(TIỂU LUẬN) the data for nine variables are collected from the worldbank of 25 countries in region a asia and 25 countries in region b america the datasets are included in the excel file

In figure 2, the value of IQR in Asia 3.875 is more significant than the value ofIQR in America 2.21, which shows that the GDP growth rate from countries in Asia is lessconsistent and ha

ECON1193 - Business Statistic 1

Semester 1 - 2021

Title of Assignment Assignment 3A: Team Assignment Report

❖ Vu Dinh Thai - s3877521

❖ Fuoc An Doanh - s3879951

Word count (excluding table,

figures, references and

appendix)

3245 words

Part 1 Data Collection

The data for nine variables are collected from the WorldBank of 25 countries in region A:Asia and 25 countries in region B: America The datasets are included in the Excel file

Part 2 Descriptive Statistics

1 M easures of central tendency

Measures of Central Tendency Region A

-Figure 1 The measures of central tendency of Asia and America regarding the GDP per

capita growth (annual%)According to the table above, it can be seen that the mode is undetectable in both regions ofAsia and America, so the mode is considered unusable in this measurement Moreover, thereare outliers identified in both regions; Asia has one lower outlier, America has two loweroutliers, and both do not have any upper outlier (Appendix 1) Because the mean is

influenced strongly by the outliers and could cause errors, so the mean is not applicable inthis situation; hence, the median is the most suitable descriptive measurement to compare andanalyze the GDP per capita growth rate in both regions In this case, the median illustratesthat 50% of countries in a region have a higher GDP growth rate than the median value, andthe remaining 50% of countries have a GDP growth rate lower than the median

As seen in figure 1, it can be observed that Asia’s (3.35%) median value is higher than inAmerica’s (1.33%) This number demonstrates that 50% of countries in Asia had a GDPgrowth rate in 2016 that is higher than 3.35%, and the others recorded less than 3.35%, andsome countries' data is not yet recorded Hence, the median results have shown that in 2016,countries in Asia had a higher GDP growth rate than most countries in America

2 M easures of variation

MEASURES OF

VARIATION

Region A Asia

The greater the IQR value is, the higher the range, hence the more massive and incoherentvariation In figure 2, the value of IQR in Asia (3.875) is more significant than the value ofIQR in America (2.21), which shows that the GDP growth rate from countries in Asia is lessconsistent and has a propensity to deviate from the core value

3 Measure of Shape

Figure 3 Box and whisker plots of GDP growth rate of Asia and America in 2016

In all the measure of shape methods, the box and whisker plot is the most suitable optionbecause the box plot can display the median, Quartile 1 & 3, and the outliers in both regions

In comparison, the histogram does not help contrast two data sets because it is highly

dependent on the bin range, making it challenging Hence, smaller to examine the actualvalues of the data

Looking at the box plot in figure 3, it can be observed that most countries in Asia have ahigher GDP growth rate (about 5.47) than countries in America However, the GDP of

countries in Asia fluctuates more than in America from -1.5 to 11.94 at the higher end of thebox plots Another application to be made is that 50% of countries in Asia have a higher GDPgrowth rate than 3.35 while the maximum GDP growth rate in America is only 5.47 Thismeans that many countries in Asia are growing fast in their economy, so they have higherGDP growth rates

It should be recognized that the data in the boxplots for Asia are right-skewed, and the

American region is left-skewed Therefore, it can be concluded that the GDP growth rate inAsia outnumbers the sameThe lower figures in the region of America

Part 3 Multiple regression

REGION A – ASIA

a) Regression Final Output and scatter plots

After applying the backward elimination method in appendix 2, the final regression model ofAsia is displayed as below

Figure 4 Final regression model of Region A: Asia

Figure 5 Scatter plot of GDP per capita (current US$) of Asia in 2016

Y: GDP per capita growth rate (annual%)

X1: GDP per capita (current US$)

Figure 5 shows the variable of X1 experiencing a downward trend and the data oftenfluctuating between 4 and 5, showing a negative relationship with Y.

b) Regression Equation

As can be observed in Figure 4, there is only one significant variable Therefore, the

regression equation is:

