(TIỂU LUẬN) school of business management course code ECON1193B course name business statistics 1

School of Business & Management Course code: ECON1193B Course name: Business Statistics 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 – Team Lecturer Nga Trinh Thu Pages 12 (excluding tables/figures, references and any appendix) Table of Contents: PART 1: DATA COLLECTION PART 2: DESCRIPTIVE ANALYSIS .3 PART 3: MULTIPLE REGRESSION .4 I Low-Income countries II Lower-Middle Income countries III Upper-Middle Income countries IV High-Income countries PART 4: TEAM REGRESSION CONCLUSION PART 5: TIME SERIES .8 I The significant trend models A Low-Income (LI) – Ethiopia: 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 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 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) 0 Number of outliers Table 2: The outliers of average births per woman of 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 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 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 Coefficient of 60.71% 43.51% 33.379% 46.720% Variation (CV) Table 3: The measures of variation of average births per woman of 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 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 income level countries The process of getting final regression model for the income level countries is presented in the appendix I Low-income countries: Figure 1: The final regression output of Low-income countries Fertility rate, total (births per woman) The scatter plot between Fertility rate, total (births per woman) and Labor force, female (% of total labor force) 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 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) 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 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 increases by 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 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 % 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 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 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: 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 = (No linear trend in the fertility rate, total in Low Income country (1990-2015)) H1: 𝛽1 ≠ (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 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 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 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 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 Quadratic Trend Model: a) Regression Output: df SS MS F 23 0.135 0.00585621 Coefficients Standard Error t Stat P-value 7.401 0.048723888 151.9033598 4.95908E-36 Intercept -0.065 0.008316407 -7.762043807 7.17214E-08 T T-squared -0.002 0.000298966 -6.379850759 1.64567E-06 Table 5: Quadratic trend regression output of Ethiopia – Low Income country (1990-2015) Residual b) Hypothesis Testing: H0: 𝛽2 = (No quadratic trend in the fertility rate, total (births per woman) in Low Income country (19902015)) H1: 𝛽2 ≠ (Quadratic trend in the fertility rate, total (births per woman) in Low Income country (1990-2015) observed) As seen in the regression output above, the p-value of variable T2 equals to 1.646 × 10 ―6, which is much smaller than the confidence level, 𝛼 (0.05) Therefore, we reject H0 and not reject H1 This means that, with 95% level of confidence, there is sufficient evidence to confirm that the quadratic trend is also a significant trend model representing for the fertility rate, total (births per woman) of the Low-Income country, Ethiopia from 1990 to 2015 c) Formula & Coefficient explanation: Y = 7.401 ― 0.065 × T ― 0.002 × T2 𝛽1 = ―0.065 , illustrates that when T = (year), the instantaneous rate of change of the fertility rate, total of Low-Income country, Ethiopia (1990-2015) is ―0.065 births per woman annually However, T = is not within this variable’s observation range Thus, this is the portion of fertility rate, total that cannot be explained by time period, T 𝛽2 = ―0.002 , indicates that for every one year, on average, the fertility rate, total of Low-Income country, Ethiopia (1990-2015) instantaneously decreases at the rate of × 0.002 = 0.004 births per woman annually This quadratic trend model has concave curve shape Exponential Trend Model: a) Regression Output: df SS MS F 24 0.003339461 0.000139 Residual Coefficients Standard Error t Stat P-value 0.894 0.004763529 187.6062 1.61622E-39 Intercept -0.009 0.00030845 -27.5832 1.09334E-19 T Table 6: Exponential trend regression output of Ethiopia – Low Income country (1990-2015) b) Hypothesis Testing: H0: 𝛽1 = (No exponential trend in the fertility rate, total in Low Income country (1990-2015)) H1: 𝛽1 ≠ (Exponential 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 1.093 × 10 ― 19, which is much smaller than the confidence level, 𝛼 (0.05) Therefore, we reject H0 and not reject H1 This means that, with 95% level of confidence, there is sufficient evidence to confirm that the exponential trend is also a significant trend model representing for the fertility rate, total (births per woman) of the Low-Income country, Ethiopia from 1990 to 2015 c) Formula & Coefficient explanation: - Linear format: log (Y) = 0.894 ― 0.009(T) - Non-linear format : Y = 7.828 × 0.981 T (Note: 7.828 ≈10 0.894 & 0.981 ≈ 100.009) 𝛽1 = 0.981 Thus, the estimated annual compound growth rate of the fertility rate, total of Low-Income country, Ethiopia (1990-2015) = (0.981 ― 1) × 100%= ― 1.90% This illustrates that for every year, on average, the fertility rate, total of Low-Income country, Ethiopia (1990-2015) is estimated to decrease by 1.90% B Lower-Middle Income (UMI) – Lao PDR: Linear Trend Model: a) Regression Output: df SS MS F 24 1.048066 0.043669 Coefficients Standard Error t Stat P-value 6.119 0.084389 72.51421 1.24989E-29 Intercept -0.143 0.005464 -26.0997 3.95442E-19 T Table 7: Linear trend regression output of Lao PDR – Lower Middle Income country (1990-2015) Residual b) Hypothesis Testing: H0: 𝛽1 = (No linear trend in the fertility rate, total in Lower Middle-Income country (1990-2015)) H1: 𝛽1 ≠ (Linear trend in the fertility rate, total in Lower Middle-Income country (1990-2015) observed) As seen in the regression output above, the p-value of variable T equals to 3.954 × 10 ― 19, which is much smaller than the confidence level, 𝛼 (0.05) Therefore, we reject H0 and 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 Lower Middle-Income country, Lao PRD from 1990 to 2015 c) Formula & Coefficient explanation: Y = 6.119 ― 0.143 × T (non-linear format) 𝛽0 = 6.119, shows that the fertility rate, total of Lower Middle-Income country, Lao PDR (1990-2015) is expected to be around 6.119 births per when the time period, T is 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 = ―0.143 , illustrates that for every year, on average, the fertility rate, total of Lower Middle-Income country, Lao PDR (1990-2015) is predicted to decrease by 0.143 births per woman, approximately This also indicates the downward sloping of its linear trend model Quadratic Trend Model: a) Regression Output: df SS MS F 23 0.121042 0.005263 Residual Coefficients Standard Error t Stat P-value 6.593 0.046189 142.7471 2.07E-35 Intercept -0.244 0.007884 -30.9725 2.95E-20 T 0.004 0.000283 13.27215 2.88E-12 T-squared Table 8: Quadratic trend regression output of Lao PDR – Lower-Middle Income country (1990-2015) 10 b) Hypothesis Testing: H0: 𝛽2 = (No quadratic trend in the fertility rate, total (births per woman) in Lower Middle-Income country (1990-2015)) H1: 𝛽 ≠ (Quadratic trend in the fertility rate, total (births per woman) in Lower Middle-Income country (1990-2015) observed) As seen in the regression output above, the p-value of variable T equals to 2.88 × 10 ―12, which is much smaller than the confidence level, 𝛼 (0.05) Therefore, we reject H0 and accept H1, which means, with 95% level of confidence, there is sufficient evidence to confirm that the quadratic trend is a significant trend model representing for the fertility rate, total (births per woman) of the Lower Middle-Income country, Lao PDR from 1990 to 2015 c) Formula & Coefficient explanation: Y = 6.593 ― 0.244 × T + 0.004 × T2 𝛽1 = ―0.244 shows that when T = year, the instantaneous rate of change of the fertility rate, total of Lower Middle-Income country, Lao PDR (1990-2015) is ―0.244 births per woman, annually However, T = is not within this variable’s observation range Thus, this is the portion of fertility rate, total that cannot be explained by time period, T 𝛽2 = 0.004, indicates that for every one year, on average, the fertility rate, total of Lower Middle-Income country, Lao PDR (1990-2015) instantaneously increases at the rate of × 0.004 = 0.008 births per woman annually This quadratic trend model is convex curve Exponential Trend Model: Regression Output: df SS MS F 24 0.00307 0.000128 Residual Coefficients Standard Error t Stat P-value 0.807 0.004568 176.7281 6.77E-39 Intercept -0.015 0.000296 -49.8185 9.64E-26 T Table 9: Exponential trend regression output of Lao PDR – Lower-Middle Income country (1990-2015) Hypothesis Testing: H0: 𝛽1 = (No exponential trend in the fertility rate, total in Lower Middle-Income country (1990-2015)) H1: 𝛽1 ≠ (Exponential trend in the fertility rate, total in Lower Middle-Income country (1990-2015) observed) As seen in the regression output above, the p-value of variable T equals to 9.64 × 10 ―26, which is much smaller than the confidence level, 𝛼 (0.05) Therefore, we reject H0 and accept H1 This leads to the fact that, with 95% level of confidence, the exponential trend model is significant enough to represent for the fertility rate, total (births per woman) of the Lower Middle-Income country, Lao PDR from 1990 to 2015 Formula & Coefficient explanation: - Linear format: log (Y) = 0.807 ― 0.015(T) - Non-linear format : Y = 6.415 × 0.967 T (Note: 415 ≈ 10 0.807 & 0.967 ≈ 10 0.015) 𝛽1 = 0.967 Thus, the estimated annual compound growth rate of the fertility rate, total of Lower MiddleIncome country, Lao PDR (1990-2015) = (0.967 ― 1) × 100% = ― 3.30% This illustrates that for every year, on average, the fertility rate, total of Lower Middle-Income country, Lao PDR (1990-2015) is predicted to drop by 3.30% C Upper- Middle Income (UMI)– Malaysia: Linear model 11 a) Regression output: df SS MS 24 0.440934615 0.018372276 Coefficients Standard Error t Stat 3.608 0.054736589 65.9084941 Intercept -0.069 0.003544325 -19.55436041 T Table 10: Linear trend regression output of Malaysia (1990 – 2015) F Residual p-value 1.22361E-28 2.98486E-16 b) Hypothesis test: H0: β = (There is no linear trend in the total fertility rate in Malaysia) H1: β ≠ (There is a linear trend in the total