Marked-ECON1993 - Assignment 3A - Group 6 - Team 5 PDF

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School of Business & ManagementCourse code: ECON1193BCourse name: Business Statistics 1Semester Sem C 2020Title of Assignment Assignment 3A: Team Assignment ReportName and Student ID + Nguyen Le Thanh Tung - s + Vu Thanh Nam - s + Hua Thanh Thanh - s + Phan Huynh Anh Thy - s + Le Thi Mai Thao - ...

Description

School of Business & Management Course code: ECON1193B Course name: Business Statistics 1 Semester

Sem C 2020

Title of Assignment

Assignment 3A: Team Assignment Report

Name and Student ID

+ Nguyen Le Thanh Tung - s3818087 + Vu Thanh Nam - s3817688 + Hua Thanh Thanh - s3741199 + Phan Huynh Anh Thy - s3817741 + Le Thi Mai Thao - s3864168

Location

Saigon South - Vietnam

Class Group

SGS – Group 6 – Team 5

Lecturer

Nga Trinh Thu

Pages

12 (excluding tables/figures, references and any appendix)

1

Table of Contents: PART 1: DATA COLLECTION ................................................................................................................3 PART 2: DESCRIPTIVE ANALYSIS.......................................................................................................3 PART 3: MULTIPLE REGRESSION.......................................................................................................4 I.

Low-Income countries ...................................................................................................................4

II.

Lower-Middle Income countries ..................................................................................................5

III.

Upper-Middle Income countries...................................................................................................6

IV.

High-Income countries ..................................................................................................................7

PART 4: TEAM REGRESSION CONCLUSION ....................................................................................7 PART 5: TIME SERIES .............................................................................................................................8 I.

The significant trend models...........................................................................................................8 A. Low-Income (LI) – Ethiopia: ..............................................................................................8 B. Lower-Middle Income (LMI) – Lao PDR: ......................................................................10 C. Upper-Middle Income (UMI) – Malaysia:.......................................................................11 D. High-Income (HI) – Poland: .............................................................................................13

II.

Recommended Trend Model for Prediction & Explanation......................................................14

III.

Predictions for fertility rate, total (births per woman) in 2018, 2019, 2020 .............................15

PART 6: TIME SERIES CONCLUSION ...............................................................................................16 I.

Graph Analysis...............................................................................................................................16

II.

Recommended trend model ..........................................................................................................17

PART 7: OVERALL TEAM CONCLUSION ........................................................................................17 REFERENCES...........................................................................................................................................19 APPENDICES ............................................................................................................................................20

