PHAM MAI PHUONG – S3753738

Contents
Assignment
Case Study –2Inferential
– Individual
PART 1: Introduction 2

Statistics
PART 2: Descriptive Statistics
PART 3: Confidence Intervals
3
6
PART 4: Hypothesis Testing 10
PART 5: Regression analysis 11
PART 6: Conclusion 23
PART 7: Reference list 23

ECON1193 – Business Statistics

Lecturer: Pham Thi Minh Thuy
PART 1: Introduction

According to the United Nations (2015), the fertility model in the world has seen dramatic
changes in recent years. The worldwide fertility has reached an unparalleled low degree,
however, there is still a distinct in childbirth rate between different countries. As reported by
2015 revision of World Population Prospects, the overall pregnancy ratio is now 2.5 children per
woman in global. In the present day, 46% of the world’s population in different regions with low
levels of pregnancy ratio where women have less than 2.1 children on average, which consists of
Asia, Europe, and Northern America and, Latin America and the Caribbean. In addition, the
other 46% and 8% live in an intermediate stage of fertility and a high stage of fertility have
witnessed a considerable decrease (United Nations, 2015).

In the past decade, girls and women continue to go through discrimination and violence in every
nation and region (UNICEF 2017). These gender discriminations have prevented girls and
women’s decision in every aspect of their life with a poor gender uniform. Therefore, it is vital to
develop gender equality of UNICEF’s main mission to support as a protector and fulfillment of
children rights. (UNICEF 2017, p.4). Gender equality is one of the principles of human rights
and also an essential foundation of a sustainable and thriving world (UNICEF 2017, p.4). The
global child marriage has recognized a huge decrease as a girl’s possibility of early marriage
before age 18 has plunged by roughly 45% in 2010 to 30% in 2015 (UNICEF 2017, p.8). Also,
the high popularity of child marriage is linked with high fertility ratios between adolescents.
Besides, high birth rate with lack of nutrition in adolescent girls and women raises the risk of
maternal and childbearing fatality (UNICEF 2017, p.8).

Regarding Guillaume Vandenbroucke (2016), the decreasing relationship between adolescent

birth rate and gross national income (GNI) illustrates the relation between fertility choices and
economic consideration. Low-Income countries will have higher ratios of fertility than High-
Income countries. Particularly, countries with GDP per capita is less than $1000 a year, women
often give birth no more than three children, hower, countries with high GDP more than $10.000
year then women will have less than two children (Guillaume Vandenbroucke 2016). In addition,
the relationship carries at the individual degree which wealthy families tend to have a smaller
amount of children compared to the poor families (Guillaume Vanderbroucke 2016).
PART 2: Descriptive Statistics

a) A table with the measures of Central Tendency

Central Tendency Mean Median Mode

Low-Income Countries (LI) 105.4304 98.8795 #N/A

Middle-Income Countries (MI) 47.46749474 48.201 #N/A

High-Income Countries (HI) 8.649345455 7.827 #N/A

Table 1: Central Tendency table of three country categories Adolescent fertility rate

Regarding table 1, it can be seen that the Mean illustrates the average adolescent birth ratio of
Low-Income Countries (105.4304) is larger than the average adolescent birth ratio of both
Middle-Income Countries (47.467) and High-Income Countries (8.649). The Median represents
the middle level of adolescent birth rate in the list of Low-Income Countries (98.879) is greater
than the Median of Middle-Income Countries (48.201) and High-Income Countries (7.827) list.

In addition, the Mean of adolescent fertility ratio of Low-Income Countries (105.4304) is

greater than the Median (98.8795) which indicates the data set is right-skewed (Positive
skewed). Similarly, the Mean of adolescent fertility ratio of High-Income Countries (8.649) is
also larger than the Median (7.827), therefore, the data is right-skewed.

Besides, there is no mode in three countries data because the adolescent pregnancy ratio of those
countries has varying so that there is no repeated value in the sample. Since the data set has no
outlier, Mean is the best measure of Central Tendency table of three countries categories and
precisely representative of the data set.

