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TEAM ASSIGMENT ECON 1193 – BUSINESS STATISTICS 1

MEMBERS Nguyen Dinh Long - s3750067 Nguyen Ngoc Diep - s3762761 Nguyen Ngoc Minh - s3697113

LECTURER: PHAM THI MINH THUY

Table of Contents I.

Multiple Regression.................................................................................................................2 1.

All countries (ALL)..............................................................................................................2

2.

Low Income (LI) - GNI per capita < $1000.........................................................................4

3.

Middle Income (MI) - $1000 < GNI per capita < $12,500...................................................5

4.

High Income (HI) – GNI per capita > $12,500....................................................................7

II.

Team Regression conclusion................................................................................................9

III.

Time Series...........................................................................................................................9

1.

Finland – FIN (Nguyen Dinh Long).....................................................................................9

2.

Mali – MLI (Nguyen Dinh Long).......................................................................................13

3.

Ireland – IRL (Nguyen Ngoc Diep)....................................................................................17

4.

Brazil – BRA (Nguyen Ngoc Diep)....................................................................................20

5.

Congo, Dem.Rep – COD (Nguyen Ngoc Minh)................................................................24

6.

Colombia – COL (Nguyen Ngoc Minh).............................................................................28

IV.

Team Times Series conclusion............................................................................................31

V.

Overall conclusion..............................................................................................................31

VI.

Reference list......................................................................................................................31

VII.

Appendices.........................................................................................................................31

1|Page

I.

Multiple Regression IDENTIFICATION OF DEPENDENT AND INDEPENDENT VARIABLES:

1.   -

Independent variables: GNI per capita, Atlas method (current US$) Domestic general government health expenditure per capita, PPP (current international $) Immunization, measles (% of children ages 12-23 months) Compulsory education, duration (years) Dependent variables Mortality rate, under-5 (per 1,000 live births) All countries (ALL) We have: The level of significance: α = 0.05 (5%) Level of confidence: 1- α =0.95 (95%) Sample size n= 51 State: Null hypothesis: H0: β1 = 0 (no linear relationship) Alternative hypothesis: H1: β1 ≠ 0 (linear relationship exists) →This is a two-tail test

- Population Standard Deviation (σ) is unknown → we will use the t-table: Critical value of t distribution with 46 degrees of freedom with an area of 0.025 in each tail is: tα/2, n-5=t0.025,46 = ±2.2129=> Reject H0 if tstat >2.0129 or tstat < -2.0129 → Regression output 1 (All variables included) Significant variables: Immunization, measles (% of children ages 12-23 months) (tstat = -4.909) - Non-significant variables: GNI per capita (tstat = -0.3), Compulsory education (tstat = -0.627) and Domestic general government health expenditure (tstat = -0.575) → Backward elimination: GNI per capita (0.766) -

- GNI per capita is eliminated: 3 independent variables remain → Regression output 2 Critical value of t distribution with 47 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-4=t 0.025,47 = ±2.0117=> Reject H0 if tstat > 2.0117 or tstat < -2.0117 Significant variables: Domestic general government health expenditure (tstat = -3.329) and Immunization, measles (tstat = -4.956) - Non-significant variables: Compulsory education (tstat = -0.623) → Backward elimination: Compulsory education (0.536) -

2|Page

Compulsory education is eliminated: 2 independent variables remain → Regression output 3 Critical value of t distribution with 48 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-3=t 0.025,48 = ±2.0106 => Reject H0 if tstat > 2.0106 or tstat < -2.0106 -

Significant variables: Domestic general government health expenditure (tstat = -3.595) and Immunization, measles (tstat = -5.325)

-

Non-significant variables: None

Regression output 3 for all countries → The regression equation with two significant variables: ^ Y =b 0 +b1 X 1 + b2 X 2 CMR = 176.462 – 1.544*(Immunization, measles) - 0.007*( Domestic general government health expenditure) → Interpretation: -

Child mortality rate will decrease by 1.544 (number of deaths per 1,000 people) for each percentage of children ages 12-23 months added to the immunization

