School of Business Management Measurements of Central Tendency

PART 1: DATA COLLECTIONIn this assessment, the dataset of countries in Europe and Africa is specifically in 2013, iscollected from World Bank database with a total of 9 variables: GDP pe

School of Business Management

Student Name & ID Number PHAM TRAN HOAN MY S3879526

TRAN KIEN S3878405NGUYEN NGOC MINH ANH S3879526ĐOAN THI THANH HANG S3881225

CONTENT TABLE

PART 1: DATA COLLETION 4

PART 2: DESCRIPTIVE STATISTICS 4

1 Measurements of Central Tendency 4

2 Box and Whisker Plot 4, 5 3 Measurements of Variation 5

PART 3: MULTIPLE REGRESSION 5

1 Africa 6

a Regression output 6

b Regression equation 7

c Regression coefficient of the significant independent variables 7

d Interpret the coefficient of determination 7

2 Europe 7

a Regression output 8

b Regression equation 9

c Regression coefficient of the significant independent variables 9

d Interpret the coefficient of determination 9

PART 4: TIME SERIES 9

I Linear (LIN), Quadratic (QUA), Exponential (EXP) trend models 9, 10 1 Low-income countries………10, 11 2 High-income countries……… 11, 12 II Recommend Trend Model 13

1 Africa 13

2 Europe………13, 14 III The estimate GDP per capita growth rate 14

PART 7: OVERALL TEAM CONCLUTION 15

1 The main factor that impact GDP per capita growth rate 16

2 Predict GDP growth rate in year 2030 17

3 Recommendation 17

REFFERENCES & APPENDIX ……….18-22

First name Student ID Part Contributed Contribution % Signature

PART 1: DATA COLLECTION

In this assessment, the dataset of countries in Europe and Africa is specifically in 2013, iscollected from World Bank database with a total of 9 variables: GDP per capita growth rate(annual %); GDP per capita (current US$); GNI per capita, Atlas method (current US$); Lifeexpectancy at birth, total (years); Imports of goods and services (%of GDP); Exports ofgoods and services (% of GDP); Foreign direct investment, net inflow (% of GDP); Trade (%

of GDP) and Population (ages 15-64 (total) years) Regarding the data cleaning process, weexcluded countries missing even one variable At the end, we have 39 countries in Europeand 50 countries in Africa In this report, to make the statistics conducted more smoothly, weselected 39 and 30 countries in Europe and Africa respectively These datasets are contained

in the attached Excel file

PART 2: DESCRIPTIVE STATISTICS

1 Measurements of Central Tendency

Although the Mean is the most frequently used measure and covers all values in the data set

in general However, in this case, the Mean will not be used to interpret since there is theexistence of outliers (Appendix 1) Based on the calculation, Median now is the mostappropriate measurements because it is not influenced by extremely large values On thesurface, there is a large difference in the middle number of total GPD between Europe andAfrica According to figure 1, the median of Europe’s GPD (0,819%) is lower than Africa’s(1.868%) As a result, it can be assumed that Africa’s GPD is higher than in Europe

2 Box and Whisker plot

As can be seen in Box-and-whisker plots of both data, the difference in the skewness of datadistribution is confirmed Due to the presence of extreme value in the datasets, the GDP ofAfrica received left-skewed distribution Thus, Afica’s Box also points out that over about50% of GDP recorded are concentrated in higher growth On the other hand, Europe’s boxplot is observed to be right-skewed, due to the positive outlier As the result, both Africa’sbox and median are larger than Europe’s, point out Africa’s GDP per capita growth rate ishigher than European countries.

3 Measurements of Variantion

Since other measurements is based on the average, it will not utilize the comparison betweentwo samples due to extreme values are detected in both data The IQR is the best measure ofvariation for skewed distributions or data sets with outliers It based on values that come fromthe middle half of the distribution and unlikely to be affected by outliers According to figure

3, it illustrates the IQR of Europe’s GDP (2.613%) are lower than Africa’s (3.148%) whichalso means Africa’s data distribution is farther around the median than Europe’s In otherwords, the economic growth in Africa countries is less consistent than in Europe

PART 3: MULTIPLE REGRESSION

1 Africa

After building the regression by applying the backward elimination (Appendix A.3), Trade

(% of GDP), and Population (ages 15-64 (total) years) are indicated to be significantvariables that have a strong relationship with GDP per capita growth rate (annual%), at 5%level of significant

a Regression output:

From the two above scatter plots of the Africa region, it can be observed that the trend line ofthe data has a tendency to move up from the left to the right This indicates that GDP percapita growth rate has a positive relationship with trade and population variables as whenGDP increases, these mentioned variables also climb up

b Regression equation:

= b0+b 1X1+b2X2

= -9.948+0.113X1+0.000X2

c Regression coefficient of the significant independent variables:

B0= -9.948 depicts the average GDP per capita growth rate, which recorded in 2013

B1= 0.113 shows that the rate of GDP will rise 0.113% when the Trade increase 1%

B2= 0.000 indicates that when the population increase extremely small value

d Interpret the coefficient of determination:

The coefficient of determination (R square=0.204) shows that 20.4% of GDP per capitagrowth rate (annual%) in 2013 can be explained by Trade (% of GDP), and Population (ages15-64 (total) years) Moreover, the other 79.6% show that GDP per capita growth rate (annual

%) could be affected by the other factors

2 Europe

After using backward elimination, four categories including life expectancy at birth, total(years), GDP per capita (current US$), Exports of goods and services (% of GDP), and Trade(% of GDP) have a relationship with GDP per capita growth rate (annual%), 5% significantlevel

a) Regression output and scatter plot:

From the three above scatter plots of the Europe region, it can be observed that the trend line

of the data of Exports of goods and services, and Trade have tendency to move up from theleft to the right This indicates that GDP per capita growth rate has a positive relationshipwith trade and exports of goods and service variables as when GDP increases, thesementioned variables also climb up In contracy, Life expectancy at birth has a negativerelationship with GDP as when the rate of birth increase, the GDP per capital growth ratedecrease

b) The regression equation

= b + b0 1X1 + b2X2 + b3X3

= 15,304 - 0,205X - 0,206X + 0,120X 1 2 3

c) Regression coefficient of significant level

B0= 15.305 illustrates that the average GDP per capita growth rate record in 2013

B1= -0,205 illustrates that the GDP will decrease 0,205% when life expectancy increases 1year

B2= -0.206 shows that the decreasing GDP by 0.206% when 1% increase in export of goodsand services

B3= 0.120 describes that when the Trade increase 1%, the GDP will increase 0.244%

d) Interpret the coefficient of determination

The coefficient of determination (R spare= 0.516) shows that 51.6% of GDP per capitagrowth rate (annual%) in 2013 can be explained by Life expectancy at birth, total (years),Exports of goods and services (% of GDP), and Trade (% of GDP) Furthermore, the other42.6% show that GDP per capita growth rate (annual%) could be affected by the otherfactors

PART 4: TEAM REGRESSION CONCLUSION

It is evident from all of the multiple regression equations in part 3 that the two regions havedifferent numbers of significant variables Although four independent variables influenced thepercentage of GDP in Europe, only two independent variables had a significant effect inAfrica

By comparing the coefficients of determination (R square) between Africa and Europe , wecan clearly see that the Europe received higher R2 than Africa (0.516% > 0.204%) In otherwords, Europe received higher proportion of the GDP per capita growth that can be explained

by the variation in four variables mentioned above Despite having a lower R than the EU,2Africa's proportion is more likely to be explained by only two significant variables.Nonetheless, Africa's population coefficient is extremely small, accounting for 0.0000003%,

which also means that the majority of the increase in GDP per capita in Africa can beexplained by the percentage of trade at a 0.05 significance level

Regardless of the significance of the variable, the R square value will always rise In thiscase, European countries’ GDP depends on more variables than Africans Adjusted R squarecalculates R square using only those variables in the model that is significantly affecting thedata Although adjusted R squares in both regions point to the same conclusion as the Rsquares We can be sure of the GDP per capita growth in Africa is less dependent on othersignificant variables than in Europe To sum up, for almost countries in both regions, thetrade has the highest impact on the GDP, and it could be predicted that the GDP per capitalgrowth rate in Africa and Europe will increase when the trade increase

Based on the analyzed data in part 2, the measure of the dataset's center, as well as the data'sdispersion and the regression models are taken into account The result shows that the trade

of Africa region received stronger relationship with the GDP growth than in Europe.Consequently, Africa shows higher economy growth than Europe region

PART 5: TIME SERIES

I Linear (LIN), Quadratic (QUA), Exponential (EXP) trend models:

This is a collection of data for GDP per capita growth rate in two regions in years

1990-2015 In this report, the Exponential trend model is not possible to be built as the GDP isnegative and not able to calculate log(Y)

1 Low-income countries

a) Mali:

 LIN:

Formula: =1.408 + 0.007T

Interpretation of the Coefficient of Significant Variable:

B0=1.408 shows that the estimated GDP per capita growth rate of Mali in years

1990-2015 is 1.408% when T=0

B1=0.007, describes that for each year, the Mali’s GDP in years 1990-2015 ispredicted to increase by 0.007% This also indicates the upward trend of the Lineartrend model

 QUA:

Formula: = -0.447 + 0.404T – 0.015T2

Interpretation of the Coefficient of Significant Variable:

B0= -0.447 describes that when T=0, the prediction of GDP per capita growth rate ofMali from 1990 to 2015 go down by 0.447%