Ŷ = b + b0 1X1

Ŷ = 4.882 - 0.00007*(GDP per capita)

· Ŷ: predicted GDP per capita growth rate (annual %)

· X1: GDP per capita, Atlas method (current US$)

c) Regression coefficient of the significant independent variables

· b0 = 4.882 shows that Y would be estimated for 48.82% when the GDP per capita(current US$) variable is zero, but it will make no sense

· b1 = -0.00007 means that Y decreases by 0.0007% for every US$ in X , holding the GDP1

per capita (current US$) as constant

d) The coefficient of determination

In figure 4, the coefficient of determination (R2) for this region is displayed at 0.176 or

17.6% This assumes that 17.6% of the variation in GDP per capita growth rate (annual %)can be clarified by the variation in the GDP per capita The remaining 82.4% of the GDP percapita growth rate variation in 2016 may be answered by other factors that are not included inthis study

REGION B - AMERICA

a) Regression Final Output and scatter plots

After applying the backward elimination method in appendix 3, the final regression model ofAmerica is displayed as below

Figure 6 Final regression output of Region B - America

Figure 7 Scatter plot of trade (% of GDP) of America in 2016

Y: GDP per capita growth rate (annual%)

X1: Trade (% of GDP)

Figure 7 shows the variable of X1experiencing a dramatic downward trend (fluctuating from

3 to - 0.5), showing a negative relationship with Y As can be observed from figure 5, the datapredicted for GDP per capita growth rate in Asia is more stable than in America

b) Regression Equation

According to figure 6, the regression equation is:

Ŷ = b + b0 1X1

Ŷ = -0.667 + 0.027*(GDP per capita)

● Ŷ: predicted GDP per capita growth rate (annual %)

● X1: Trade (% of GDP)

c) Regression coefficient of the significant independent variables

According to figure 6 and appendix 3, there is no significant independent variable becauseafter applying the backward elimination, Trade (% of GDP) is the only independent variableleft (0.06) which is higher than the significance level is 0.05, so the regression coefficient isnot available here in this case

d) The coefficient of determination

In figure 6, the coefficient of determination (R2) for this region is displayed at 0.142 or14.2% This assumes that 14.2% of the variation in GDP per capita growth rate (annual %)can be clarified by the variation in the Trade (% of GDP) The remaining 85.8% of the GDPper capita growth rate variation in 2016 may be answered by other factors not included in thisstudy

Part 4 Team Regression Conclusion

According to the research in part 3, it is recognizable that the two regions Asia and America have adifferent number of significant variables While Asia has one independent variable that can affect theGDP per capita growth rate is the GDP per capita (current US$), America is affected by none of thevariables However, in the American region, although it is not affected by any independent variable,

we can still compare other aspects in the result of the final regression output between the two regions

to have the most objective perspective In comparison, it is witnessed that the coefficient of

determination in Asia is higherR2than in America (17.6% > 14.2%) Thus, there is a higherproportion of the variation in the GDP per capita growth rate in Asia that could be explained

by the variation in the GDP per capita (current US$) of the countries In region B, the

dependent variable is not affected by any other independent variable due to (Appendix 3) sonone of the variables could have a high impact on the GDP per capita growth rate in America

In contrast, in region A the dependent variable's effect on only one independent variable isthe GDP per capita (current US$) so this is the only variable that could have the highestimpact on the GDP per capita growth rate in Asia

To summarize, this study shows that in Asia, the GDP per capita (current US$) variable can

be used to forecast the GDP per capita growth rate in Asia, whereas in America there is noindependent variable that can be used to predict the GDP per capita growth rate in 2016

Part 5 Times Series

Low-Income countries (LI): Nepal(Asia)(C1), Honduras(America)(C3)

High-Income countries (HI): Singapore(Asia)(C2), United States(Ameria)(C4)

I Trend Models

Region A - Asia

Low-Income Country Asia

After applying the hypothesis for trend models in Nepal country (appendix 3.1), the findingsimply that linear, quadratic and exponential trend models are significant for this country