-

Child mortality rate will decrease by 0.007 (number of deaths per 1,000 people) for each current international $1 added to the expenditure of domestic general government in health

-

The R2 (coefficient of determination) here is =0.554 (55.4%) which suggests that 55.4% of the changes in child mortality rate is explained by the percentage of children ages 123|Page

23 months taking immunization against measles and the expenditure of domestic general government in health

2.   -

Low Income (LI) - GNI per capita < $1000 We have: The level of significance: α = 0.05 (5%) Level of confidence: 1- α =0.95 (95%) Sample size n= 8 State: Null hypothesis: H0: β1 = 0 (no linear relationship) Alternative hypothesis: H1: β1 ≠ 0 (linear relationship exists) →This is a two-tail test Population Standard Deviation (σ) is unknown → we will use the t-table:

Critical value of t distribution with 3 degrees of freedom with an area of 0.025 in each tail is: tα/2, n-5=t0.025,3 = ±3.1824=> Reject H0 if tstat >3.1824 or tstat < -3.1824 → Regression output 1 (All variables included) -

Significant variables: None Non-significant variables: GNI per capita (tstat = -1.172), Compulsory education (tstat =2.534), Domestic general government health expenditure (tstat = -2.123) and Immunization, measles (tstat = 1.256)

→ Backward elimination: GNI per capita has the highest p-value (0.326) -

GNI per capita is eliminated: 3 independent variables remain

→ Regression output 2 Critical value of t distribution with 4 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-4=t 0.025,4 = ±2.7763=> Reject H0 if tstat > 2.7763 or tstat < -2.7763 -

Significant variables: None Non-significant variables: Domestic general government health expenditure (tstat = -2.245), Compulsory education (tstat = 2.281) and Immunization, measles (tstat = 1.571)

→ Backward elimination: Immunization, measles has the highest p-value (0.191) Immunization, measles variable is eliminated: 2 independent variables remain → Regression output 3 4|Page

Critical value of t distribution with 5 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-3=t 0.025,5 = ±2.5705=> Reject H0 if tstat > 2.5705 or tstat < -2.5705 Significant variables: None -

Non-significant variables: Domestic general government health expenditure (tstat = -2.202), Compulsory education (tstat = 1.529)

→ Backward elimination: Compulsory education has the highest p-value (0.187) -

Compulsory education is eliminated: 1 independent variable remains

→ Regression output 4 Critical value of t distribution with 6 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-2=t 0.025,6 = ±2.4469=> Reject H0 if tstat > 2.4469 or tstat < -2.4469 -

Significant variables: None Non-significant variables: Domestic general government health expenditure (tstat = -1.491)

→ Backward elimination: Domestic general government health expenditure has the highest pvalue (0.187) -

Domestic general government health expenditure is eliminated → no significant independent variables

→ Interpretation: It is impossible to build a final regression model with significant variables for Low-Income Countries (LI) since no variable has a significant linear relationship with the child mortality rate, under-5 (per 1,000 live births). 3.   -

Middle Income (MI) - $1000 < GNI per capita < $12,500 We have: The level of significance: α = 0.05 (5%) Level of confidence: 1- α =0.95 (95%) Sample size n= 26 State: Null hypothesis: H0: β1 = 0 (no linear relationship) Alternative hypothesis: H1: β1 ≠ 0 (linear relationship exists) →This is a two-tail test Population Standard Deviation (σ) is unknown → we will use the t-table:

Critical value of t distribution with 21 degrees of freedom with an area of 0.025 in each tail is: tα/2, n-5=t0.025,21 = ±2.0796=> Reject H0 if tstat >2.0796 or tstat < -2.0796 5|Page

→ Regression output 1 (All variables included) -

Significant variables: None Non-significant variables: GNI per capita (tstat = -0.743), Compulsory education (tstat =0.381), Domestic general government health expenditure (tstat = -0.861) and Immunization, measles (tstat = -1.672)