2

PART 1: DATA COLLECTION The first step we determine the information that we need to collect. From the WorldBank database, data of five different variables were collected by searching specific keywords, which are Fertility rate, total (births per woman); GNI per capita, Atlas method (current US$); Life expectancy at birth, total (years); Labor force, female (% of total labor force); and Compulsory education, duration (years). These data are specifically in 2017. From the achieved data of 217 countries, the selection process was conducted to eliminate any countries missing even one variable. This results in 125 countries. Therefore, based on those countries meeting all the required variables, 102 countries were then chosen to be raw data for further processes. Moreover, the collected data were then grouped into four different categories (Low-Income, Lower-Middle Income, UpperMiddle Income, High-Income countries) based on the GNI, as specified in the question. PART 2: DESCRIPTIVE ANALYSIS Low-income Lower-middle income Upper-middle income High-income 2.171 2.467 2.432 2.667 Mean 1.74 1.979 2.243 2.249 Median #N/A #N/A 1.43 1.62 Mode Table 1: The central tendency of average births per woman of 4 categorized countries (Low-, Lower-Middle, Upper-Middle, High-Income) in 2017. Low-income Lower-middle income Upper-middle income High-income Observation value < 1.007 -0.286625 0.054 -1.22925 Q1- 1.5*IQR (lower bound) Observation value > 2.695 4.962375 4.63 6.54875 Q3 + 1.5*IQR (Higher bound) 1 0 0 0 Number of outliers Table 2: The outliers of average births per woman of 4 categorized countries (Low-, Lower-Middle, UpperMiddle, High-Income) in 2017. Mean measurement is not applicable in this circumstance because the outliers would make the results of Mean incorrect. In table 2, it is clear that only low-income nations have a single outlier in their dataset whereas others do not have outliers. Moreover, the mode is eliminated owing to that the low-income and lower-middleincome countries are not detected. This leads to having a problematic comparison between the countries if use mode approach. Thus, the median is the best descriptive measurements to examine the births per women of country categories because it is not affected by the outliers. From table 1, the country categories which had the biggest median was high-income countries, with 2.249 births per woman and followed that is upper-middle-income countries which were 2.243 births per woman. The number of births per woman in high-income nations was bigger than in upper-middle-income nations but that was not a tremendous gap between the two numbers, which was 0.0065. Inferring that over 50 percent of births per women of high-income countries was greater than 2.249 compared to 2.243 of upper-middle-income countries. Besides, the lower-middle-income countries got the third rank in the list, with 1.979 births per woman while lower-income countries accounted for the smallest median number and stand at the bottom of the list, 1.74 births per woman. It means that the fertility rate of upper-middle-income countries was 0.2395 higher than the figure for lower-income nations. All in all, the fertility rate of upper-middle- and high-income countries was high and that could lead to a population bomb if the officials do not restrain this rate. Low-income 4.324 Range 0.422 Interquartile Range Standard deviation 1.318 1.737 Variance

Lower-middle income 3.289 1.312 1.073 1.152

Upper-middle income 2.982 1.144 0.812 0.659

High-income 4.297 1.944 1.246 1.553 3

Coefficient of 60.71% 43.51% 33.379% 46.720% Variation (CV) Table 3: The measures of variation of average births per woman of 4 categorized countries (Low-, LowerMiddle, Upper-Middle, High-Income) in 2017. To the best of my knowledge, I would use the coefficient of variation (CV) as the best measurement in this scenario because the CV represents the density and dispersion of standard deviation data around the mean point (Corporate Finance Institute n.d.). The number of data dispersed around the average point tensely when the CV is great. From table 3, the low-income nations had the greatest CV compared to others, 60.71% and it was nearly double than the upper-middle-income nations which were 33.37%. Lower-middle- and highincome countries accounted for 43.51% and 46.72% respectively. Therefore, the number of the low-income countries’ data dispersed more closely to the mean in comparison with other country categories. This means that the fertility rate of low-income nations dispersed around 2.171 births per woman and they almost had a low fertility rate. PART 3: MULTIPLE REGRESSION In the case, to build a multiple regression model measuring the number of babies per woman based on the collected dataset, it is crucial to identify the independent variable and dependent variable. It is clear that there are 4 independent variables including X1, X2, X3, X4 below, whereas there is only one dependent variable denoted by Y. Y: Fertility rate, total (births per woman)

X3: Labor force, female (% of total labor force)

X1: Compulsory education, duration (years)

X4: GNI per capita, Atlas method (current US$)

X2: Life expectancy at birth (years) In order to remove the significant independent variable and get the independent variables relating to the dependent variable Y, the backward elimination method is applied in this part to construct the final regression model of the 4 income level countries. The process of getting final regression model for the 4 income level countries is presented in the appendix 1. I.

Low-income countries:

Figure 1: The final regression output of Low-income countries

4

Fertility rate, total (births per woman)

The scatter plot between Fertility rate, total (births per woman) and Labor force, female (% of total labor force) 6 5 4 3 2 1 0

0

10

20

30

40

50

60

Labor force, female (% of total labor force)

Figure 2: The scatter plot displayed the relationship between the total fertility rate (births per woman) and the female labor force (% of total labor force) Based on the final data of low-income countries from the figure 1, the regression equation would be calculated as below: Ŷ = b0+ b3 X3 = 16.39 – 0.24X3 + Ŷ: Fertility rate, total (births per woman)

+ X3: Labor force, female (% of total labor force)

b3 = – 0.24 illustrates that the predicted total fertility rate will decrease by 0.24 births per woman when the female labor force increases by 1% in the total labor force. The coefficient of determination (R2) is 0.8185 = 81.85 %, representing that 81.85 % of the change in the total fertility rate (births per woman) (dependent variable Ŷ) can be explained by the variation in the female labor force (% of total labor force) (independent variable X3). II.

