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# Use time series to predict the old age dependency ratio trend (total 1000words)

Anonymous

*label*Statistics

*timer*Asked: Dec 28th, 2018

**Question description**

**Use data set 1 in attached file**

**Do Part 3 + 4**

**Times New Romans/ Double Space/ size 12**

**Limit: 800 words for part 3 and 200 words for part 4**

__Individual (by each team member)__

- Use data set 1 of the countries A and B for the years
*1980 - 2011* - Apply the following time trend models
__for each country__(Country A / Country B)- Linear trend model (LIN)
- Quadratic trend model (QUA)
- Exponential trend model (EXP)

- Based on the results found in 2):
- Which trend model will you recommend to predict the old age dependency ratio for Country A?
- Which trend model will you recommend to predict the old age dependency ratio for Country B?

__For each trend model __(LIN / QUA / EXP)

- Provide the regression output in the report
- Provide the formula of the trend model
- Predict the old age dependency ratio for the years
**2012**,**2013**,**2014**and**2015**

- Calculated the errors for the years
**2012**,**2013**,**2014**and**2015**

- Calculated the MAD and SSE

Explain your answers.

__ __

__ __

__Part 4: Team Time Series conclusion:__

In part 3, your team has looked at several trend models to predict the old age dependency ratio over time. In this part your team will write a conclusion based on your findings in part 3.

Task: **Write a conclusion to predict the old age dependency ratio over time **

- Provide a line chart of old age dependency ratio over time from 1980 - 2015, including the countries of
the team members.*all* - Comment on the line chart. Are all the countries following the same trend?
- Compare the trend models of the countries analyzed by each team member in part 3.
- Which countries are following the same trend model?
- Which trend model does your team consider to be the best old age dependency ratio predictor? Explain your answer.

Write your conclusion in an unbiased manner to a non-technical audience.

Indicator:
Year
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Adolescent fertility rate (births per 1,000 women ages 15-19)
Benin
Spain
107.425
23
109.74
22.124
112.055
21.248
114.264 20.0218
116.473 18.7956
118.682 17.5694
120.891 16.3432
123.1
15.117
123.8332 14.0294
124.5664 12.9418
125.2996 11.8542
126.0328 10.7666
126.766
9.679
125.9774
9.3544
125.1888
9.0298
124.4002
8.7052
123.6116
8.3806
122.823
8.056
121.3902
8.499
119.9574
8.942
118.5246
9.385
117.0918
9.828
115.659
10.271
114.263 10.6604
112.867 11.0498
111.471 11.4392
110.075 11.8286
108.679
12.218
106.2162
11.574
103.7534
10.93
101.2906
10.286
98.8278
9.642
96.365
8.998
94.3112
8.918
92.2574
8.838
90.2036
8.758
88.1498
8.678
Development over time period
140
120
100
80
60
40
20
0
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998
Benin
Box and Whisker plot of Benin
2
1
80
85
90
95
100
105
110
Development over time period
1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
Benin
Spain
Central Tendency
Adolescent fertility birth rate in Benin
Mean
113.310
Median
115.659
Mode
No mode
Adolescent fertility birth rate in Spain
Mean
12.102
Median
10.660
Mode
No mode
Variation