→ Backward elimination: Compulsory education has the highest p-value (0.399) -

Compulsory education is eliminated: 3 independent variables remain

→ Regression output 2 Critical value of t distribution with 22 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-4=t 0.025,22 = ±2.0739=> Reject H0 if tstat > 2.0739 or tstat < -2.0739 -

Significant variables: None Non-significant variables: GNI per capita (tstat = -0.796), Domestic general government health expenditure (tstat = -0.893) and Immunization, measles (tstat = -1.739)

→ Backward elimination: GNI per capita has the highest p-value (0.191) GNI per capita is eliminated: 2 independent variables remain → Regression output 3 Critical value of t distribution with 23 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-4=t 0.025,23 = ±2.0687=> Reject H0 if tstat > 2.0687 or tstat < -2.0687 -

Significant variables: Domestic general government health expenditure (tstat =-3.310)

-

Non-significant variables: Immunization, measles (tstat = -1.701)

→ Backward elimination: Immunization, measles has the highest p-value (0.102) Immunization, measles is eliminated

6|Page

→ Regression output 4

Final regression output for middle income countries Critical value of t distribution with 24 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-2=t 0.025,24 = ±2.0639=> Reject H0 if tstat > 2.0639 or tstat < -2.0639 -

Significant variables: Domestic general government health expenditure (tstat =-4.331)

-

Non-significant variables: None

→ The regression equation with one significant variable:

CMR = 53.903 - 0.063 (Domestic general government health expenditure) → Interpretation: -

Child mortality rate will decrease by 0.063 (number of deaths per 1,000 people) for each current international $1 added to the expenditure of domestic general government in health

-

The R2 (coefficient of determination) here is =0.439 (43.9%) which suggests that 43.9% of the changes in child mortality rate is explained by the fund of domestic general government in health

4.  -

High Income (HI) – GNI per capita > $12,500 We have: The level of significance: α = 0.05 (5%) Level of confidence: 1- α =0.95 (95%) Sample size n= 16 7|Page

 State: - Null hypothesis: H0: β1 = 0 (no linear relationship) - Alternative hypothesis: H1: β1 ≠ 0 (linear relationship exists) →This is a two-tail test - Population Standard Deviation (σ) is unknown → we will use the t-table: -

Critical value of t distribution with 11 degrees of freedom with an area of 0.025 in each tail is: tα/2, n-5=t0.025,21 = ±2.201=> Reject H0 if tstat >2.201 or tstat < -2.201

→ Regression output 1(All variables included)

-

Significant variables: Compulsory education (tstat=5.441), Domestic general government health expenditure (tstat = -3.662) Non-significant variables: GNI per capita (tstat = 1.849) and Immunization, measles (tstat = -1.425) → Backward elimination: Immunization, measles has the highest p-value (0.182)

-

Immunization, measles is eliminated: 3 independent variables remain

-

→ Regression output 2 Critical value of t distribution with 12 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-4=t 0.025,13 = ±2.1788=> Reject H0 if tstat > 2.1788 or tstat < -2.1788 Significant variables: Domestic general government health expenditure (tstat = -3.587), Compulsory education (tstat = 5.0960  Non-significant Variables: GNI per capita (tstat = 1.870) → Backward elimination: GNI per capita has the highest p-value (0.086) 

GNI is eliminated: 2 independent variables remain → Regression output 3 Critical value of t distribution with 13 degrees of freedom with an area of 0.025 in each tail is: t α/2, n-4=t 0.025,13 = ±2.1604=> Reject H0 if tstat > 2.1604 or tstat < -2.1604  

Significant Variables: Domestic general government health expenditure per capita (tstat = -3.961), Compulsory education, duration (tstat = 4.471) Non-significant variables: none

8|Page

→ The regression equation with two significant variables: ^ Y =b 0 +b1 X 1 + b2 X 2 CMR = -1.755 – 0.001*(Domestic general government health expenditure per capita) + 0.894*(Compulsory education, duration) → Interpretation: 

Child mortality rate will increase by 0.894 (number of deaths per 1,000 people) for each year added to the compulsory education