fertility rate in Malaysia) Based on the calculations, the p-value of linear trend model is approaching to ( 2.98E ― 16 ≈ 2.98 ∗ 10 ―16 ≈ 0), and smaller than the confidence level (α= 0.05), so we can reject H0 As a result, with 95% level of confidence, it can be claimed that there is a linear trend model for total fertility rate (births per women) for upper-middle country – Malaysia yearly c) Formula & Coefficient explanation: Y = 3.608 ― 0.069(T) Firstly, 𝛽0 = 3.068, shows that the fertility rate, total of Upper-Middle Income country, Malaysia (1990-2015) is expected to be around 3.068 births per when the time period, T is 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 We have 𝛽1 = ―0.069, so there is a decrease in every unit in time period T From that, the slope indicates that for every one year, on average the total fertility rate is predicted to decrease by 0.069 births per women in Malaysia And the downward sloping of its linear trend model Quadratic trend model: a) Regression output: df SS MS 23 0.191888406 0.008342974 Residual Coefficients Standard Error t Stat 3.853 0.05815594 66.25737611 Intercept -0.122 0.009926311 -12.28524084 X Variable 0.002 0.00035684 5.46360782 X Variable Table 11: Quadratic trend regression output of Malaysia (1990 – 2015) F P-value 9.17879E-28 1.38099E-11 1.48803E-05 b) Hypothesis test: H 0: β2 = (There is no quadratic trend in the total fertility rate in Malaysia) H 1: β2 ≠ (There is a quadratic trend in the total fertility rate in Malaysia) From the above figure, as both p-values are approaching to (1.38E ― 11 ≈ 1.38 ∗ 10 ―11 ≈ & 1.488E ― 05 ≈ 1.488 ∗ 10 ―05 ≈ 0), and smaller than the confidence level (α = 0.05) Thus, we can reject H0 and not reject H1 That means with the confidence level of 95%, there is a quadratic trend in the total fertility rate in Malaysia yearly c) Formula & Coefficient explanation: Y =3.853 ― 0.122(T)+ 0.002 (T2) The coefficient 𝛽1 = ―0.122 that shows when T=0, the instantaneous rate of change is -0.122, but is not in the range of the observed values of T The coefficient 𝛽 = 0.002 that shows for every one year, one average the instantaneous rate of change of the total fertility rate in Malaysia increases by 2*0.002 = 0.004, which is a positive direction, and the quadratic trend has U-shape (convex curve) 12 Exponential trend model: a) Regression output: df 24 Residual Intercept X Variable SS 0.00861386 MS 0.000358911 F Coefficients 0.569 Standard Error 0.007650495 t Stat 74.34712901 P-value 6.88327E-30 -0.011 0.000495388 -22.5034285 1.21291E-17 Table 12: Exponential trend regression output of Malaysia (1990 – 2015) b) Hypothesis test: H 0: β1 = (There is no exponential trend in the total fertility rate in Malaysia) H 1: β1 ≠ (There is an exponential trend in the total fertility rate in Malaysia) Similarly, we can reject H0 because the p-value is close to (1.21E ―17 ≈ 1.21 ∗ 1017 ≈0 ), and smaller than (α = 0.05) Thus, we are 95% confident that there is an exponential trend model for fertility rate, total (births per women) for Malaysia yearly c) Formula & Coefficient explanation: - Linear format: log (Y) = 0.569 ― 0.011(T) - Non-linear format : Y = 3.707(0.975T) (Note: 3.707 ≈ 100.569 & 0.975 ≈ 100.011) 𝛽 = 0.975 Thus, (0.975 - 1) *100% = -2.5% is the estimated annual compound growth rate of the total fertility rate of Malaysia (1990-2015) This shows that for every one year, on average, the total fertility rate of Upper-Middle Income country, Malaysia MYS (1990-2015) is predicted to decrease by 2.5% D High-Income (HI) – Poland: Linear model a) Regression output: df SS MS 24 0.683851692 0.028493821 Residual Coefficients Standard Error t Stat 1.831 0.068166594 26.86359821 Intercept -0.027 0.00441395 -6.022862892 T Table 13: Linear trend regression output of Poland (1990 – 2015) F P-value 2.02282E-19 3.22112E-06 b) Hypothesis test: H0 : β1 = (There is no linear trend in the total fertility rate (births per woman) in Poland (1990-2015)) H1 : β1 ≠ (There is a linear trend in the total fertility rate (births per woman) in Poland (1990-2015)) Based on the calculation from Excel (Figure 1), the p-value of linear trend model is approaching to ( 3221 E ― 06 ≈ 3.221 ∗ 10 ―06 ≈ 0), and smaller than the confidence level ( α = 0.05) Thus, we can reject H0 As a result, with 95% level of confidence, it can be claimed that there is a linear trend model for total fertility rate (births per women) for high income country – Poland yearly c) Formula & Coefficient explanation: Y = 1.831 ― 0.027(T) Firstly, 𝛽0 = 1.831, shows that the fertility rate, total of High-Income country, Poland (1990-2015) is expected to be around 1.831 births per when the time period, T is 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 We have β1 = ―0.027 , so there is a decrease in every unit in time period T From that, the slope indicates that for every one year, on average the total fertility rate is predicted to decrease by 0.027 births per women in Poland and the downward sloping of its linear trend model 13 Quadratic trend model: a) Regression output df SS MS 23 0.125659726 0.005463466 Residual Coefficients Standard Error t Stat 2.199 0.047061717 46.72522313 Intercept -0.105 0.0080327 -13.12040855 T 0.003 0.000288767 10.10782359 T squared Table 14: Quadratic trend regression output of Poland (1990 – 2015) F P-value 2.66869E-24 3.64797E-12 6.24174E-10 b) Hypothesis test: H 0: β2 = (There