects Economic Growth, www.intechopen.com/books/linear-and-non-linear-financial-econometrics-theory-Worldbank, viewed

on 30 May 2021, <econometrics-theory-and-practice/relationship-between-economic-growth-

www.intechopen.com/books/linear-and-non-linear-financial-unemployment-inflation-and-current-account-balance-theory-and-c.>

Kingsley Ighobor August 2012, “African economy capture world attention”, [Access

online],viewed 29 May 2021, <