To conclude, women from 15 – 19 years old in Low-income Countries are observed to giving
births more comparing to Middle and High-income countries. This means that women living in
wealthier countries are less likely to giving birth in the ages between 15 and 19.
b) A table with measures of Variation

Variation Low-Income Middle-Income High-Income

Countries (LI) Countries (MI) Countries (HI)
Range 104.0492 103.5902 10.4214

Interquartile Range 37.95555 37.9598 4.396

Variance 1071.667388 672.3671598 10.95636637

Standard Deviation 32.73633132 25.93004357 3.310040237

Coefficient of 31% 55% 38%

Variation
Table 2: Variation table of three countries categories Adolescent fertility rate

According to table 2, we can see that most of the values of Low-Income Countries are larger
than the values of both Middle-Income Countries and High-Income Countries. In particular, the
interquartile range and the standard deviation of Low-Income Countries are 37.955 and 32.736
respectively, comparing to 37.9598 (MI), 4.396 (HI) and 25.930 (MI), 3.310 (HI) of both
Middle-Income and High-Income Countries. This shows that Low and Middle-Income Countries
has a higher variability of the adolescent fertility ratio than High-income countries. Moreover,
since three groups of countries have no outlier, the best measurement is using the standard
deviation to demonstrates variation about the mean.

Furthermore, the coefficient of variation of Middle-Income Countries (55%) is larger than that
of both two countries LI and HI 31% and 38%, which mean the adolescent birth ratio of Middle-
Income Countries (MI) has a greater level of dispersion around the average adolescent birth
ratio compared to Low and High-Income Countries.

In short, Middle-income Countries has a higher variation in the spread of adolescent birth rate
than both Low and High-Income countries. This mean Low and High-Income countries have a
more precise estimation of adolescent pregnancy rate than Middle-income Countries.
c) A chart with the Box and Whisker plots of three countries categories

Table 3: Box and Whisker plots of three countries categories

From table 3, it can be seen that Middle-Income Countries has the greatest variation of
adolescent birth rate. Additionally, the variation within the middle of Low and Middle-Income
Countries has more variations and much wider than the box and whisker of High-Income
Countries. This means the variation of adolescent fertility rate of High-Income Countries is
more density than the other two. And also, the adolescent birth rate of Low and Middle-Income
Countries seem to be less consistent comparing to High-Income Countries.

To illustrate, the lower and upper whisker of High-Income Countries are quite equal 2.0374 and
3.988 respectively. Moreover, the left box (1.6146) is slightly smaller than the right box (2.7814)
Therefore, the left half (3.652) is smaller than the right half (6.7694). As a consequence, the data
set of High-income countries is right-skewed. In addition, as we look at table 3, the distribution
of the adolescent birth rate of Low-income Countries has the same shape as High-income
Countries, which is also positive skewed (right-skewed).

On the other hand, the lower whisker of Middle-Income Countries (18.369) is largely smaller
than the upper whisker (47.2614). However, the left box (22.2042) is bigger than the right box
(15.7556). Also, the left half (40.5732) is smaller than the right half (63.017). As a result, the
shape of the data of Middle-Income Countries is right-skewed (Positive skewed).

In summary, the shape of adolescent fertility rate from all these three groups of countries is right
skewed (positive skewed). This means more than half of adolescent birth rate is lower than the
average adolescent pregnancy rate. There is more low adolescent birth rate than the high
adolescent birth rate.

PART 3: Confidence Intervals

a. The confidence interval is used in the inferential method, which is the process of making a
decision or prediction about population. In this case, the confident interval is used to analyze and
interpret the Adolescent fertility rate (AFR), Gross National Income (GNI) and Domestic general
government health expenditure per capita to make the world average estimation (DGG).

-  The level of significance for each confidence interval is chosen to be equal to 5% (α = 0.05),
thus the confident level is 95% (1 - α = 0.95).

-  The sample size of three data sets (AFR, GNI and DGG) is equal to 38 (n = 38)
-  The population standard deviation is unknown, we use the sample standard deviation (S).

+ The T-distribution table is used in calculation.

+ The degree of freedom is equal to the sample size minus 1 (d.f = n - 1 = 38 – 1 = 37)
+ Upper tail = α/2 = 0.05 /2 = 0.025

Therefore, by looking up the T table, we can detect the T-value is 0.0262.