is no quadratic trend in the total fertility rate in Poland (1990-2015)) H 1: β2 ≠ (There is a quadratic trend in the total fertility rate in Poland (1990-2015)) From Figure above, as both p-values are approaching to (3.65E ― 12 ≈ 3.65 ∗ 10 ―12 ≈ & 6.24E ― 10 ≈ 6.24 ∗ 10 ―10 ≈ ), and they are smaller than the confidence level (α = 0.05) Thus, we can reject H0 and not reject H1 That means with the confidence level of 95%, there is a quadratic trend in the total fertility rate in Poland yearly c) Formula & Coefficient explanation: Y =2.199 ― 0.105(T)+ 0.003 (T2) The coefficient β1 = ―0.105that shows when T=0, the instantaneous rate of change is -0.105, but is not in the range of the observed values of T The coefficient β2 = ― 0.003 that shows for every one year, one average the instantaneous rate of change of the total fertility rate in Poland increases by 2*0.003=0.006, which is a positive direction, and the quadratic trend has concave curve shape Exponential trend model: Regression output: df SS MS F Residual 24 0.050607392 0.002108641 Coefficients Standard Error t Stat P-value Intercept 0.259 0.018543752 13.99388668 4.87426E-13 T -0.007 0.001200752 -6.010352361 3.32168E-06 Table 15: Exponential trend regression output of Poland (1990 – 2015) Hypothesis test: H0 : β1 = (There is no exponential trend in the total fertility rate in Poland (1990-2015)) H1 : β1 ≠ (There is an exponential trend in the total fertility rate in Poland (1990-2015)) Similarly, we can reject H0 because the p-value is close to (3.32E ― 06 ≈ 3.32 ∗ 10 ―06 ≈ 0), and smaller than (α = 0.05) Thus, we are 95% confident that there is an exponential trend model for fertility rate, total (births per woman) of the High-Income, Poland from 1990 to 2015 Formula & Coefficient explanation: - Linear format: log (Y) = 0.259 ― 0.007(T) - Non-linear format : Y = 1.818(0.984T) (Note: 1.818≈ 10 0.259 & 0.984 ≈10 0.007) 𝛽 = 0.984 Thus, (0.984 - 1) *100% = -1.65% is the estimated annual compound growth rate of the total fertility rate of Poland (1990-2015) This shows that for every one year, on average, the total fertility rate of High-Income country, Poland POL (1990-2015) is predicted to decrease by 1.65% II Recommended Trend Model for Prediction & Explanation Note: Sum of Squared Errors (SSE), Mean Absolute Deviation (MAD) Error Measurement Linear Quadratic Exponential 14 SSE 0.373 0.169 0.766 MAD 0.100 0.067 0.143 SSE 1.049 0.279 0.294 LMI-Lao PDR MAD 0.178 0.096 0.093 SSE 0.442 0.198 0.288 UMI-Malaysia MAD 0.111 0.073 0.092 SSE 0.685 0.152 0.625 HI-Poland MAD 0.149 0.066 0.136 Table 16: Error measurement for the three trend models of LI-Ethiopia, LMI-Lao PDR, UMI-Malaysia, and HI- Poland (1990-2015) LI- Ethiopia Upper Middle-Income – Lao PDR Births per woman First quartile Q1 3.257 5.109 Third quartile Q3 1.851 Inter-quartile range IQR 0.480 Lower bound Q1-1.5*IQR 7.885 Upper bound Q3+1.5*IQR None Outliers Table 17: Table of checking outliers of fertility rate, total (births per woman) of Lower Middle-Income country, Lao PDR (1990-2015) Based on the table 16, the quadratic trend models of all three countries, including LI-Ethiopia, UMI-Malaysia, and HI-Poland have the lowest SSE and the lowest MAD values This means that when comparing three trend models, quadratic generates less error than the other two While, in LMI-Lao PDR, the quadratic trend model performs the lowest SSE value, and exponential trend model has the lowest MAD value This might generate a contradiction while evaluating the most recommended trend model for our data Besides, observed data of the fertility rate, total (births per woman) of LMI-Lao PDR have no outliers As SSE methodology is sensitive to outliers while MAD is not, SSE’s result is more preferred Thus, the quadratic trend model would be preferred for Lao PDR Overall, the quadratic trend model is the most reliable model to present and predict the fertility rate, total (births per woman) of Low-Income country, Ethiopia; Lower-Middle country, Lao PDR; Upper-Middle Income country, Malaysia; and High-Income country, Poland within 1990-2015 period and upcoming years III Predictions for fertility rate, total (births per woman) in 2018, 2019, 2020: As quadratic trend model is determined to be the most reliable trend model to estimate the average number of births per woman of all four countries, their total fertility rate (births per woman) in 2018, 2019 and 2020 are calculated based on quadratic trend model formula as follows: The quadratic trend formulas for the average number of births per woman LI- Ethiopia Y = 7.401 ― 0.065 × T ― 0.002 × T2 LMI-Lao PDR Y = 6.593 ― 0.244 × T + 0.004 × T2 UMI-Malaysia Y = 3.853― 0.122 × T + 0.002 × T HI-Poland Y = 2.199― 0.105 × T + 0.003 × T Table 18: The quadratic trend formulas used for prediction of the average number of births per woman of LIEthiopia, LMI-Lao PDR, UMI-Malaysia, and HI- Poland in 2018, 2019 and 2020 Notes: Y T Year births per woman years the predicted value of fertility rate, total in country in 2018, 2019 and 2020 the independent variable of time period Corresponding Time Period, T Predicted average number of births per woman LI-Ethiopia LMI-Lao UMIHI-Poland PDR Malaysia 15 2018 29 3.834 2.881 1.997 1.677 2019 30 3.651 2.873 1.993 1.749 2020 31 3.464 2.873 1.993 1.827 Table 19: Corresponding time period and predicted average number of births per woman in year 2018, 2019, 2020 of