Lower-Middle Income countries:

Figure 3: The final regression output of Lower-Middle income countries

5

Fertility rate, total (births per woman)

The scatter plot between the fertility rate, total (births per woman) and the life expectancy at birth, total (years) 6 5 4 3 2 1 0

0

10

20

30

40

50

60

70

80

90

Life expectancy at birth, total (years)

Figure 4: The scatter plot displayed the relationship between the total fertility rate (births per woman) and the total life expectancy at birth (years) Based on the final data of low-middle income countries from the figure 3, the regression equation would be calculated as below: Ŷ = b0+ b2 X2 = 10.49 – 0.10X3 + Ŷ: Fertility rate, total (births per woman)

+ X2 : Life expectancy at birth, total (years)

b2 = – 0.10 indicates that the predicted total fertility rate will decrease by 0.10 births per woman when the total life expectancy at birth increases by 1 year. The coefficient of determination (R2) is 0.4519 = 45.19 %, representing that 45.19% of the change in the total fertility rate (births per woman) (dependent variable Ŷ) can be explained by the variation in the total life expectancy at birth (years) (independent variable X3). III.

Upper-Middle Income countries:

Figure 5: The final regression output of Upper-Middle income countries. Based on the final data of upper-middle income countries from the figure 5, the regression equation would be calculated as below: Ŷ = b0+ b1 X1 + b2 X2 + b3 X3 = 12.91 + 0.05X1 – 0.13X2 – 0.04X3 + Ŷ: Fertility rate, total (births per woman)

+ X2: Life expectancy at birth (years)

+ X1: Compulsory education, duration (years)

+ X3: Labor force, female (% of total labor force)

The duration of compulsory education (years) has a regression coefficient of 0.05, representing that the predicted total fertility rate will increase by 0.05 births per woman when the duration of compulsory education 6

increases by 1 year, given that the life expectancy at birth (years) and the female labor force (% of total labor force) remain constant. The life expectancy at birth (years) has a regression coefficient of – 0.13, representing that the predicted total fertility rate will decline by 0.13 births per woman when the life expectancy at birth increases by 1 year, given that the duration of compulsory education (years) and the female labor force (% of total labor force) remain stable. The female labor force (% of total labor force) has a regression coefficient of - 0.04, meaning that the predicted total fertility rate will decrease by 0.04 births per woman when the female labor force increases by 1 % in the total labor force, given that the duration compulsory education (years) and the life expectancy at birth (years) remain constant. The coefficient of determination (R2) is 0.7820 = 78.20% representing that 78.20% of the change in the total fertility rate (births per woman) (dependent variable Ŷ) can be explained by the variation in the total life expectancy at birth (years) (independent variable X2), the duration of compulsory education (years) (independent variable X1) and the female labor force ( % of total labor force) (independent variable X3) IV.

High-Income countries:

Figure 6: The final regression output of High-income countries Based on the final data of high-income countries from the figure 6, the regression equation would be calculated as below: Ŷ = b0+ b1 X1 + b3 X3 = 1.75 + 0.1X1 – 0.02X3 + Ŷ: Fertility rate, total (births per woman)

+ X3: Labor force, female (% of total labor force)