·         Adolescent fertility rate (AFR) (births per 1,000 women ages 15 – 19)

Adolescent fertility rate  

   
Mean 48.43337895
Standard Error 6.700847899
Median 42.2712
Mode #N/A
Standard Deviation 41.30680062
 Sample Variance 1706.251778
Kurtosis 0.662039879
Skewness 0.976878468
Range 168.8632
Minimum 4.175
Maximum 173.0382
Sum 1840.4684
Count 38
Confidence Level(95.0%) 13.57720751
Lower Bound 34.85617144
Upper Bound 62.01058646

Interpretation:

We are 95% confident the world average of Adolescent fertility rate is between 34.8561 and
62.0106 births per 1000 women between ages 15 – 19.  This means it is 95% confident that in
1000 girls ages from 15 to 19, there are between 34.8561 and 62.0106 adolescents become
pregnant.

·         Gross National Income (NGI) per capita (current US$)

GNI per capita, Atlas

method  
   
Mean 14577.8947
Standard Error 3100.31447
Median 4025
Mode 790
Standard Deviation 19111.6219
Sample Variance 365254093
Kurtosis -0.2858759
Skewness 1.18847835
Range 57330
Minimum 550
Maximum 57880
Sum 553960
Count 38
 Confidence
Level(95.0%) 6281.83381
Lower Bound 8296.06093
Upper Bound 20859.7285

Interpretation:
We are 95% confident the world average of Gross National Income per capita is between
$8296.0609 and $20859.7285. This means it is 95% confident that the average of Gross National
Income per capita of the world is ranging from $8296.0609 to $20859.7285.

·         Domestic general government health expenditure per capita

Domestic general
government health
expenditure per capita  
   
Mean 1134.81034
Standard Error 252.780699
Median 302.854717
Mode #N/A
Standard Deviation 1558.24488
Sample Variance 2428127.1
Kurtosis -0.2070301
Skewness 1.20835691
Range 4508.68668
Minimum 16.2203903
Maximum 4524.90707
Sum 43122.7927
Count 38
Confidence Level(95.0%) 512.182346
Lower Bound 622.627989
Upper Bound 1646.99268

Interpretation:
·         We are 95% confident the world average of Domestic general government health
expenditure per capita is between $622.6280 and $1646.9927. This means we are 95 percent sure
that the average money that government spends on health per unit of the population is between
$622.6260 and $1614.9945.

b. It is not required to have an assumption to calculate these confident intervals because the
sample size is equal to 38 (n = 38), which is large enough (n > 30). Therefore, we can conclude
that the population in these estimations is normally distributed.

c. We suppose that the world (or population) standard deviation is known. Thus, we assume
that the sample standard deviation is equal to the population standard deviation. Therefore:
-  the Z-distribution table is used.
- Upper tail = α/2 = 0.05 /2 = 0.025
Therefore, by looking up the Z table, we can detect the Z-value is 1.96

Calculation is in the table below:

Adolescent Gross National Domestic general
pregnancy rate Income (NGI) government health
expenditure per capita

Lower Bound 35.2998 8501.2786 639.3061

Upper Bound 61.5671 20654.5114 1630.2604

As looking at these numbers, as the population standard deviation is known, there are small
changes in the confident interval for the world average of three data sets. The upper limit of the
world average of three data sets is bigger and the lower limit of the world average of three data
sets is smaller when the population standard deviation is known.

As the sample standard deviation depends on the sample size; it has greater variability.
Therefore, the sample standard deviation is greater than the population standard deviation.
Secondly, a high standard deviation means that the number is spread out. Thus, when the
population standard deviation is known, the limit of the average value of these three data has a
smaller range.

The smaller standard deviation means that most of the number is very close to average (mean).
As the population standard deviation is calculated based on the population size and it has smaller
variability, the confidence interval results are more likely to be accurate than using the sample
standard deviation.
PART 4: Hypothesis Testing
a. Prediction

Figure 1: United Nations, Adolescent birth rate, World fertility patterns, 2015

Based on part 3a, the world average birth rate within the range of 34.8561 and 62.0106
adolescents will give birth, therefore it will narrow the upper and lower limits. I predict that the
world adolescent fertility ratio will decline in the future. Based on the graph of adolescent birth
rate by region, 1990-1995 and 2010-2015, we can see that 6 regions in global have a downward
over the year. Specifically, in Asia, Northern America and Europe, the larger size decline of
teenage pregnancy have lead to a reduction in the adolescent birth rate. Even though Africa and
Latin America and the Caribbean have the highest point adolescent birth rate but still, decline
over time. For this reason, the adolescent fertility ratio is forecasted to decrease in the near future
based on the data above and part 3a.

b. Hypothesis Testing

- Significant level chosen (the rejection region): 5% (α = 0.05)

As the sample size is equal to 38 (n = 38), which is large enough (n > 30). Therefore, we can
conclude that the population in these estimations is normally distributed.