LI-Ethiopia, LMI-Lao PDR, UMI-Malaysia, and HI- Poland From 2018 to 2020, all three countries, including LI-Ethiopia, LMI-Lao PDR and UMI-Malaysia, slightly decreases in the predicted fertility rate, total (births per woman) Meanwhile, HI-Poland observes a relatively rise in the estimated average number of births per woman in these upcoming years However, in the long-term estimation, LI-Ethiopia’s average number of births per woman is predicted to decline, which is opposite to the predicted trends of other three countries PART 6: TIME SERIES CONCLUSION I Graph analysis: Fertility rate (births per women) Average number of births per women, 1990-2015 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Year Low Income- Ethiopia Lower Middle Income -Lao PDR Upper Middle Income - Malaysia High Income - Poland Figure 7: Line chart of average number of births per woman for years 1990-2015 of Low-, Lower Middle-, Upper Middle- and High-Income countries The line graph above illustrates the change in total feritility rate among countries from different income classifications, including LI, LMI, UMI, HI, from 1990 to 2015 Regarding High-Income country, Poland, there was a slightly decline in around first half years (from 1990 to 2004); then followed by an unexpected rise until 2015 However, its avarage number of births per woman in 2015 is still relatively lower than 1995’s fertility rate, (1.32 compared to 2.06 births per woman) Besides, the fertility rate of three other countries, including Ethiopia, Lao, and Malaysia were continuously decreasing during the 26-year period These trends were proven by the downward sloping of trendlines These fertility reductions did follow the findings of the negative relationship between fertility rates and economic considerations (Vandenbroucke 2016) However, it is observed that Low-Income countries, such as Ethiopia, experienced a remarkable decline in their fertility rate as time passes Over two decades, the two representatives of the Middle-Income countries, Lao PDR and Malaysia, both had their average number of births per woman significantly dropped by approximately 40% Despite huge reduction, Low-Income country, Ethiopia still had the highest fertility rate among countries, at around births per woman The other three countries’ values range between and closely births per woman 16 Although there are numbers of variations between fertility rates of each country, the overall trend observed for the four countries were still determined to be quadratic model This was due to the impressively high coefficients of determination, R-squared, achieved in all regression outputs These implied that it is approximately 90% of the observed variation could be explained by the interdependent variable – time period, T in the regression model (Fernando 2020) These four tests are considered to be relatively good test Based on the analysis conducted in Part 5, all investing countries follow the same quadratic trend model II Recommended trend model for fertility rate, total (births per woman) of different income groups: In the previous part, quadratic trend model is considered to best illustrate the average number of births per women during 1990 – 2015 period of four income-based countries Therefore, quadratic trend model is determined to be the most reliable model for the prediction of the average number of births per woman in the world in following years LI – Ethiopia LMI – Lao PDR UMI – Malaysia HI – Poland Sum of Squared Errors (SSE) 0.169 0.279 0.198 0.152 Mean Absolute Deviation (MAD) 0.067 0.093 0.073 0.066 Table 20: Sum of Squared Errors (SSE) and Mean Absolute Deviation (MAD) of Quadratic trend model of four level income countries According to table 20, both SSE and MAD measurements of Poland are significantly lowest values, that means having lowest errors in estimation Therefore, for better accuracy, using the formula of quadratic trend model of High-Income Poland is the optimal option to predict the average number of births per woman worldwide Formula of the world’s quadratic trend model: 𝐘 =𝟐.𝟏𝟗𝟗 ― 𝟎.𝟏𝟎𝟓(𝐓) +𝟎.𝟎𝟎𝟑 (𝐓 𝟐) PART 7: OVERALL TEAM CONCLUSION I Main factors that impact the average number of births per woman: Multiple regressions on average births per woman of four different income-based countries were conducted in part and to investigate the correlation between dependent variable, Fertility rate, total (births per woman) and four independent variables including Compulsory education, duration (years); Life expectancy at births (years); Labor force, female (% of total labor force) and Gross national income per capita, Atlas method (current US$) in year 2017 Among these four independent variables, Labor force, female (% of total labor force) and Compulsory education, duration (years) are considered to closely affect the average number of births per woman in general In Low-, Upper-Middle and High-Income countries, labor force, female (% of total labor force) is inversely proportional to the Fertility rate, total (births per woman) This conclusion is directly drawn from three negative coefficients of independent variable, Labor force, female (% of total labor force) observed in their regression equation, which are ―0.24 (LI ); ― 0.04(UMI); ― 0.02(HI) For Upper-Middle and High-Income categories, the reverse trend is observed The total fertility rate positively related to the duration of compulsory