REPORT ON

BIVARIATE ANALYSIS

ASSIGNMENT 1

Submitted to:

Dr. Prahlad Mishra

Social Research Methods

Submitted by:

Adyasha Dash

Amaresh Panda

UM14007

UM14009

Ankit Jain UM14011

Ayushi Gilra UM14017

Girish Kuttisankaran

Robin Karlose

Sambit Mishra

Saurabh Arora

Sumukh Savanur

Vijendra Kumar

UM14026

UM14044

UM14048

UM14051

UM14057

UM14060

Effect of GDP per capita on Life Expectancy

Introduction

Life expectancy

1. Life Expectancy is a statistical average of the number of years a human lives,

assuming mortality conditions during a given time period. This will vary

according to region and time period.

2. There are great variations in life expectancy between different parts of the

world, mostly caused by differences in public health, medical care, and diet.

3. Other factors affecting an individual's life expectancy are genetic disorders,

drug use, tobacco smoking, excessive alcohol consumption, obesity, access to

health care, diet and exercise

GDP per capita

1. GDP per capita is one of the primary indicators of a country's economic

performance.

2. Per capita GDP is sometimes used as an indicator of standard of living as well,

with higher per capita GDP being interpreted as having a higher standard of

living.

Objective

Analyze the relation between GDP per capita and life expectancy of a country using a

cross section data set consisting of data of 180 countries.

Identify trends in the life expectancy of India using a time-series data over the period

2000-2013.

A priori Reasoning

Real GDP per capita is the main indicator of the average person’s standard of living. Having a

large GDP enables a country to afford better schools, a cleaner environment, proper health

care, etc which in turn increases the life expectancy of people in the country.

Hypothesis

Null Hypothesis: The life expectancy of a country is not directly related to its GDP per

capita.

Alternate Hypothesis: The life expectancy of a country is directly related to its GDP per

capita.

Variables used

For the Bi-variate Cross-Sectional Analysis, the GDP per capita is the independent variable

& the life expectancy is the dependent variable. The dataset used is for 180 nations for the

year 2013.

For the Bi-variate Time-Series Analysis, the year is the independent variable & the life

expectancy is the dependent variable. The dataset used is for India between the years 2000

to 2013.

Sources

a. Human Development Index and its components

http://hdr.undp.org/en/content/table-1-human-development-index-and-its-

components

b. GDP per capita, PPP

http://data.worldbank.org/indicator/NY.GDP.PCAP.PP.CD

c. Life expectancy - total (years) in India

http://www.tradingeconomics.com/india/life-expectancy-at-birth-total-

years-wb-data.html

Summary of Output

Dependent

Variable

Independent Variable

Life

Expectancy

Constant

(significance level)

B1

(significance level)

B2

(significance level)

B3

(significance level)

R2

Linear 65.573

(.000)

.000

(.000)

- - 0.342

Log Linear 1.533 (.000)

0.079 (.000)

- - 0.502

Quadratic 62.879 (.000)

.001 (.000)

-4.045E-9 (.000)

- 0.464

Cubic 61.262

(.000)

.001

(.000)

-1.348E-8

(.000)

5.778E-14

(.000)

0.492

Semi-log -3.381 (.000)

.003 (.000)

- - 0.994

Linear trends

-700.138 (.000)

.381 (.000)

- - 0.994

The output from SPSS for all the models is included in the following file:

Analysis Output of SPSS

We have used cross section data for the first 4 models, i.e., linear, log linear, quadratic and

cubic.

We can see of all the 4 models the R2 value for log linear model is the highest. So, log linear

model has higher explanatory power. However, the R2 value is not so high and stands at

0.502 though significant. So we can’t properly explain the relationship, i.e. life expectancy of

a country is directly related to its GDP.

In case of semi log and linear trend model, both the models are effective in explaining the

chosen model because their R2 values are very high, i.e. 0.994 and all the elasticities are

also quite significant.

1. SIMPLE LINEAR REGRESSION

Correlations

Life expectancy

GDP per

Capita

Pearson

Correlation

Life

expectancy 1.000 .588

GDP per Capita .588 1.000

Sig. (1-tailed) Life

expectancy . .000

GDP per Capita .000 .

N Life

expectancy 180 180

GDP per Capita 180 180

2. Log Linear Model

Correlations

Log Life

expectancy at

birth

Log GDP per

Capita

Pearson Correlation Log Life expectancy at

birth 1.000 .711

Log GDP per Capita .711 1.000

Sig. (1-tailed) Log Life expectancy at

birth . .000

Log GDP per Capita .000 .