Null Hypothesis: H 0 : μ≥ 44 (world average Adolescent fertility rate is equal or more than
44 per 1000 women ages 15 – 19) in the future.
 Alternative Hypothesis: H A : μ< 44 (world average Adolescent fertility rate is lower than 44
per 1000 women ages 15 – 19) in the future.
Since the Alternative Hypothesis H A : μ ≥ 44 , the rejection region is located below the mean,
so this is one tail test (lower tail test).

- Compute test value

x̄−µ 48.4334−44
+ test value = t= = = 0.6616
s / √❑ 41.3068/ √ ❑

The population standard deviation is unknown, so we use T table.

+ d.f = n - 1 = 38 – 1 = 37
+ α = 0.05
As using the T table, t cv=−1.6871

Test value = 0.6616 >Critical value = -1.6871. This means the Test value is not in the
rejection region. Therefore, we do not reject Null Hypothesis H 0 .

Interpretation:
As the null hypothesis H 0 is not rejected, it can be concluded that the world average
Adolescent fertility rate is equal or more than 44 births per 1000 women aged 15 – 19 in the
future. This means in the future; the Adolescent fertility rate is not decreased.

Null hypothesis H 0 is not rejected when H 0 is not true. This means the statement: “world
average adolescent fertility rate is equal or more than 44 per 1000 women ages 15 – 19)” is
false and we fail to reject it, when the actual situation is world average Adolescent fertility
rate is decreased in the future. Therefore, we have committed type II error (β).

To minimize this type II error, we can increase the sample size (n), which means increase
more observed number in the sample in order to increase the variation. Moreover, we can
increase the level of significant (α) or decrease the confident level (1- α) to reduce type II
error.

PART 5: Regression analysis

a) Dependent variable (DV)

● Adolescent fertility rate (births per 1.000 women ages 15-19)
 Independent variable (IV)
● GNI per capita, Atlas method (current US$)
● Compulsory education, duration (years)
● Domestic general government health expenditure per capita, PPP (current
international $)
● Life expectancy at birth, total (years)

a) Simple Linear Regression

1. Gross National Income (GNI) per capita, Atlas method (current US$)

● We can see that the relationship between the adolescent fertility rate (DV) and
GNI per capita (IV) is negative which means the countries with higher GNI
will have a lower adolescent fertility ratio in women ages 15 to 19.
● Scatter plot of the DV and IV: There is a strong linear relationship between
the adolescent pregnancy ratio and the gross national income (GNI) since
most of the data are concentrated near the regression line.

Adolescent fertility rate & GNI per capita, Atlas method

Adolescent fertility rate (births per 1.000 women ages 15-

70000

60000

50000

40000
19)

30000
f(x) = − 292.941559499446 x + 28766.0442975119
20000 R² = 0.400875952024014

10000

0
0 20 40 60 80 100 120 140 160 180 200
GNI per capita, Atlas method (current US$)

Table 4: Adolescent fertility rate & GNI per capita, Atlas method

Comment: There is strong negative linear relationship between adolescent teenage birth rate and
GNI per capita, Atlas method (current US$).
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.63314765
R Square 0.40087595
Adjusted R
Square 0.38423362
Standard
Error 32.41377
Observations 38
ANOVA
Significanc
  df SS MS F eF
Regression 1 25307.826 25307.826 24.08772327 1.99E-05
Residual 36 37823.489 1050.6525
Total 37 63131.315      

Standard
  Coefficients Error t Stat P-value
Intercept 68.3825027 6.64607717 10.2891527 0.00000000000288
GNI per capita, Atlas method (current US$) -0.0013685 0.00027882 -4.9079245 0.0000199

Upper Lower Upper

Lower 95% 95% 95.0% 95.0%
54.903633 54.903633
5 81.861372 5 81.861372
-0.0019339 -0.000803 -0.0019339 -0.000803

● Simple linear regression:

● The adolescent pregnancy rate evaluates the regression line equation is
Y^ i=b0 +b1 X i where Y illustrates the birth rate of teenage girls from age 15 to 19
and X illustrates the gross national income (GNI) per capita (current US$).