education owning to the positive coefficients of independent variable, Compulsory education, duration (years), which are 0.05 (UMI) and 0.1 (HI) These two trends are also supported by the relatively high coefficients of determination, R-squared, calculated in three regression models (81.85% (LI);78.20%(UMI);39.06%(HI) ) as these are indicators of better goodness of fit for the observations (Glen n.d.) Life expectancy at births is also negatively proportional to fertility rate, total in Middle-Income countries, to some extends However, apart from the relationship between aforementioned independent variables and average number of births per woman, the economic factor, GNI per capita, Atlas method (current $US) is believed to directly contributed to the variation of Fertility rate, total among countries From the Time Series’ calculations and findings, the world’s fertility rate, total decreased over the 1990-2015 period Specifically, countries with higher gross national income, GNI per capita are considered to have lower fertility rate, total in overall The world’s fertility rate is estimated to follow the quadratic trend model, Y = 2.199― 0.105 (T) +0.003(T2), with low measurement errors 17 II Predicted number of births per woman in year 2030: As illustrated in part 6, the world’s average number of births per woman is estimated by the quadratic trend model formula, Y =2.199 ― 0.105(T) +0.003 (T2 ) In year 2030, the corresponding time period variable, T equals to 41 Therefore, by plugging into the estimated formula, the world’s average fertility rate, total is predicted to be 2.937, which is approximately births per woman in year 2030 This fertility rate is relatively higher than previous years due to the upward trend However, this predicted fertility rate is only an estimation for reference Although High-Income countries provided the most reliable regression trend model with lowest measure errors (SSE and MAD), over- or underestimation could occur In addition, to present the world’s fertility rate (births per woman), more countries need to be involved in the investigation process, instead of being randomly chosen among countries from four different income groups The four chosen representative countries could not accurately present the whole world’s actual fertility rate Moreover, there are various factors that affect the fertility rate yearly, both economically and socially (Norville, Gomez & Brown 2003) This actually generated measurement errors from the early beginning Besides, the fertility rate, total used for analysis and forecast processes were collected in the 1990-2015 time period These data are considered to be relatively outdated, which should not be used to predict the number of births per woman in year 2030 This might conceal some possible errors which hinder the time series forecast’s accuracy as long-term forecast is believed to generate significant uncertainty due to unforeseeable events (Morikawa 2020) III Recommendations: Throughout the report analysis, the female participation in labor force (%), Compulsory education, duration (years) and national income are considered to be the most influencing factors on total fertility rate (births per woman) Norville, Gomez and Brown (2003) claimed that together with the country’s urbanisation, female’s increasing literacy also contributes to the fertility decline This is also supported by Shenk (n.d., cited in University of Misssouri-Columbia 2013) who emphasized the close correlation between the higher educational attainment and declining fertility rates These female education-related findings counter the above results of regression model between compulsory education, duration, and total fertility rate On the other hand, the increasing participation of female in total labor force was argued to drive the fertility rate decline (Lim n.d.), which strengthens the reliability of this report’s findings Besides, country’s economic prosperity, especially the GNI is proven to reduce fertility with the shift to a market economy due to the rising costs and spendings on children upbringing (University of Missouri-Columbia 2013) This validates the observed trend of total fertility rate between different income-based countries which is illustrated on the above line graph Therefore, these studies might lead to the concern to reinvestigate the impacts of factors on the total fertility rate as the inaccuracy might be driven from the country selection Furthermore, it is believed that the variations in fertility rates are correlated with either economic situations, social patterns, or political factors (Norville, Gomez & Brown 2003; Moran 2020) Risk and mortality; economic and investment; cultural transmission are also indicated to be possible explanations for declines in the total fertility rates (University of Misssouri-Columbia 2013) Besides, as the world’s current fertility rate is falling and expected to fall below 1.7 by 2100 (Gallagher 2020), the predicted value of 2030’s global fertility rate might not as accurate as expected Therefore, the report is recommended to expand the scope of investigated variables for a better prediction and analysis of average number of births per woman As seen throughout the report and supporting studies, the global fertility rate is reducing, which would lead to tremendous social and economic changes (Gallagher 2020) Hence, strategies to