1 Linear Trend

a) Regression Output

Figure 8 Linear trend regression output of Nepal – Low-Income country (1990-2015)

b) Formula & Coefficient explanation

Y =1.357―0.0043×T

𝛽0= 1.357 shows that the GNI of a Low-Income country, Nepal (1990-2015), is expected to

be around $1367.5 when the time period, T, is 0 years However, this does not make sense asbeing out of our observation scope Therefore, this is the portion of Gross National Income,total that is not explained by time period T

𝛽1= -0.0043, illustrates that for every one year, on average, the GNI, total of Low-Incomecountry, Nepal (1990-2015), is estimated to decrease by $0.0043 per head approximately.This also indicates the downward sloping of its linear trend model

2 Quadratic Trend Model

a) Regression Output

Figure 9 Quadratic trend regression output of Nepal – Low-Income country (1990-2015)

b) Formula & Coefficient explanation

Y =1357.5―0.0043×T―0.00001×T2

𝛽1= ―0.0043, illustrates that when T = 0 (year), the instantaneous rate of change of the GNIper head, a total of Low-Income country, Nepal (1990-2015) is ―0.0043 $USD per head

annually However, T = 0 is not within this variable’s observation range Thus, this is theportion of GNI, total that cannot be explained by time period, T.

𝛽2= ―0.001a indicates that for every one year, on average, the GNI, total of the

Low-Income country, Nepal (1990-2015), instantaneously decreases at the rate of 2 ×

0.00001 = 0.00002 USD per head annually This quadratic trend model has a concave curvedshape

3 Exponential Trend

a) Regression Output

Figure 10 Exponential trend regression output of Nepal – Low-Income country (1990-2015)

b) Formula & Coefficient explanation

- Linear format: log(Y)= 0.2588― 0.0141(T)

- Non-linear format : Y = 1.814 × 1.033T

𝛽1= 1.033 Thus, the estimated annual compound growth rate of the Gross National Income,

a total of Low-Income country, Nepal (1990-2015) = (1.033 ― 1) × 100% = 3.3%

This illustrates that for every one year, on average, the GNI, total of Low-Income country,Nepal (1990-2015) is estimated to increase by 3.3%

High-Income Country Asia

After applying the hypothesis for trend models in Singapore country (appendix 3.2), thefindings imply that linear trend, quadratic and exponential models are significant for thiscountry

1 Linear Trend

a) Regression Output

Figure 11 Linear trend regression output of Singapore (1990 – 2015)

b) Formula & Coefficient explanation

Y = 4.771 ― 3.542 E-10 X (T) (non-linear)

Firstly, = 4.771 shows that the GNI, total of High-Income country, Singapore (1990-2015),𝛽0

is expected to be around $4771 per head when the time period, T, is 0 year However, this

does not make sense as being out of our observation scope Therefore, this is the portion ofGNI that is not explained by time period T.

We have = ―3.542, so there is a decrease in every single unit in time period T From that,𝛽1the slope indicates that for every one year, on average, the GNI rate is predicted to decrease

by $3.542per person in Singapore And the downward sloping of its linear trend model

2 Quadratic Trend Model

a) Regression Output

Figure 12 Quadratic Trend Regression Output of Singapore (1990 – 2015)

b) Formula and Coefficient explanation

As seen in the regression output above, the p-value of variable T equals 1,1922× 10-o9,2which is much smaller than the confidence level, (0.05) Therefore, we reject H and do not𝛼 0reject H This means that, with a 95% level of confidence, there is sufficient evidence to1confirm that the quadratic trend is also a significant trend model representing the GNI, total(GNI per head) of the High-Income country, Singapore, from 1990 to 2015

3 Exponential Trend Model

a) Regression Output

Figure 13 Exponential trend regression output of Singapore (1990 – 2015)

b) Hypothesis Testing

According to appendix 3, this shows that for every one year, on average, the total fertility rate

of the High-Income country, Singapore (1990-2015) is predicted to decrease by 6.68%.Region B - America

Low-Income Country America

After applying the hypothesis for trend models in Honduras country (appendix 4.1), thefindings imply that linear, quadratic and exponential trend models are significant for thiscountry

