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

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 X1 experiencing a dramatic downward trend fluct

ECON1193 - Business Statistic 1

Word count (excluding table,

figures, references and

3245 wordsappendix)

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

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 of Asia and America, so the mode is considered unusable in this measurement Moreover, there are outliers identified in both regions; Asia has one lower outlier, America has two lower

outliers, and both do not have any upper outlier (Appendix 1) Because the mean is influencedstrongly by the outliers and could cause errors, so the mean is not applicable in this situation; hence, the median is the most suitable descriptive measurement to compare and analyze the GDP per capita growth rate in both regions In this case, the median illustrates that 50% of countries in a region have a higher GDP growth rate than the median value, and the 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 in America’s (1.33%) This number demonstrates that 50% of countries in Asia had a GDP growth rate in 2016 that is higher than 3.35%, and the others recorded less than 3.35%, and some 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

Figure 2 The measures of variation of Asia and America regarding the

GDP per capita growth (annual%)

In this case, the standard deviation is not applicable for the measurement because it was

affected strongly by the outliers The preferred indicator must transcend the effect of several extreme values present in both data strings to make an unbiased comparison An extensive range between the means of the two listed regions and the size of two data strings is another factor that could contribute to skewed assumptions Thus, the Interquartile Range (IQR) is the most suitable variable to compare the variation between Asia and America

The greater the IQR value is, the higher the range, hence the more massive and

incoherent variation In figure 2, the value of IQR in Asia (3.875) is more significant than the value of IQR in America (2.21), which shows that the GDP growth rate from countries

in Asia is less consistent 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 option because 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 actual values of the data.

Looking at the box plot in figure 3, it can be observed that most countries in Asia have a higher 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 the box plots Another application to be made is that 50% of countries in Asia have a higher GDP growth rate than 3.35 while the maximum GDP growth rate in America is only 5.47 This means that many countries in Asia are growing fast in their economy, so they have higher GDP 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

in Asia 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 of Asia 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 often fluctuating 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= b0 + b1X1

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 X1,

holding the GDP 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 per capita growth rate variation in 2016 may be answered by other factors that are not included in this study.

REGION B - AMERICA

a) Regression Final Output and scatter plots

After applying the backward elimination method in appendix 3, the final regression model of America 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 X1 experiencing a dramatic downward trend (fluctuatingfrom 3 to - 0.5), showing a negative relationship with Y As can be observed from figure 5,the data predicted 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 = b0 + b1X1

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 because after applying the backward elimination, Trade (% of GDP) is the only independent variable left (0.06) which is higher than the significance level is 0.05,

so the regression coefficient is not 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

or 14.2% 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 GDP per capita growth rate variation in 2016 may be answered by other factors not included in this study.

Part 4 Team Regression Conclusion

According to the research in part 3, it is recognizable that the two regions Asia and America have a different 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 the variables 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 higher R2 than in America (17.6% > 14.2%) Thus, there is a higher proportion 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) so none 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 is the GDP per capita (current US$) so this is the only variable that could have the highest impact 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 no independent 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 findings imply 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

0 = 1.357 shows that the GNI of a Low-Income country, Nepal (1990-2015), isexpected to be around $1367.5 when the time period, T, is 0 years However, thisdoes not make sense as being out of our observation scope Therefore, this is theportion of Gross National Income, total that is not explained by time period T

1 = -0.0043, illustrates that for every one year, on average, the GNI, total of Income country, Nepal (1990-2015), is estimated to decrease by $0.0043 per headapproximately This also indicates the downward sloping of its linear trend model

Low-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

1 = ―0.0043, illustrates that when T = 0 (year), the instantaneous rate of change of the GNI per 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 the portion of GNI, total that cannot be explained by time period, T.

2 = ―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 curved shape.

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

1 = 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), the findings imply that linear trend, quadratic and exponential models are significant for this country.

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, 0 = 4.771 shows that the GNI, total of High-Income country, Singapore (1990-2015), 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 of GNI that is not explained by time period T.

We have 1 = ―3.542, so there is a decrease in every single unit in time period T From that,the 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 T2 equals 1,1922× 10-o9, which is much smaller than the confidence level, (0.05) Therefore, we reject H0 and do not reject H1 This means that, with a 95% level of confidence, there is sufficient evidence

to confirm 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), the findings imply that linear, quadratic and exponential trend models are significant for this country.