prevent infertility and protect human fertility at local, national and international levels are urgent requirements (Nargund 2009) Publicly funded reproductive health and social care; reproductive benefits are recommended be provided to encourage younger population’s contribution (Nargund 2009) Additionally, maternity and paternity leave, free childcare, financial incentives, extra employment rights and others should be enhanced to assist parents with respect to economic concerns for long-term progress (Nargun 2009) 18 REFERENCES: Corporate Finance Institute n.d., Coefficient of Variation, Corporate Finance Institute, viewed 10 January 2021, Federal Reserve Bank of St Louis 2016, The Link between Fertility and Income, Federal Reserve Bank of St Louis, viewed January 2021, Fernando, J 2020, R-Squared Definition, Investopedia, viewed January 2021, Gallagher, J 2020, ‘Fertility rate: ‘Jaw-dropping’ global crash in children being born’, BBC NEWS, 14 July, viewed 11 January 2021, Glen, S n.d., Coefficient of Determination (R Squared): Definition, Calculation, StatisticsHowTo, viewed 11 January 2021, < https://www.statisticshowto.com/probability-and-statistics/coefficient-of-determination-rsquared/> Lim, L n.d., Female Labour-Force Participation, United Nations Development, viewed 11 January 2021, Moran, A 2020, What Factors Affect the Total Fertility Rate, or TFR?, Population Education, viewed 11 January 2021, Morikawa, M 2020, The accuracy of long term growth forecasts by economics researchers, VoxEU & CEFR, viewed 11 January 2020, Nargund, G 2009, ‘Declining birth rate in Developed Countries: A radial policy re-think is required’, Facts, views & Vision, vol 1, no 3, pp 191-193, viewed 12 January 2021, Norville, C, Gomez, R & Brown, R 2003, Some Causes of Fertility Rates Movements, University of Waterloo, viewed 11 January 2020, < https://uwaterloo.ca/waterloo-research-institute-in-insurancesecurities-and-quantitative-finance/sites/ca.waterloo-research-institute-in-insurance-securities-andquantitative-finance/files/uploads/files/03-02.pdf> University of Missouri-Columbia, ‘Economics influence fertility rates more than other factors’, ScienceDaily, 30 April, viewed 11 January 2021, 19 APPENDICES: Appendix 1: The process of getting final model of income level countries by using the backward elimination method in part In part 3, with a view to identifying whether or not there is a relationship between the dependent variable and each independent variable, in particular, the relationship between the total fertility rate (births per woman) and each independent variable in income level countries by applying the hypothesis testing as below: + The null hypothesis: H0 = (there is no relationship between dependent variable Y and the independent variables X1, X2, X3, X4) + The alternative hypothesis: H1 ≠ (there is at least independent variable X that has a relationship with the dependent variable Y) The k value is 1,2,3,4,5 correspondingly It is noticeable that in this section, we will apply p-value test with the α = 0.05 to measure the significant independent variable and the insignificant independent variable + p-value < α = 0.05 => Reject the null Hypothesis (H0) and accept the alternative hypothesis (H1) => this variable is significant + p-value ≥ α= 0.05 => Do not reject the null hypothesis (H0) and reject the alternative hypothesis (H1) => this variable is insignificant  Low-income countries Figure 8: The first regression output of full model of low-income countries Among independent variables in figure 7, It is noticeable that there are nonsignificant independent variables, which are the duration of compulsory education, the total life expectancy at birth, and the GNI per capita using the Atlas method (0.13, 0.14, 0.3 correspondingly) because their p-values are greater than the α= 0.05, whereas there is only one significant independent variable (0.04), which is the female labor force as its p-value is smaller than the α= 0.05 Applying the backward elimination, the total life expectancy at birth would be removed first in the collected dataset due to having the largest p-value of three insignificant variable Figure 9: The second regression output of full model of low-income countries 20 After eliminating the total life expectancy at birth, we have updated a table in figure It can be noticed that there are nonsignificant independent variables, which are GNI per capita using the Atlas method and the duration of compulsory education (0.7 and 0.4 respectively) Because the p-value of GNI per capita using the Atlas method is greater than α = 0.05 and is the largest (0.7), it is deleted from the regression model Figure 10: The third regression output of full model of low-income countries After deleting the GNI per capita using the Atlas method, we have updated a table as above It can be seen that there is only nonsignificant independent variable, which is the duration of compulsory education (0.45) Because the p-value of the duration of compulsory education is greater than α = 0.05 and is the largest, it is removed from the regression model Figure 11: The final regression output of Low-income countries It is observed that there is the only independent variable (the female labor force), which its p-value is smaller than α = 0.05, representing that we reject the null hypothesis (H0) and accept the alternative hypothesis (H1) Therefore, this