Business Statistics PDF

Preview

Summary

ECON1193 - Business Statistic 1Semester 1 - 2021Title of Assignment Assignment 3A: Team Assignment ReportName and Student ID ❖ Le Thien Ai - s ❖ Vu Dinh Thai - s ❖ Fuoc An Doanh - sLocation Saigon South - VietnamClass Group SGS - Group 7Lecturer Tuan CTWord count (excluding table, figures, reference...

Description

ECON1193 - Business Statistic 1 Semester 1 - 2021

Title of Assignment Name and Student ID

Assignment 3A: Team Assignment Report ❖ Le Thien Ai - s3864119 ❖ Vu Dinh Thai - s3877521 ❖ Fuoc An Doanh - s3879951

Location

Saigon South - Vietnam

Class Group

SGS - Group 7

Lecturer

Tuan CT

Word count (excluding table, figures, references and appendix)

3245 words

1

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. Measures of central tendency Measures of Central Tendency

Region A Asia

Region B - America

Mean

3.825

1.102

Median

3.35

1.33

Mode

-

-

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 influenced strongly 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

2. Measures of variation

MEASURES OF VARIATION

Region A Asia

Region B - America

Standard Deviation

3.398

2.266

Sample Variance

11.549

5.135

Range

12.99

9.54

Interquartile range

3.875

2.21

Coefficient of Variation

88.83%

205.65%

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

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.

4

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$)

5

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 = b 0 + b1 X 1 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.

6

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 (fluctuating from 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 = b 0 + b1 X 1

7

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 the GDP 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) 8

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 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 as being 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-Income country, 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×T 2 𝛽1 = ―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 9

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. 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 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 × 1.033 T 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), 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, 𝛽0 = 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 10

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 𝛽1 = ―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, 𝛼 (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.

11

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 as being 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-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.

2. Quadratic Trend Regression Output

Figure 15. Quadratic trend regression output of Honduras – Low-Income country (1990-2015)

3. Exponential Trend a) Regression Output

Figure 16. Exponential trend regression output of Honduras – Low-Income country (1990-2015)

12

b) Formula & Coefficient explanation - Linear format: log (Y) = -0.2543― 0.02(T) - Non-linear format : Y = 0.556 × 1.047 T 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 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, 𝛽0 = 2.332, shows that the GNI, total of High-Income country, USA (1990-2015), 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. We have 𝛽1 = ―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

13

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%.

II.

Recommended 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 Quadratic Trend 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 in both 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.

14

III.

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 ...