Adolescent fertility birth rate in Benin
Mean
113.310
Min
88.150
Max
126.766
Range
38.616
Quartile 1
104.9848
Quartile 3
122.9615
IQR
17.9767
Variance
125.954
Standard deviation
11.223
CV (%)
9.90%
Adolescent fertility birth rate in Spain
Mean
12.102
Min
8.056
Max
23
Range
14.944
Quartile 1
8.930
Quartile 3
12.580
IQR
3.650
Variance
17.921
Standard deviation
4.233
CV (%)
34.98%
Box-and-Whisker plot
Adolescent fertility birth rate in Benin
Adolescent fertility birth rate in Spain
Box 1
88.150
Box 1
8.056
Whisker Bottom
16.835
Whisker Bottom
0.874
Box 2
Box 3
Whisker Top
10.674
7.302
3.805
Box 2
Box 3
Whisker Top
1.730
1.920
10.420
Box and Whisker plot of Spain
Whisker plot of Benin
2
1
110
115
120
125
130
6
8
10
12
14
16
d Whisker plot of Spain
18
20
22
24
YEAR
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
No.
Country Name
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Belgium
Benin
Brazil
Comoros
France
Georgia
Germany
Ghana
Haiti
Honduras
Iceland
India
Indonesia
Kenya
Lebanon
Malawi
Mali
Mexico
Nigeria
Norway
Pakistan
Philippines
Portugal
Qatar
Senegal
Spain
Sweden
Tanzania
Togo
Tunisia
Turkey
Uganda
United Kingdom
Vietnam
Zimbabwe
Country Code
BEL
BEN
BRA
COM
FRA
GEO
DEU
GHA
HTI
HND
ISL
IND
IDN
KEN
LBN
MWI
MLI
MEX
NGA
NOR
PAK
PHL
PRT
QAT
SEN
ESP
SWE
TZA
TGO
TUN
TUR
UGA
GBR
VNM
ZWE
Adolescent fertility rate
GNI per capita,
(births per 1,000 women
Atlas method
ages 15-19)
(current US$)
5.3384
44230
90.2036
870
63.7578
10100
68.989
790
8.9614
40730
48.201
4120
7.1462
45790
68.677
1490
38.976
810
73.5778
2090
7.827
49960
25.9968
1600
48.6144
3430
83.0942
1310
12.5314
8040
141.779
340
173.0382
790
62.5464
9860
111.218
2850
5.7708
93050
38.4744
1430
59.211
3520
10.4192
20440
10.4604
75660
77.0508
980
8.758
28420
5.3086
57880
118.1232
910
90.1494
610
7.6278
3930
28.006
12000
114.5604
670
14.5964
43720
30.7942
1950
107.5554
890
Contigency Table
Level of Adolescent fertility rate
High (>30)
Low
Total
Level of GNI per capita
Low (<$1,045) Middle High (>$12,736)
10
11
0
0
4
10
10
15
10
Total
21
14
35
Benin
88.1498
90.2036
92.2574
94.3112
96.365
98.8278
101.2906
103.7534
106.2162
107.425
108.679
109.74
110.075
111.471
112.055
112.867
114.263
114.264
115.659
116.473
117.0918
118.5246
118.682
119.9574
120.891
121.3902
122.823
123.1
123.6116
123.8332
124.4002
124.5664
125.1888
125.2996
125.9774
126.0328
126.766
n = 37
Quartile 1 = X (37+1/4) =
104.985
Quartile 3 = X (3x38/4) =
122.962
Spain
8.056
8.3806
8.499
8.678
8.7052
8.758
8.838
8.918
8.942
8.998
9.0298
9.3544
9.385
9.642
9.679
9.828
10.271
10.286
10.6604
10.7666
10.93
11.0498
11.4392
11.574
11.8286
11.8542
12.218
12.9418
14.0294
15.117
16.3432
17.5694
18.7956
20.0218
21.248
22.124
23
n = 37
Quartile 1 =
8.930
Quartile 3 =
12.580
Indicator Name
Adolescent fertility rate (births per 1,000 women ages 15-19)
GNI per capita, Atlas method (current US$)
Long definition
Adolescent fertility rate is the number of births per 1,000 women ages 15-19.
GNI per capita is the gross national income, converted to U.S. dollars using the World Bank Atlas method, divided
by the midyear population. GNI is the sum of value added by all resident producers plus any product taxes (less
subsidies) not included in the valuation of output plus net receipts of primary income (compensation of