+ X1: Compulsory education, duration (years) The duration of compulsory education (years) has a regression coefficient of 0.1, representing that the predicted total fertility rate will increase by 0.1 births per woman when the duration of compulsory education increases by 1 year, given that the female labor force (% of total labor force) remains constant. The female labor force (% of total labor force) has a regression coefficient of - 0.02, meaning that the predicted total fertility rate will decline by 0.02 births per woman when the female participation in labor force increases by 1% in the total labor force, given that the duration compulsory education (years) remains stable. The coefficient of determination (R2) is 0.3906 = 39.06 % representing that 39.06 % of the change in the total fertility rate (births per woman) (dependent variable Ŷ) can be explained by the variation in the duration of compulsory education (years) (independent variable X1) and the female labor force (% of total labor force) (independent variable X3). PART 4: TEAM REGRESSION CONCLUSION After executing several calculations of the multiple regression in part 3, not all the introduced models have the same crucial independent variables from the received outcomes. For almost nations in the dataset, two independent variables – labor force and compulsory education have a huge impact on the fertility rate at a 0.05 significant level, but the lower-middle-income countries were influenced by only other variables which were 7

life expectancy at birth. It is clear that two of those independent variables affected tremendously the fertility rate of high-income countries at a 0.05 significant level. Upper-Middle income countries have another independent variable out of the two mentioned variables, life expectancy at birth, which affected the fertility rate at 0.05 significant level. Whereas the low-income countries were merely impacted by the labor force. Besides, the regression model of low-income nations got the highest coefficient of variable determination, 0.818 compared to other country categories. This illustrates that the fertility rate of low-income countries can be explained excellently by the variation in the female labor force. On the other hands, the labor force and compulsory education would build the best regression model to demonstrate of the birth per woman assessment. The fact that labor force is considered as a significant independent variable for almost country categories, excepting low-income countries because it was the last variable after eliminating all variables. Especially, lower-middle-income countries were not affected by any of two noticed independent variables. For almost countries, the labor force was the best regression model, and it could be predicted that the fertility rate will decrease when the labor force increase. Similarity, life expectancy at birth was the most outstanding variable for the regression model of lower-middle-income countries. It could be understanded that the fertility rate went up if the life expectancy at birth went down, given that other factors was unchanged. In terms of part 2, the low-income countries had the lowest average fertility rate, with 2.171 births per woman while the high-income countries had the highest average fertility which was 2.667 births per woman. Theoretically, the fertility rate is expect to decline in the developed countries, which leads to a reduction the birth rate of that country (Nargund 2009). PART 5: TIME SERIES

I.

The significant trend models

Notes: Throughout section I, Y T

births per woman years

the estimated value of fertility rate, total in country (1990-2015) the independent variable of time period

A. Low Income (LI) – Ethiopia: 1. Linear Trend Model: a) Regression Output: df SS MS 24 0.373 0.015543965 Coefficients Standard Error t Stat 7.642 0.050347413 151.7783879 Intercept -0.116 0.003260115 -35.59718798 T Table 4: Linear trend regression output of Ethiopia – Low Income country (1990-2015)

F

Residual

P-value 2.6037E-37 2.76596E-22

b) Hypothesis Testing: H0: 𝛽1 = 0 (No linear trend in the fertility rate, total in Low Income country (1990-2015)) H1: 𝛽1 ≠ 0 (Linear trend in the fertility rate, total in Low Income country (1990-2015) observed) As seen in the regression output above, the p-value of variable T equals to 2.766 × 10 ―22, which is much smaller than the confidence level, 𝛼 (0.05). Therefore, we reject the null hypothesis H0 and do not reject H1. This means that, with 95% level of confidence, there is sufficient evidence to confirm that the linear trend is a significant trend model representing for the fertility rate, total (births per woman) of the Low-Income country, Ethiopia (1990-2015). c) Formula & Coefficient explanation: Y = 7.642 ― 0.116 × T 8

𝛽0 = 7.642, shows that the fertility rate, total of Low-Income country, Ethiopia (1990-2015) is expected to be around 7.642 births per 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 fertility rate, total that is not explained by time period T. 𝛽1 = -0.116, illustrates that for every 1 year, on average, the fertility rate, total of Low-Income country, Ethiopia (1990-2015) is estimated to decrease by 0.116 births per woman, approximately. This also indicates the downward sloping of its linear trend model. 2. Quadratic Trend Model: a) Regression Output: df SS M...