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

0 = -0.267 shows that the GNI of a Low-Income country, Nepal (1990-2015), isexpected to be around -$0.267 when the time period, T, is 0 years However, thisdoes not make sense as being out of our observation scope Therefore, this is theportion of Gross National Income, total that is not explained by time period T

1 = -0.001, illustrates that for every one year, on average, the GNI, total of Low-Income country, 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

1 = 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 findings imply 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, 0 = 2.332, shows that the GNI, total of High-Income country, USA 2015), is expected to be around $2332 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 of GNI that is not explained by time period T.

(1990-We have 1 = ―2.16, so there is a decrease in every single unit in time period T From that,the 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

Y = 2.332 ― 2.162 E-05(T) + 4,67 E-10 ( T2)

The coefficient β1 = ―02.162 E-05 that shows when T=0, the instantaneous rate

of change is -0.105, but 0 is not in the range of the observed values of T.

The coefficient β2 = 4,67 E-10 that shows for every one year, one average the

instantaneous rate of change of the total fertility rate in Poland increases by 2* 4,67 E-10

=0.006, which is a positive direction, and the quadratic trend has a concave curved shape

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%

AI R ecommended Trend Model for Prediction & Explanation

The country I would recommend to predict GDP per capita growth rate in region A would

be the Low-income country Nepal (C1) since there is a significance in both QuadraticTrend and Exponential 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

be the High-Income Country United States of America (C4) since there is a significance inboth Quadratic 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 shows which countries are increasing and decreasing in GNI on a yearly average

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

According to appendix 5, from 2021 to 2023, two countries, including LI-Honduras, and HI-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 countries LI-Nepal and HI-Singapore in Asia and LI-Honduras and HI-USA from 1990 to 2015 Nepal has 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 up and 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 its GDP 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 United States of America has demonstrated to be an economic powerhouse that keeps its steady growth over the year and on its way to rise

up, suffered its lowest year in 2008 due to the Great 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 the interdependent 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, concerning countries 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

in Asia and LI-Honduras and HI-USA were performed to examine the relationships

between GDP per capita growth and all the independent variables There is only one independent variable that has a significant relationship with the GDP per capita growth (annual %) in Asia, and it is the GDP per capita (current US$) Taken the Regression Equation of Asia in Part 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 per capita, 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 GDP per 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 variable output is higher than the level of significance α (0.06

> 0.05) Therefore, hypothesis H₀: no relationship between the GDP per capita growth and the independent variables is not rejected and there is no variable left.

On the other hand, the study is limited as it only focuses on Asia and America and eight independent variables It is safe to assume that there are other variables that affect the GDP per capita growth According to Barro (1996), the GDP per capita growth can be affected by variables like life expectancy, the level of education, fertility rate, government consumption expenditure, terms of trade, rule of law maintenance, and inflation rate.b) GDP predictions in 2030

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 the estimated 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

of the High-Income countries so the country is considered to be a reliable source to predictthe world'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 amore accurate prediction of the GDP growth rate We are now in the year 2021, data from previous years may 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 is needed to convey a more accurate prediction

c) Recommendations

Throughout the report analysis, the only variable that was proven to affect the GDP per capita growth rate in Asia was the GDP per capita However, it has only a minor impact on the GDP per capita growth Usually, high GDP per capita associates with rich countries and small populations 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 In addition, the GDP per capita growth rate is 6.27%, meaning that the GDP percapita 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 countries and also the highest GDP per capita, reaching nearly 58,000 USD

References

Amadeo, K 2020, What Is GDP Per Capita?, The Balance, viewed 28th May 2021,

< and-lowest-3 305848 >

https://www.thebalance.com/gdp-per-capita-formula-u-s-compared-to-highest-Barro, R 1996, DETERMINANTS OF ECONOMIC GROWTH: A CROSS-COUNTRY EMPIRICAL STUDY, National Bureau of Economic Research, viewed 28th May 2021,

<https://www.nber.org/system/files/working_papers/w5698/w5698.pdf>

Investopedia 2020, Per capita GDP, Investopedia, viewed 28th May

2021, <https://www.investopedia.com/terms/p/per-capita-gdp.asp>