Child mortality rate will decrease by 0.001 (number of deaths per 1,000 people) for each current international $1 added to the expenditure of domestic general government in health



The R2 (coefficient of determination) here is =0.714 (71.4%) which suggests that 71.4% of the changes in child mortality rate is explained by the duration of compulsory education and the expenditure of domestic general government in health

II. III.

Team Regression conclusion Time Series Because the regression output is formatted to 3 decimals, there is a little difference between the predicted value and the actual value in the tables below versus the predicted value and the actual value calculated from the data in the formatted regression output

1. Finland – FIN (Nguyen Dinh Long) a) Linear model Regression output 9|Page

Linear Regression output for Finland’s child mortality rate in Linear model →Linear equation: Predicted value= 7.425-0.174*(Time period)  Prediction and error: Predicted value

Actual value

Error

2015

2.041

2.4

0.359

2016

1.867

2.3

0.433

2017

1.693

2.3

0.607

Prediction and Errors of Finland’s child mortality rate in Linear model

= 0.685

= 0.466

b) Quadratic model 10 | P a g e

Regression output

Quadratic Regression output for Finland’s child mortality rate →Quadratic equation: Predicted value=7.924 - 0.268*(Time period) + 0.003*(Squared time)  Prediction and Error

Predicted value

Actual value

Error

2015

2.521

2.4

0.121

2016

2.443

2.3

0.143

2017

2.372

2.3

0.072

Prediction and Errors of Finland’s child mortality rate in Quadratic model

= 0.04

11 | P a g e

=0.112

c) Exponential model Regression output

Exponential Regression output for Finland’s child mortality rate →Exponential equation: log(predicted value)=0.905-0.016*(time period) ⟷ Predicted value=100.905-0.016*(time period)  Prediction and Error Predicted value

Actual value

Error

2015

2.564

2.4

0.164

2016

2.472

2.3

0.172

2017

2.382

2.3

0.082

Prediction and Errors of Finland’s child mortality rate in Exponential model = 0.063 12 | P a g e

= 0.14 d) Recommendation: Based on the calculated results of SSE and MAD, it is recommended that the Exponential Model should be used to predict the child mortality rate for Finland because of its smallest errors (SSE and MAD: 0.04 and 0.112 respectively) 2. Mali – MLI (Nguyen Dinh Long) a) Linear model Regression output

Linear Regression output for Mali’s child mortality rate in Linear model →Linear equation: Predicted value= 297.429-5.903*(Time period)  Prediction and error: Predicted value

Actual value

Error

2015

114.436

113.7

0.736

2016

108.533

109.6

1.067

13 | P a g e

2017

102.63

106

3.37

Prediction and Errors of Mali’s child mortality rate in Linear model

= 13.037

= 1.724

b) Quadratic model Regression output

Quadratic Regression output for Mali’s child mortality rate →Quadratic equation: Predicted value=281.083 – 2.838*(Time period) – 0.099*(Squared time)  Prediction and Error Predicted value

Actual value

Error

2015

98.094

113.7

15.606

2016

89.027

109.6

20.573 14 | P a g e

2017

79.763

106

26.237

Prediction and Errors of Mali’s child mortality rate in Quadratic model

=1355.155

=20.805

c) Exponential model Regression output

Exponential Regression output for Mali’s child mortality rate →Exponential equation: log(predicted value)= 2.505-0.013*(time period) ⟷ Predicted value=102.505-0.013*(time period) 15 | P a g e

 Prediction and Error Predicted value

Actual value

Error

2015

126.474

113.7

12.774

2016

122.744

109.6

13.144

2017

119.124

106

13.124

Prediction and Errors of Mali’s child mortality rate in Exponential model

= 508.173

= 13.014 d) Recommendation: Based on the calculated results of SSE and MAD, it is recommended that the Linear Model should be used to predict the child mortality rate for Mali because of its smallest errors (SSE and MAD: 13.037 and 1.724 respectively) 3. Ireland – IRL (Nguyen Ngoc Diep) a) Linear model Regression output

16 | P a g e

Linear Regression output for Ireland’s child mortality...