N Log Life expectancy at

birth 180 180

Log GDP per Capita 180 180

Quadratic Model

Correlations

Life expectancy GDP per Capita

GDP per Capita

Square

Pearson Correlation Life expectancy 1.000 .588 .349

GDP per Capita .588 1.000 .880

GDP per Capita Square .349 .880 1.000

Sig. (1-tailed) Life expectancy . .000 .000

GDP per Capita .000 . .000

GDP per Capita Square .000 .000 .

N Life expectancy 180 180 180

GDP per Capita 180 180 180

GDP per Capita Square 180 180 180

Cubic Model

Correlations

Life

expectancy

GDP per

Capita

GDP per

Capita

Square

GDP per

Capita Cube

Pearson

Correlation

Life expectancy 1.000 .588 .349 .201

GDP per Capita .588 1.000 .880 .713

GDP per Capita

Square .349 .880 1.000 .953

GDP per Capita

Cube .201 .713 .953 1.000

Sig. (1-tailed) Life expectancy . .000 .000 .003

GDP per Capita .000 . .000 .000

GDP per Capita

Square .000 .000 . .000

GDP per Capita

Cube .003 .000 .000 .

N Life expectancy 180 180 180 180

GDP per Capita 180 180 180 180

GDP per Capita

Square 180 180 180 180

GDP per Capita

Cube 180 180 180 180

Linear Trend

Correlations

Life Expectancy Year

Pearson Correlation Life Expectancy 1.000 .997

Year .997 1.000

Sig. (1-tailed) Life Expectancy . .000

Year .000 .

N Life Expectancy 14 14

Year 14 14

Semi-Log

Correlations

Log Life

Expectancy Year

Pearson Correlation Log Life Expectancy 1.000 .997

Year .997 1.000

Sig. (1-tailed) Log Life Expectancy . .000

Year .000 .