● Based on the excel output above, the Simple Linear Regression equation is: Y =
68.382 – 0.0013 Xi, where Y illustrates the fertility rate and X represents the GNI
(current US$).
Explanation:
+ If Gross national income (X) equal to zero (0), adolescent fertility rate (Y) is estimated to
be equal to 68.382.
+ If Gross national income (X) increase by 1, adolescent fertility rate (Y) is estimated to be
decreased.

● b1 = -0.0013 is the regression slope coefficient which demonstrates that for every dollar
increase in the GNI per capita, the birth rate per 1000 adolescent women aged 15 to 19
will decrease by 0.0013.

● R2 = 0.4008 is the coefficient of determination. This indicates that 40.08% of the variance
in the adolescent birth ratio can be explained by the variation of GNI per capita.

● Test the significant of the independent variable with α = 0.05

▪ Null hypothesis H0 : b1 = 0 (there is no relationship between teenage birth rate and

GNI per capita).

▪ Alternative hypothesis H1: b1 ≠ 0 (there is a relationship between teenage birth

rate and GNI per capita.

▪ It’s a two tailed test.

▪ P-value approach: From the excel data, P-value is 0.0000199.
Since P-value is very small that there is 4 first decimal places are 0, P-value is less than
significant level (0.0000199 < 0.05), as a result, H0 is rejected.

▪ Critical value approach:

Since population standard variation is unknown, we use t-table
d.f = n-2 = 38 - 2= 36
Upper tail = α/2 = 0.05 / 2 = 0.025
Using the t-table, tCV = ± 2.0281

b1−β 1 −0.0013−0
T-test: t = t= = = -4.90
S b1 0.0003

Since the t = -4.90 < -2.0281, the t statistic fall into the rejection region, therefore H0 is
rejected.

▪ For this reason, there is a sufficient evidence that the fertility rate per 1000
adolescent women aged from 15 to 19 has a significant relationship with the GNI
per capita. Gross National Income is a good estimation of adolescent fertility rate.
 2. Compulsory education, duration (years)

▪ It can be seen that the relationship between the adolescent fertility rate (DV) and
Compulsory of education, duration (IV) is negative which means the countries
with lower years of obligatory education will experience a higher adolescent
fertility ratio in women ages 15 to 19.

▪ Scatter plot of the DV and IV: There is a weak linear relationship between the
adolescent pregnancy ratio and the gross national income (GNI) since most of the
data are spread out and far from the regression line.

Adolescent fertility rate & Compulsory education, du-

ration
Adolescent fertility rate (births per 1.000 women ages 15-19)

16

14

12

10
f(x) = − 0.00972626880738475 x + 10.2868655365762
R² = 0.033606572697153
8

0
0 20 40 60 80 100 120 140 160 180 200
Compulsory education, duration (years)

Table 5: Adolescent fertility rate & Compulsory education, duration

Comment: There is a weak negative linear relationship between adolescent birth rate of 1.000
girls age from 15 to 19 and Compulsory education, duration (years).

SUMMARY OUTPUT

Regression Statistics
0.18332095
Multiple R 5
 0.03360657
R Square 3
Adjusted R 0.00676231
Square 1
41.1668989
Standard Error 9
Observations 38

ANOVA
Significanc
  df SS MS F eF
Regression 1 2121.62715 2121.62715 1.251908987 0.27059862
Residual 36 61009.6886 1694.71357
Total 37 63131.3158      

Standard
  Coefficients Error t Stat P-value

Intercept 82.34926684 31.03907963 2.6530834 0.01179319

Compulsory education,
duration (years) -3.455237909 3.088101578 -1.1188874 0.270598615

Lower Upper
Lower 95% Upper 95% 95.0% 95.0%
19.3990957 145.299438 19.3990957 145.299438
-9.7181982 2.80772238 -9.7181982 2.80772238

● Simple linear regression:

● The adolescent pregnancy rate evaluates the regression line equation is
Y^ i=b0 +b1 X i where Y illustrates the birth rate of teenage girls from age 15 to 19
and X illustrates the compulsory of education, duration (years).

