Team-assignment-report A3 Group 4 PDF

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School of Business Management Student Name & ID Number

PHAM TRAN HOAN MY

S3879526

TRAN KIEN

S3878405

NGUYEN NGOC MINH ANH

S3879526

ĐOAN THI THANH HANG

S3881225

Subject Name

Business Statistics

Subject Code

ECON1193B

Lecturer

Tuan Chu

School Location

SGS

Word Count

3066

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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

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First name

Student ID

Part Contributed

Contribution %

My

S3879526

Part 1,3,4,5,6,7

100%

Kien

S3878405

Part 1,2,5,6,7

100%

Anh

S3879526

Part 1,3,4,5,6,7

100%

Hang

S3881225

Part 1,2,5,6,7

100%

3

Signature

PART 1: DATA COLLECTION In this assessment, the dataset of countries in Europe and Africa is specifically in 2013, is collected from World Bank database with a total of 9 variables: GDP per capita growth rate (annual %); GDP per capita (current US$); GNI per capita, Atlas method (current US$); Life expectancy at birth, total (years); Imports of goods and services (%of GDP); Exports of goods 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, we excluded countries missing even one variable. At the end, we have 39 countries in Europe and 50 countries in Africa. In this report, to make the statistics conducted more smoothly, we selected 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 the existence of outliers (Appendix 1). Based on the calculation, Median now is the most appropriate measurements because it is not influenced by extremely large values. On the surface, there is a large difference in the middle number of total GPD between Europe and Africa. 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

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As can be seen in Box-and-whisker plots of both data, the difference in the skewness of data distribution is confirmed. Due to the presence of extreme value in the datasets, the GDP of Africa received left-skewed distribution. Thus, Afica’s Box also points out that over about 50% of GDP recorded are concentrated in higher growth. On the other hand, Europe’s box plot is observed to be right-skewed, due to the positive outlier. As the result, both Africa’s box and median are larger than Europe’s, point out Africa’s GDP per capita growth rate is higher than European countries. 3. Measurements of Variantion

Since other measurements is based on the average, it will not utilize the comparison between two samples due to extreme values are detected in both data. The IQR is the best measure of variation for skewed distributions or data sets with outliers. It based on values that come from the 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%) which also means Africa’s data distribution is farther around the median than Europe’s. In other words, 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 significant variables that have a strong relationship with GDP per capita growth rate (annual%), at 5% level of significant. a. Regression output:

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Intepretation: From the two above scatter plots of the Africa region, it can be observed that the trend line of the data has a tendency to move up from the left to the right. This indicates that GDP per capita growth rate has a positive relationship with trade and population variables as when GDP increases, these mentioned variables also climb up. b. Regression equation: = b0+b1X1+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 capita growth rate (annual%) in 2013 can be explained by Trade (% of GDP), and Population (ages 15-64 (total) years). Moreover, the other 79.6% show that GDP per capita growth rate (annual %) could be affected by the other factors.

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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% significant level. a) Regression output and scatter plot:

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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 the left to the right. This indicates that GDP per capita growth rate has a positive relationship with trade and exports of goods and service variables as when GDP increases, these mentioned variables also climb up. In contracy, Life expectancy at birth has a negative relationship with GDP as when the rate of birth increase, the GDP per capital growth rate decrease. b) The regression equation = b0 + b1X1 + b2X2 + b3X3 = 15,304 - 0,205X1 - 0,206X2 + 0,120X3 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 1 year. B2= -0.206 shows that the decreasing GDP by 0.206% when 1% increase in export of goods and 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 capita growth 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 other 42.6% show that GDP per capita growth rate (annual%) could be affected by the other factors. PART 4: TEAM REGRESSION CONCLUSION

It is evident from all of the multiple regression equations in part 3 that the two regions have different numbers of significant variables. Although four independent variables influenced the percentage of GDP in Europe, only two independent variables had a significant effect in Africa. By comparing the coefficients of determination (R square) between Africa and Europe , we can clearly see that the Europe received higher R2 than Africa (0.516% > 0.204%). In other words, 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 2 than the EU, Africa'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%,

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which also means that the majority of the increase in GDP per capita in Africa can be explained 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 this case, European countries’ GDP depends on more variables than Africans. Adjusted R square calculates R square using only those variables in the model that is significantly affecting the data. Although adjusted R squares in both regions point to the same conclusion as the R squares. We can be sure of the GDP per capita growth in Africa is less dependent on other significant variables than in Europe. To sum up, for almost countries in both regions, the trade has the highest impact on the GDP, and it could be predicted that the GDP per capital growth 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's dispersion 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 19902015. In this report, the Exponential trend model is not possible to be built as the GDP is negative 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 19902015 is 1.408% when T=0. B1=0.007, describes that for each year, the Mali’s GDP in years 1990-2015 is predicted to increase by 0.007%. This also indicates the upward trend of the Linear trend model.

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

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 of Mali 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 2 (number of year). 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 years 1990-2015 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.

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

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 of Niger 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 to decrease by 0.058% each year. This also indicates the downward trend of the Linear trend model.

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

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 of France 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 T2 . 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 is 1.918% 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 trend model.

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

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% each year. 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 of Squared Errors (SSE) to find the trend model has lower MAD and SSE, which means fewer errors for prediction. 1. Africa:

In figure 20, the error measurement’s result of Mali is higher than Niger. For Niger, the Quadratic trend model has the smallest MAD (2.18) and SSE (189.213), 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 Africa.

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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 a decline in GDP in the upcoming years, meaning that Europe’s GDP is on a downward trend.

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PART 6: TIME SERIES CONCLUSION a. Line chart

b. Explanation The line chart shows Gross Domestic Product (GDP) per capita growth rate for years 19902015 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 in Africa also have started with negative rates and ended up with positive rates in 2015. For Europe, the GDP ratios of both countries occur to be less volatile than for countries in Africa and tended to decrease. However, there is an irregular component in 2009, the GDP of France and Germany dropped dramatically, but then increased again. Based on the analysis results from part 5.2, it can be concluded that all countries in Africa and Europe follow the same trend, which is the Quadratic trend model. Therefore, the 15

Quadratic trend model would be appropriate for predicting GDP per capita growth rate in both region. Conducting from previous findings, MAD and SSE value of the Quadratic trend model is is lower. Hence, the Quadratic trend model is considered to be the best reliable model for predicting the GDP per capita grow rate in the world.

According to Figure 26, both the France MAD and SSE measurements have significantly smallest values, indicating that it has the lowest errors in estimation. Thus, for greater accuracy, using the formula of the high-income France Quadratic trend model is the optimal choice for predicting the GDP per capita growth rate worldwide. Formula of the world’s Quadratic trend model: = 1.193 + 0.082T – 0.005T2 PART 7: OVERALL TEAM CONCLUSION Overall, the purpose of the report is to investigate the factors affecting economic growth in Europe and Africa. In this report, we conducted descriptive statistics, built regression models and applied time series to predict the trend of GDP per capita growth rate. In general, the findings in the descriptive statistic shows that Africa’s GDP is higher than Europe’s . In the multiple regression, trade has been the highest effect on GDP of both regions. Besides, Africa’s trade has a stronger relationship with GDP, so Africa likely has higher economic growth. For time series, countries in both regions follow the Quadratic trend model, however, Africa’s GDP tends to increase in the coming years. Moreover, France has the smallest errors when predicting GDP, so the formula of France Quadratic trend model is used to predict the GDP per capita growth rate in ...