Business Statistics ECON1193 - Semester 3, 2018
Assessment Task 3: Team assessment Statistics (35%)
Course learning outcomes (CLO):
CLO 1: Illustrate and describe information using a range of numerical and graphical
procedures both written and in Excel.
CLO 2: Using sample information, apply the scientific process to arrive at probable
conclusions about population values.
CLO 3: Highlight statistical relationships between variables in data sets and to predict values
of strategic variables using regression and correlation analysis.
CLO 4: Critically analyse, in team based collaboration, the statistical findings published by
the media, research agencies and the Government to validate and verify its accuracy.
CLO 5: Communicate statistical findings and results in an unbiased manner to a nontechnical audience such as decision makers, stakeholders and the general public.
Submission: Team assessment is due on 11th January (Week 12), Friday (midnight)
The team leader will need to complete the following:
o Report submission in TII through Canvas
o Upload the Excel file in Canvas
o The Excel file is for the lecturer’s reference only. The Excel file will NOT be
marked.
o The front page of the report should state:
▪ The topic
▪ The name of the team members
▪ The student number of each member
▪ The lecturer’s name
▪ Your group number
Each team will have at most 4 team members. Contact your lecturer for your team
formation.
1 out of 8
Version OLD – Age dependency ratio, old (% of working-age population)
The United Nations has set 17 Sustainable Development Goals (SDG) for 2030. SDG 3 is
the Good Health and Well-being goal: Ensure healthy lives and promote well-being for all at
all ages. One way to measure this is by looking at the age dependency ratio.
In this assignment you will use the data sets from the World Bank. These are the same data
sets you have used in your first and second assignment.
Your case study report must contain the following 5 parts:
1.
2.
3.
4.
5.
Multiple Regression
Team Regression conclusion
Time Series
Team Time Series conclusion
Overall conclusion
2 out of 8
Part 1: Multiple Regression (use data set 2):
In this part you will build a regression model that will estimate the old age dependency ratio.
You will use the data of all the team members.
Task: Building regression models to estimate the old age dependency ratio
1. Combine data set 2 from all the team members.
2. Remove countries that appear more than once; ie if “Australia” is given 3 times in the
combined data set, remove the 2 extra “Australia” from the data set.
3. Define this as Data set I: All Countries (ALL)
4. Split up Data set I: All Countries (ALL) into Low / Middle / High Income.
Define Low / Middle / High income as follows
• GNI less than $1,045 per capita are classified as Low-Income (LI) countries.
• GNI greater than $12,736 per capita are considered High-Income (HI)
countries.
• GNI in between, are Middle- Income countries (MI).
Split up the data set into 3 data sets:
• Data set II: Low income countries (LI)
• Data set III: Middle income countries (MI)
• Data set IV: High income countries (HI)
5. Build a regression model for the data sets:
a. Data set I: All Countries (ALL)
b. Data set II: Low income countries (LI)
c. Data set III: Middle income countries (MI)
d. Data set IV: High income countries (HI)
For each data set (ALL / LI / MI / HI) apply backward eliminations to build your model
i. Identify the dependent and the independent variables in the data set.
ii. Perform a multiple regression with all the variables in the data set.
iii. Provide the regression output in the report
iv. Determine the significant and non-significant independent variables.
Use 𝛼 = 0.05.
v. Identify the non-significant independent variable with the highest pvalue.
vi. Remove the non-significant variable with the highest p-value from the
data set.
vii. Perform another multiple regression with the remaining independent
variables.
viii. Provide the regression output of the updated regression in the report.
ix. Repeat this process until only significant independent variable(s)
remain.
x. In the final model (FINAL) only significant variables remain.
3 out of 8
6. From the final regression model (FINAL) of each data set (ALL / LI / MI / HI):
a. Provide the Regression output in your report.
b. Provide the Regression Equation in your report.
c. Interpret the regression coefficient of the significant independent variable(s) in
the context of your research.
d. Interpret the coefficient of determination in the context of your research.
4 out of 8
Part 2: Team Regression conclusion:
In part 1, your team has built several regression models to predict the old age dependency
ratio, depending on factors like GNI and/or other factors. In this part your team will write a
conclusion based on your findings in part 1.
Task: Write a conclusion to estimate old age dependency ratio based on
regression
•
•
Compare the final regressions of each data set (ALL / LI / MI / HI)
o Do all the models have the same significant independent variable(s)?
o Which regression model will provide the best old age dependency ratio
estimation? Explain your answer.
Write your conclusion in an unbiased manner to a non-technical audience.
Word limit: 150 words
5 out of 8
Part 3: Time Series (use data set 1):
In this part you will use time to predict the trend of old age dependency ratio. Part 3 is an
individual task. Each team member will analyze the trend of his/her countries A and B over
time of their data set 1. This is the same data set 1 as used for the individual assessment 1.
Task: Use time series to predict the old age dependency ratio trend
Individual (by each team member)
1. Use data set 1 of the countries A and B for the years 1980 - 2011
2. Apply the following time trend models for each country (Country A / Country B)
• Linear trend model (LIN)
• Quadratic trend model (QUA)
• Exponential trend model (EXP)
For each trend model (LIN / QUA / EXP)
a. Provide the regression output in the report
b. Provide the formula of the trend model
c. Predict the old age dependency ratio for the years
o 2012, 2013, 2014 and 2015
d. Calculated the errors for the years
o 2012, 2013, 2014 and 2015
e. Calculated the MAD and SSE
3. Based on the results found in 2):
a. Which trend model will you recommend to predict the old age dependency
ratio for Country A?
b. Which trend model will you recommend to predict the old age dependency
ratio for Country B?
Explain your answers.
6 out of 8
Part 4: Team Time Series conclusion:
In part 3, your team has looked at several trend models to predict the old age dependency
ratio over time. In this part your team will write a conclusion based on your findings in part 3.
Task: Write a conclusion to predict the old age dependency ratio over time
a. Provide a line chart of old age dependency ratio over time from 1980 - 2015,
including the countries of all the team members.
b. Comment on the line chart. Are all the countries following the same trend?
c. Compare the trend models of the countries analyzed by each team member in part 3.
o Which countries are following the same trend model?
o Which trend model does your team consider to be the best old age
dependency ratio predictor? Explain your answer.
Write your conclusion in an unbiased manner to a non-technical audience.
Word limit: 200 words
7 out of 8
Part 5: Overall Team Conclusion:
In assessment 1, you provided descriptive statistics. In assessment 2 you provided
inferential statistics. In assessment 3, your team built regression models and used time
series to find the trend of the old dependency ratio. Write on overall conclusion based on the
(calculated) findings of all your assessments.
Task: Write an overall conclusion on old age dependency ratio
Your conclusion needs to answer the following questions:
1.
2.
3.
4.
Is old age dependency ratio and country income related?
What is/are the main factor(s) that will determine the old age dependency ratio?
According to your team, where will the old age dependency ratio be in 2020?
According to your team, is the projection of the United Nations correct of having a
world average old age dependency ratio will be exceeding 20% by 2030?
●
●
●
●
All four questions need to be answered.
Support your answer of each question with at least 1 calculated result.
o This calculated result can be coming from your assessments 1, 2 or 3.
o This calculated result can be a new calculation.
Use in-text reliable references to support your answers.
Write your conclusion in an unbiased manner to a non-technical audience.
Word limit: 450 words
(*)
Note for part 1 and part 3:
Regression output should not exceed 3 decimals
- End of the Assessment -
8 out of 8

## Tutor Answer

Dec 28th, 2018

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