● Based on the excel output below, the Simple Linear Regression equation is: Yi =
82.3492 – 3.4552 Xi, where Y illustrates the fertility rate and X represents the
compulsory of education, duration (years).
Explanation:
+ If having compulsory of education in years (X) equal to zero (0), adolescent fertility rate
(Y) is estimated to be equal to 82.3492.
+ If having compulsory of education in years (X) increase by 1, adolescent fertility rate (Y)
is estimated to be decreased.

● b1 = -3.4552 is the regression slope coefficient which demonstrates that for every one
more year in the complusory education, the birth rate per 1000 adolescent women aged
15 to 19 will decrease by 3.4552.

● R2 = 0.0336 is the coefficient of determination. This indicates that 3.36% of the variance
in the adolescent birth ratio can be explained by the variation of the compulsory in
education (years).

● Test the significant of the independent variable with α = 0.05

▪ Null hypothesis H0 : b1 = 0 (there is no relationship between teenage birth rate and

compulsory years of education, duration).

▪ Alternative hypothesis H1: b1 ≠ 0 (there is a relationship between teenage birth

rate and compulsory years of education, duration).
▪ It’s a two tailed test.

▪ P-value approach: From the excel data, P-value is 0.2705

Since P-value is larger than the significant level (0.2705 > 0.05), as a result, H0 is not
rejected.

▪ Critical value approach:

Since population standard variation is unknown, we use t-table
d.f = n-2 = 38 - 2= 36
Upper tail = α/2 = 0.05 / 2 = 0.025
Using the t-table, tCV = ± 2.0281
b1−β 1 −3.445−0
T-test: t = = = -1.12
S b1 3.088

Since the t = -1.12 > -2.0281, the t statistic did not fall into the rejection region, therefore
H0 is not rejected.

▪ For this reason, the fertility rate per 1000 adolescent women aged from 15 to 19
does not have a significant relationship with compulsory of education.
Compulsory of education is not a good estimation of adolescent fertility rate.
 3. Domestic general government (DGG) health expenditure per capita, PPP (current
international $)

▪ It can be seen that the relationship between the adolescent fertility rate (DV) and
DGG health expenditure per capita, PPP (IV) is negative which means the
countries with lower international $ of DGG health expenditure will experience a
higher adolescent fertility ratio in women ages 15 to 19.

▪ Scatter plot of the DV and IV: There is a strong linear relationship between the
adolescent pregnancy ratio and the DGG health expenditure per capita since most
of the data are focus near the regression line.

Adolescent fertility rate & Domestic general gov-

ernment health expenditure per capita, PPP
Adolescent fertility rate (births per 1.000 women ages 15-

5000
4500
4000
3500
3000
2500
19)

2000 f(x) = − 24.240489169118 x + 2308.8591331851

R² = 0.412909105386867
1500
1000
500
0
0 20 40 60 80 100 120 140 160 180 200

Domestic general government health expenditure per capita, PPP (current international $)

Table 6: Adolescent fertility rate & Domestic general government health expenditure per capita,PPP

Comment: There is a strong negative linear relationship between Adolescent birth rate per 1000
women aged 15-19 and DGG health expenditure per capita (international $).

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.64258004
R Square 0.41290911
Adjusted R 0.39660102
Square
Standard Error 32.0866105
Observations 38

ANOVA
Significanc
  df SS MS F eF
26067.495
Regression 1 1 26067.4951 25.31929541 1.3631E-05
37063.820
Residual 36 7 1029.55057
63131.315
Total 37 8      

Standard
  Coefficients Error t Stat P-value
Intercept 67.76358 6.4692518 10.4747167 0.00000000000177
Domestic general government
health expenditure per capita,
PPP (current international $) -0.017034 0.003385 -5.0318282 0.0000136

Lower Upper
Lower 95% Upper 95% 95.0% 95.0%
54.6433289 80.8838304 54.6433289 80.8838304
-0.0238994 -0.0101683 -0.0238994 -0.0101683

● Simple linear regression:

● The adolescent pregnancy rate evaluates the regression line equation is
Y^ i=b0 +b1 X i where Y illustrates the birth rate of teenage girls from age 15 to 19
and X illustrates the health expenditure of DGG per capita, PPP (international $).