1 Linear Trend

a) Regression Output

Figure 14 Linear Trend Regression Output of Honduras (1990 – 2015)

b) Formula & Coefficient explanation

Y =-0.2671―0.0001×T

𝛽0= -0.267 shows that the GNI of a Low-Income country, Nepal (1990-2015), is expected to

be around -$0.267 when the time period, T, is 0 years However, this does not make sense asbeing out of our observation scope Therefore, this is the portion of Gross National Income,total that is not explained by time period T

𝛽1= -0.001, illustrates that for every one year, on average, the GNI, total of Low-Incomecountry, Honduras (1990-2015), is estimated to decrease by $0.0001 per head approximately.This also indicates the downward sloping of its linear trend model

b) Formula & Coefficient explanation

- Linear format: log(Y)= -0.2543― 0.02(T)

- Non-linear format : Y = 0.556 × 1.047T

𝛽1= 1.047 Thus, the estimated annual compound growth rate of the Gross National Income,

a total of Low-Income country, Honduras (1990-2015) = (1.047 ― 1) × 100% = 4.7%

This illustrates that for every one year, on average, the GNI, total of Low-Income country,Honduras (1990-2015) is estimated to decrease by 4.7%

High-Income Country America

After applying the hypothesis for trend models in US country (appendix 4.2), the findingsimply that linear, quadratic and exponential trend models are significant for this country

1 Linear Trend

a) Regression Output

Figure 17 Linear trend regression output of United States (1990 – 2015)

b) Formula & Coefficient explanation

Y = 2.332 ― 2.16 E-10 X (T) (non-linear)

Firstly, = 2.332, shows that the GNI, total of High-Income country, USA (1990-2015), is𝛽0expected to be around $2332 per head when the time period, T is 0 year However, this doesnot make sense as being out of our observation scope Therefore, this is the portion of GNIthat is not explained by time period T

We have = ―2.16, so there is a decrease in every single unit in time period T From that,𝛽1the slope indicates that for every one year, on average the GNI rate is predicted to decrease

by $2.16 per person in Singapore And the downward sloping of its linear trend model

2 Quadratic Trend

a) Regression Output

Figure 18 Quadratic Trend regression output of USA (990 – 2015)

b) Formula & Coefficient explanation

3 Exponential Trend Model

a) Regression Output

Figure 19 Exponential trend regression output of USA (1990 – 2015)

b) Hypothesis Testing

This shows that for every one year, on average, the total Gross National Income of the

High-Income country, USA(1990-2015) is predicted to decrease by 3%

II. Recommended Trend Model for Prediction & Explanation

The country I would recommend to predict GDP per capita growth rate in region A would bethe Low-income country Nepal (C1) since there is a significance in both Quadratic Trend andExponential Trend of increasing GNI in the country every single year by 3.3%

(This illustrates that for every one year, on average, the GNI, total of Low-Income country,Nepal (1990-2015) is estimated to increase by 3.3%.)

The country I would recommend to predict GDP per capita growth rate in region B would bethe High-Income Country United States of America (C4) since there is a significance in bothQuadratic and Exponential trend of increasing GNI in the USA

Overall, the quadratic trend model is the most reliable model to present and predict the GNI

of countries would be the Exponential Trend model out of the four countries because it showswhich countries are increasing and decreasing in GNI on a yearly average

III Predictions for GNI per countries in 2021, 2022, 2023

According to appendix 5, from 2021 to 2023, two countries, including LI-Honduras, andHI-America, slightly decrease in the predicted GNI per head However, LI-Nepal, HI

Singapore has shown a slight rise in the average number of these years in the future

Nonetheless, in the long-term estimation, HI-America’s average number of GNI has shown to

be decreased

Part 6 Time Series Conclusion

Figure: Line chart of the average number of GDP % per head for years 1990-2015 of Low

and High-Income countries

The line graph above illustrates the changes in total GDP growth rate among 4 countriesLI-Nepal and HI-Singapore in Asia and LI-Honduras and HI-USA from 1990 to 2015 Nepalhas shown us the steadiest rise from 1990-2015 even though there was a slight decrease in