variable is significant and the process of the backward elimination is finished with only one significant independent variable  Lower-middle income countries Figure 12: The first regression output of full model of low-middle income countries Among independent variables in figure 11, It is remarkable that there are nonsignificant independent variables, which are the duration of compulsory education, the female labor force and the GNI per capita using the Atlas method (0.48, 0.96, 0.65 correspondingly) because their p-values are greater than the α= 0.05, whereas there is only one significant independent variable (0.0001), which is the total life expectancy at birth as its p-value is smaller than the α= 0.05 Applying the backward elimination, female labor force would be removed first in the collected dataset due to having the largest p-value of three insignificant variable 21 Figure 13: The second regression output of full model of low-middle income countries After eliminating the total life expectancy at birth, we have updated a table in figure 12 It can be seen that there are nonsignificant independent variables, which are GNI per capita using the Atlas method and the duration of compulsory education (0.63 and 0.47 respectively) Because the p-value of GNI per capita using the Atlas method is greater than α = 0.05 and is the largest (0.63), it is removed from the regression model Figure 14: The third regression output of full model of low-middle income countries After deleting the GNI per capita using the Atlas method, we have updated a table as above It can be seen that there is only nonsignificant independent variable, which is the duration of compulsory education (0.54) Because the p-value of the duration of compulsory education is greater than α = 0.05 and is the largest, it is deleted from the regression model Figure 15: The final regression output of low-middle income countries It is observed that there is the only independent variable (the total life expectancy at birth), which its p-value is smaller than α = 0.05, meaning that we reject the null hypothesis (H0) and accept the alternative hypothesis (H1) Thus, this variable is significant and the process of the backward elimination is finished with only one significant independent variable  Upper-middle income countries 22 Figure 16: The regression output of full model of upper-middle income countries Among independent variables in figure 15, It is observed that there is only one independent variables (the GNI per capita using the Atlas method), which p-value (0.69) is greater than the α= 0.05 This means that we not reject the null hypothesis (H0) and this variable is nonsignificant Applying the backward elimination, the GNI per capita using the Atlas method is eliminated in the collected dataset Figure 17: The final regression output of upper-middle income countries After removing the GNI per capita using the Atlas method, we have updated a table as above It can be seen that there are independent variables (the duration of compulsory education, the total life expectancy at births and the female labor force), which their p-value is smaller than the α = 0.05, representing that we reject the null hypothesis (H0) and accept the alternative hypothesis (H1) Thus, these variables are significant and the process of the backward elimination is finished with significant independent variables  High-income countries Figure 18: The first regression output of full model of high-income countries Among independent variables in figure 17, It is clear that there are independent variables (the GNI per capita using the Atlas method and the total life expectancy at birth), which p-value (0.5 and 0.16) is greater than the α= 0.05 This means that we not reject the null hypothesis (H0) and these variables are 23 nonsignificant Applying the backward elimination, the GNI per capita using the Atlas method is eliminated from the regression model due to having the greatest p-value Figure 19: The second regression output of full model of high-income countries After deleting the GNI per capita using the Atlas method, we have updated a table as above It can be seen that there is only nonsignificant independent variable, which is the total life expectancy at birth Because its p-value (0.19) is greater than α = 0.05 and is the largest, it is deleted from the regression model Figure 20: The final regression output of high-income countries It can be noticeable that there are independent variables (female labor force and the duration of compulsory education), which their p-value (0.0012 and 0.0014 respectively) is smaller than α = 0.05, meaning that we reject the null hypothesis (H0) and accept the alternative hypothesis (H1) Thus, these variables are significant, and the process of the backward elimination is finished with significant independent variables 24 ... 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 Coefficient of 60. 71% 43. 51% 33.379%... Intercept -0 .12 2 0.009926 311 -12 .28524084 X Variable 0.002 0.00035684 5.46360782 X Variable Table 11 : Quadratic trend regression output of Malaysia (19 90 – 2 015 ) F P-value 9 .17 879E-28 1. 38099E -11 1. 48803E-05... average number of births per woman LI-Ethiopia LMI-Lao UMIHI-Poland PDR Malaysia 15 2 018 29 3.834 2.8 81 1.997 1. 677 2 019 30 3.6 51 2.873 1. 993 1. 749 2020 31 3.464 2.873 1. 993 1. 827 Table 19 : Corresponding