● Based on the excel output below, the Simple Linear Regression equation is: Yi =
67.7635 – 0.0170 Xi, where Y illustrates the fertility rate and X represents the health
expenditure of DGG per capita, PPP (international $).
 Explanation:
+ If DGG expenditure on health per capita (X) equal to zero (0), adolescent fertility rate is
estimated to be equal to 67.7635.
+ If DGG expenditure on health per capita (X) increase by 1, adolescent fertility rate is
estimated to be decreased.

● b1 = -0.017034 is the regression slope coefficient which demonstrates that for every DGG
expenditure on health per capita, the birth rate per 1000 adolescent women aged 15 to 19
will decrease by 0.017034.

● R2 = 0.4129 is the coefficient of determination. This indicates that 41.39% of the variance
in the adolescent birth ratio can be explained by the variation of the DGG expenditure
health per capita, PPP.

● Test the significant of the independent variable with α = 0.05

▪ Null hypothesis H0 : b1 = 0 (there is no relationship between teenage birth rate and

expenditure on health of DGG per capita, PPP).

▪ Alternative hypothesis H1: b1 ≠ 0 (there is a relationship between teenage birth

rate and domestic general government on health expenditure per capita, PPP).

▪ It’s a two tailed test.

▪ P-value approach: From the excel data, P-value is 0.0000136

▪ Since P-value is very small that there is 4 first decimal places are 0, P-value is
less than significant level (0.0000136 < 0.05), as a result, H0 is rejected.

▪ Critical value approach:

Since population standard variation is unknown, we use t-table
d.f = n-2 = 38 - 2= 36
Upper tail = α/2 = 0.05 / 2 = 0.025
Using the t-table, tCV = ± 2.0281
b1−β 1 −0.01703−0
T-test: t= = = -5.032
S b1 0.003385

Since the t = -5.032 < -2.0281, the t statistic fall into the rejection region, therefore H0 is
rejected.
 ▪ For this reason, there is a enough evidence that the fertility rate per 1000
adolescent women aged from 15 to 19 has a significant relationship with the DGG
health expenditure per capita, PPP. DGG health expenditure per capita is a good
estimation of adolescent fertility rate.

4. Life expectancy at birth, total (years)

▪ It can be seen that the relationship between the adolescent fertility rate (DV) and
life expectancy at birth, total (years) (IV) is negative which means the countries
with lower years of life expectancy at birth in total will experience a higher
adolescent fertility ratio in women ages 15 to 19.

▪ Scatter plot of the DV and IV: There is a strong linear relationship between the
adolescent pregnancy ratio and the life expectancy at birth in total (years) since
most of the data are concentrated near the regression line.

Adolescent fertility rate & Life expectancy at birth, total

90
Adolescent fertility rate (births per 1.000

80
f(x) = − 0.185872081344663 x + 80.9569187280811
70 R² = 0.719375136670925
women ages 15-19)

60
50
40
30
20
10
0
0 20 40 60 80 100 120 140 160 180 200
Life expectancy at birth, total (years)

Table 7: Adolescent fertility rate & Life expectancy at birth, total (years)

Comment: There is a strong negative linear relationship between adolescent birth ratio per 1000
women ages 15 to 19 and the life expectancy at birth, total (years).

SUMMARY OUTPUT
 Regression Statistics
0.84815985
Multiple R 3
0.71937513
R Square 7
Adjusted R 0.71158000
Square 2
22.1837132
Standard Error 8
Observations 38

ANOVA
Significance
  df SS MS F F
Regression 1 45415.09891 45415.0989 92.28514043 1.79561E-11
Residual 36 17716.21686 492.117135
Total 37 63131.31577      

  Coefficients Standard Error t Stat P-value

Intercept 326.9167426 29.21152318 11.1913624 2.82502E-13
Life expectancy at birth, total
(years) -3.870269981 0.402879689 -9.6065155 1.79561E-11

Lower Upper
Lower 95% Upper 95% 95.0% 95.0%
267.673027
7 386.160458 267.673028 386.160458
-4.68734786 -3.0531921 -4.6873479 -3.0531921

● Simple linear regression:

● The adolescent pregnancy rate evaluates the regression line equation is
Y^ i=b0 +b1 X i where Y illustrates the birth rate of teenage girls from age 15 to 19
and X illustrates the life expectancy at birth, total (years).