B1= 0.405 shows that the nearly increasing Mali’s GDP is 0.405%

B2= -0.015 show that the decreasing of Mali’s GDP by 0.015% every T (number of2year)

b) Niger:

 LIN:

Formula: = -3.113 + 0.224T

Interpretation of the Coefficient of Significant Variable:

B0= -3.113 shows that the estimated GDP per capita growth rate of Niger in years1990-2015 decreased 3.113% when T=0

B1= 0.224 describes that for each year, the Niger’s GDP in years 1990-2015 increased

by 0.224% This also indicates the downward trend of the Linear trend model

 QUA:

Formula: = -3.931 + 0.399T – 0.006T2

Interpretation of the Coefficient of Significant Variable:

B0= -3.931 describes that when T=0, the prediction of GDP per capita growth rate ofNiger in years 1990-2015 decrease by 3.931%

B1= 0.399 indicates that the approximately increasing of Niger’s GDP is 0.399%.B2= -0.006 shows that the falling of Niger’s GDP by 0.006% every T2

2 High-income countries:

a) France:

 LIN:

Formula: = 1.847 – 0.058T

Interpretation of the Coefficient of Significant Variable:

B0= 1.847 describe that the GDP per capita growth rate of France in years 1990–2015)

is 1.847% when T=0

B1= –0.058, describes that the France’s GDP in years 1990-2015 is predicted todecrease by 0.058% each year This also indicates the downward trend of the Linear

 QUA:

Formula: = 1.194 + 0.083T – 0.005T2

Interpretation of the Coefficient of Significant Variable:

B0= 1.194 describes that when T=0, the predicted of GDP per capita growth rate ofFrance in years 1990-2015 is 1.194%

B1= 0.083 shows the nearly increasing of France’s GDP is 0.083%

B2= -0.005 shows that France’s GDP decreases by 0.005% every T 2

b) Germany:

 LIN:

Formula: = 1.918 – 0.033T

Interpretation of the Coefficient of Significant Variable:

B0= 1.918 illustrates the prediction of GDP per capita growth rate of Germany is1.918% in years 1990-2015 when T=0

B1= –0.033 shows that from 1990 to 2015, Germany’s GDP is predicted to decrease

by 0.033% each year This also indicates the downward trend of the Linear trendmodel

 QUA:

Formula: = 2.707 – 0.202T + 0.006T2

Interpretation of the Coefficient of Significant Variable:

B0= 2.707 shows an estimate of GDP per capita growth rate of German from 1990 to

2015 is 2.707% when T= 0

B1= -0.202 illustrates an approximate decrease of Germany’s GDP is 0.2022% eachyear

B2= 0.006 shows an estimate of Germany’s GDP increasing by 0.006% every T2

II Recemmend Trend Model:

In terms of recommending the country’s trend model to predict GDP per capita growth rate(%) for Africa and Europe We compare the Mean Absolute Deviation (MAD) and Sum ofSquared Errors (SSE) to find the trend model has lower MAD and SSE, which means fewererrors for prediction

1 Africa:

In figure 20, the error measurement’s result of Mali is higher than Niger For Niger, theQuadratic trend model has the smallest MAD (2.18) and SSE (189.213), meaning that thiscountry's trend model has the fewest errors for predicting As a result, the Quadratic trendmodel will be the most suitable to predict the GDP per capita growth rate in Africa

2 Europe:

In figure 21 , the error measurement’s result of Germany is higher than France As for France,the Quadratic trend model has the smallest MAD (0.983) and SSE (43.18), meaning that this country's trend model has the fewest errors for predicting As a result, the Quadratic trend model will be the most suitable to predict the GDP per capita growth rate in Europe

III The estimate GDP per capita growth rate of Niger and France in 2021, 2022, 2023: a) Niger

Formula of Quadratic trend model: = -3.931 + 0.399T – 0.006T2

c) France:

Formula of Quadratic trend model: = 1.193 + 0.082T – 0.005T2

From 2021 to 2023, Niger’s GDP per capita growth rate (anual%) is estimated to ncrease,which means Africa’s GDP tend to grow Meanwhile, France is predicted to experience adecline in GDP in the upcoming years, meaning that Europe’s GDP is on a downward trend

PART 6: TIME SERIES CONCLUSION

a Line chart

b Explanation

The line chart shows Gross Domestic Product (GDP) per capita growth rate for years

1990-2015 of Africa and Europe region respectively Overall, both regions have positive GDP rates

at the end and are volatile over time

In Africa, the GDP of Niger and Mali fluctuate continuously every year Both countries inAfrica also have started with negative rates and ended up with positive rates in 2015 ForEurope, the GDP ratios of both countries occur to be less volatile than for countries in Africaand tended to decrease However, there is an irregular component in 2009, the GDP of Franceand Germany dropped dramatically, but then increased again