N Log Life Expectancy 14 14

Year 14 14

Appendix

Bivariate Time-Series Analysis.sav

Year GDP per Capita Life Expectancy

2000 2063 61.45

2001 2176 61.97

2002 2257 62.32

2003 2444 62.67

2004 2669 63.02

2005 2966 63.37

2006 3294 63.72

2007 3662 64.07

2008 3827 64.42

2009 4129 64.78

2010 4549 65.13

2011 4883 65.96

2012 5138 66.21

2013 5410 66.4

Bivariate Cross-Section Analysis.sav

Countries Life Expectancy at birth (years) GDP per Capita

Norway 81.5 65461.17

Australia 82.5 43550.08

Switzerland 82.6 53671.86

Netherlands 81.04 43403.72

United States 78.94 53142.89

Germany 80.74 43331.7

New Zealand 81.13 34825.63

Canada 81.48 43247.04

Singapore 82.32 78744.13

Denmark 79.39 42763.76

Ireland 80.71 43304.25

Sweden 81.82 43533.48

Iceland 82.09 39996.07

United Kingdom 80.55 36196.72

Hong Kong, China (SAR) 83.38 53202.93

Korea (Republic of) 81.54 1855.38

Japan 83.58 36315.45

Israel 81.8 32760.41

France 81.81 36907.27

Austria 81.14 44149.21

Belgium 80.55 40338.15

Luxembourg 80.55 90789.65

Finland 80.54 38250.66

Slovenia 79.59 28298.41

Italy 82.39 34302.63

Spain 82.1 32103.48

Czech Republic 77.69 27344.27

Greece 80.77 25650.96

Brunei Darussalam 78.55 71759.1

Qatar 78.37 131757.56

Cyprus 79.84 29450.09

Estonia 74.44 25048.69

Saudi Arabia 75.48 53780.42

Lithuania 72.11 25416.7

Poland 76.41 23274.8

Slovakia 75.4 26114.49

Malta 79.75 30213.07

Chile 79.96 21911.3

Portugal 79.94 25899.53

Hungary 74.62 22877.51

Bahrain 76.61 43823.51

Croatia 77.05 20904.09

Latvia 72.15 23028.05

Uruguay 77.23 19589.58

Bahamas 75.24 17139.29

Montenegro 74.82 14318.36

Belarus 69.93 17615.46

Romania 73.83 18634.8

Libya 75.33 21397.26

Oman 76.55 44051.87

Russian Federation 67.98 24120.29

Bulgaria 73.55 15940.54

Palau 72.41 15092.3

Antigua and Barbuda 75.95 20976.51

Malaysia 75.02 23297.63

Mauritius 73.61 17199.95

Trinidad and Tobago 69.86 30438.56

Lebanon 80.01 17169.64

Panama 77.56 19411.48

Venezuela (Bolivarian Republic of) 74.63 2991.03

Costa Rica 79.93 13872.46

Turkey 75.26 18975.46

Kazakhstan 66.54 23205.64

Mexico 77.5 16463.39

Seychelles 73.19 24188.65

Saint Kitts and Nevis 73.57 1451.75

Sri Lanka 74.29 9735.74

Iran (Islamic Republic of) 74.05 9558.79

Azerbaijan 70.75 17139.29

Jordan 73.85 11781.62

Serbia 74.06 12373.99

Brazil 73.94 15033.78

Georgia 74.3 7164.58

Grenada 72.77 11497.98

Peru 74.83 11775.37

Ukraine 68.53 8787.83

Belize 73.88 8441.77 The former Yugoslav Republic of

Macedonia 75.2 14390.01

Bosnia and Herzegovina 76.37 9632.38

Armenia 74.56 7774.38

Fiji 69.81 7948.26

Thailand 74.4 14390.01

Tunisia 75.87 11092.15

China 75.33 11903.6

Saint Vincent and the Grenadines 72.49 1451.75

Algeria 71 13304.01

Dominica 77.67 10029.52

Albania 77.39 10488.82

Jamaica 73.53 8889.72

Saint Lucia 74.8 1451.75

Colombia 74.04 12370.94

Ecuador 76.47 10468.73

Suriname 71.02 16226.18

Tonga 72.67 5302.91

Dominican Republic 73.4 11695.78

Maldives 77.92 11653.89

Mongolia 67.5 9432.66

Turkmenistan 65.45 14000.74

Samoa 73.16 5053.73

Palestine, State of 73.2 15092.3

Indonesia 70.83 9558.79

Botswana 64.39 15675.23

Egypt 71.16 10468.73

Paraguay 72.26 8043.02

Gabon 63.48 19259.63

Bolivia (Plurinational State of) 67.26 6129.56

Moldova (Republic of) 68.9 4669.23

El Salvador 72.6 7762.24

Uzbekistan 68.24 5167.02

Philippines 68.7 6532.58

South Africa 56.92 12503.69

Iraq 69.42 15187.87

Guyana 66.3 6550.97

Viet Nam 75.94 18193.92

Cape Verde 75.09 43247.04

Guatemala 72.1 7294.8

Kyrgyzstan 67.53 3212.15

Namibia 64.48 9684.99

Timor-Leste 67.54 2241.89

Honduras 73.82 4591.47

Morocco 70.94 7200.41

Vanuatu 71.63 2991.03

Nicaragua 74.84 4570.83

Kiribati 68.91 1855.38

Tajikistan 67.25 2511.63

India 66.41 5410.29

Bhutan 68.29 7669.24

Cambodia 71.92 3041.85

Ghana 61.13 3974.5

Lao People's Democratic Republic 68.31 4812.01

Congo 58.79 1558.78

Zambia 58.11 3180.6

Bangladesh 70.66 2557.41

Sao Tome and Principe 66.34 2970.34

Equatorial Guinea 53.06 33720.22

Nepal 68.41 2244.25

Pakistan 66.57 4698.89

Kenya 61.72 2264.7

Swaziland 49 6683.5

Angola 51.9 7538.19

Rwanda 64.07 1451.75

Cameroon 55.07 2711.04

Nigeria 52.51 5601.04

Yemen 63.11 14292.55

Madagascar 64.72 1394.65

Zimbabwe 59.87 1700.02

Papua New Guinea 62.42 2538.46

Solomon Islands 67.68 2068.46

Comoros 60.87 1558.78

Tanzania (United Republic of) 61.53 1774.62

Mauritania 61.55 3042.49

Lesotho 49.45 2585.65

Senegal 63.45 2268.58

Uganda 59.21 1410.03

Benin 59.33 1790.96

Sudan 62.06 3372.15

Togo 56.54 1390.18

Haiti 63.1 1702.61

Afghanistan 60.95 1989.61

Djibouti 61.8 2998.01

Côte d'Ivoire 50.72 3011.93

Gambia 58.82 19259.63

Ethiopia 63.64 1353.79

Malawi 55.31 779.81

Liberia 60.56 877.78

Mali 55.03 1641.43

Guinea-Bissau 54.29 1242.45

Mozambique 50.25 1045.38

Guinea 56.11 1255.23

Burundi 54.1 770.62

Burkina Faso 56.34 1634.02

Eritrea 62.85 1195.38

Sierra Leone 45.56 1926.52

Chad 51.18 2080.74

Central African Republic 50.18 603.6

Congo (Democratic Republic of the) 49.96 1558.78

Niger 58.41 912.57

Korea (Democratic People's Rep. of) 70 1855.38

Marshall Islands 72.62 3710.35

South Sudan 55.26 2330.01

SPSS Analysis Spreadsheets

Cross Section Data 1

Time Series Data 1