● Based on the excel output below, the Simple Linear Regression equation is: Yi =
326.9167 – 3.8702 Xi , where Y illustrates the fertility rate and X represents the life
expectancy at birth, total (years).
 Explanation:
+ If the life expectancy at birth (X) equal to zero (0), adolescent fertility rate (Y) is
estimated to be equal to 67.7635.
+ If the life expectancy at birth (X) increase by 1, adolescent fertility rate (Y) is estimated to
be decreased.

● b1 = -3.8702 is the regression slope coefficient which demonstrates that for every year on
life expectancy at birth, the birth rate per 1000 adolescent women aged 15 to 19 will
decrease by 3.8702.

● R2 = 0.7193 is the coefficient of determination. This indicates that 71.93% of the variance
in the adolescent birth ratio can be explained by the variation of the life expectancy at
birth, total (years).

▪ Null hypothesis H0 : b1 = 0 (there is no relationship between teenage birth rate and

life expectancy at birth, total (years).

▪ Alternative hypothesis H1: b1 ≠ 0 (there is a relationship between teenage birth

rate and life expectancy at birth, total (years).

▪ It’s a two-tailed test.

▪ P-value approach: From the excel data, P-value is 0.000000000001795.

▪ Since P-value is very small that there is 13 first decimal places are 0, P-value is
less than significant level (0.000000000001795 < 0.05), as a result, H0 is rejected.

▪ Critical value approach:

Since population standard variation is unknown, we use t-table
d.f = n-2 = 38 - 2= 36
Upper tail = α/2 = 0.05 / 2 = 0.025
Using the t-table, tCV = ± 2.0281
b1−β 1 −3.870−0
T-test: t= = = -9.606
S b1 0.428

Since the t = -9.606 < -2.0281, the t statistic fall into the rejection region, therefore H0 is
rejected.

▪ For this reason, there is enough evidence that the fertility rate per 1000 adolescent
women aged from 15 to 19 has a significant relationship with the life expectancy
 birth rate, total (years). The life expectancy birth rate is a good estimation of the
adolescent fertility rate.

c) As we discuss on the question above, Gross National Income (GNI), DGG health expenditure
per capita and the life expectancy birth rate have a significant relationship with adolescent
fertility rate from women between 15 and 19. Therefore, we should focus on these three factors
in order to have deeper research on the fertility rate per 1000 adolescent women aged from 15 to
19.

PART 6: Conclusion

In summary, the adolescent fertility rate depends on different statistics factors and research. In
specific, in part 2, we can conclude that the birth rate per 1000 women ages from 15 to 19 is
decreasing based on women living in wealthier countries are less giving birth than low-income
countries. In addition, there is more low adolescent birth rate than high adolescent fertility ratio
as we can see in the box and whisker plot. In part 4, based on the prediction, the fertility ratio
will decrease in the near future, also, according to the null hypothesis, Ho μ ≥ 44 (world average
adolescent fertility rate is equal or more than 44 per 1000 women ages 15-19) is not rejected
when Ho is not true. Therefore, the present situation is the world average adolescent fertility
ratio is a decrease in the future. In part 5, all factors such as GNI per capita, Atlas method,
Domestic general government (DGG) health expenditure per capita and life expectancy at birth,
total years affect strongly to the adolescent birth rate. Between four factors, the variation in the
adolescent birth rate explained the life expectancy at birth has the highest variance percentage of
71.93%.

Consequently, there are many elements that affect to the world adolescent fertility rate that we
need to examine. Hence, people should contemplate and have a deeper understanding and
research more aspect of the information and study to find potential findings in this field.

PART 7: Reference list

Guillaume Vandenbroucke 2016, ‘The link between Fertility and Income’, Federal Reserve
Bank of ST.Louis, 13 December, viewed 15 April 2019, < https://www.stlouisfed.org/on-the-
economy/2016/december/link-fertility-income>.
United Nations 2016, Adolescent birth rate, digital image, United Nations, viewed 15 April
2019, < https://www.un.org/en/development/desa/population/publications/pdf/fertility/world-
fertility-patterns-2015.pdf>.

United Nations 2016, World Fertility Patterns 2015, company report, viewed 15 April 2019,
<https://www.un.org/en/development/desa/population/publications/pdf/fertility/world-fertility-
patterns-2015.pdf>.

UNICEF 2017, Gender Equality and Rights, company report, viewed 15 April 2019,
<https://www.unicef.org/rosa/media/1776/file>.