2002 due to the Great Recession period However, the country has steadily increased back upand reached its highest growth rate in 2015 Singapore has shown a less steady growth due to

a lot of high and low years but overall the country seems to achieve a strong standing in itsGDP growth rate, spiking its highest GDP growth rate in 2010 and then surprisingly

decreased dramatically Honduras has illustrated a continuously decreased growth rate,

however, the country was able to rise back and keep a more stable flow of GDP The UnitedStates of America has demonstrated to be an economic powerhouse that keeps its steadygrowth over the year and on its way to rise up, suffered its lowest year in 2008 due to theGreat Recession

Even though there are numbers of variations between the GDP growth rate of each country,the overall trend observed in all four countries was still determined to be a quadratic model.These imply that approximately 90% of the observed variations can also be explained by theinterdependent variable – time period, T in the regression model These four tests are

considered to be ideal Based on the analysis our team has performed in Part 5, concerningcountries has shown the same

Part 7 Overall Team Conclusion

a) Main factors that impact GDP per capita growth

Multiple Regressions of GNI per capita growth in four countries, LI-Nepal, HI-Singapore inAsia and LI-Honduras and HI-USA were performed to examine the relationships betweenGDP per capita growth and all the independent variables There is only one independentvariable that has a significant relationship with the GDP per capita growth (annual %) inAsia, and it is the GDP per capita (current US$) Taken the Regression Equation of Asia inPart 3 into account, we can see that Ŷ = 4.882 - 0.00007*(GDP per capita); since the

coefficient of GDP per capita is negative ( -0.00007), the GDP per capita is inversely

proportional to the GDP per capita growth, which means for every US$ increase in GDP percapita, the GDP per capita growth would decrease by 0.00007% Meanwhile, the coefficient

of determination level is 17.6%, which indicates that there is only a minor effect of the GDPper capita on the GDP per capita growth

Based on the findings in Figure 6, it is shown that Trade (% of GDP) is the only variable left.However, using the same elimination method, we can see from Appendix 3, that the variableoutput is higher than the level of significance α (0.06 > 0.05) Therefore, hypothesis H : no₀relationship between the GDP per capita growth and the independent variables is not rejectedand there is no variable left

On the other hand, the study is limited as it only focuses on Asia and America and eightindependent variables It is safe to assume that there are other variables that affect the GDPper capita growth According to Barro (1996), the GDP per capita growth can be affected byvariables like life expectancy, the level of education, fertility rate, government consumptionexpenditure, terms of trade, rule of law maintenance, and inflation rate

The formula for the world’s quadratic GDP growth rate:

Y^=0.2839―0.009×T―0.00003×T2

In 2030, the corresponding time period variable, T equals 30 Therefore, by plugging into theestimated formula, the world’s average fertility rate, the total is predicted to be -0.01, which

is approximately -1% in GDP growth rate in the year 2030 This GDP growth rate is

relatively lower than in previous years due to the downward trend

However, this prediction of GDP growth rate is only an estimation The USA is among one ofthe High-Income countries so the country is considered to be a reliable source to predict theworld's GDP growth rate One single country cannot simplify the whole world’s GDP

economic growth rate; there are countries that suffered from the current Covid-19 Recession.Therefore, more countries need to be involved in this process in order to give a more accurateprediction of the GDP growth rate We are now in the year 2021, data from previous yearsmay be considered to be not reliable and inaccurate to predict the year 2030 Unfortunately,unforeseen events like the current pandemic can suddenly happen and the GDP growth rate of

a lot of developing and developed countries can drop in a short period of time More data isneeded to convey a more accurate prediction

c) Recommendations

Throughout the report analysis, the only variable that was proven to affect the GDP per capitagrowth rate in Asia was the GDP per capita However, it has only a minor impact on the GDPper capita growth Usually, high GDP per capita associates with rich countries and smallpopulations and vice versa (Amadeo 2020), however, China has the biggest population

among the Asian countries, but a quite high GDP per capita, approximately $8417.93 Inaddition, the GDP per capita growth rate is 6.27%, meaning that the GDP per capita is

growing faster than the population growth (Investopedia 2020) It is the same for the

American countries, the USA with the highest population growth among the Asian countriesand also the highest GDP per capita, reaching nearly 58,000 USD