The Relationship Between Life Expectancy at Birth and Gdp Per Capita (Ppp)

Topics: Statistics, Regression analysis, Pearson product-moment correlation coefficient Pages: 17 (4204 words) Published: November 13, 2012
The relationship between Life Expectancy at birth and GDP per capita (PPP)

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Section 1: Introduction

In a given country, Life Expectancy at birth is the expected number of years of life from birth. Gross domestic product per capita is defined as the market value of all final goods and services produced within a country in one year, divided by the size of the population of that country.

The main objective of the present project is to establish the existence of a statistical relation between Life Expectancy (y) at birth and GDP per capita (x). First, we will present in Section 2 the data, from an official governmental source, containing Life Expectancy at birth and GDP per capita of 48 countries in the year 2003. We will put this data in a table ordered alphabetically and at the end of the section we will perform some basic statistical analysis of these data. These statistics will include the mean, median, modal class and standard deviation, for both Life Expectancy and GDP per capita.

In Section 3 we will find the regression line which best fits our data and the corresponding correlation coefficient r.

It is natural to ask if there is a non-linear model, which better describes the statistical relation between GDP per capita and Life Expectancy. This question will be studied in Section 4, where we will see if a logarithmic relation of type y=A ln(x+C) + B, is a better model.

In Section 5 we will perform a chi square test to get evidence of the existence of a statistical relation between the variables x and y.

In the last section of the project, other than summarizing the obtained results, we will present several possible directions to further investigation.

Section 2: Data collection

The following table shows the GDP per capita (PPP) (in US Dollars), denoted xi, and the mean Life Expectancy at birth (in years), denote yi, in 48 countries in the year 2003. The data has been collected through an online website (2). According to this website it represents official world records.

Country| GDP - per capita (xi)| Life Expectancy at birth (yi)| 1. Argentina| 11200| 75.48|
2. Australia| 29000| 80.13|
3. Austria| 30000| 78,17|
4. Bahamas, The| 16700| 65,71|
5. Bangladesh| 1900| 61,33|
6. Belgium| 29100| 78,29|
7. Brazil| 7600| 71,13|
8. Bulgaria| 7600| 71,08|
9. Burundi| 600| 43,02|
10. Canada| 29800| 79,83|
11. Central African Republic| 1100| 41,71|
12. Chile| 9900| 76,35|
13. China| 5000| 72,22|
14. Colombia| 6300| 71,14|
15. Congo, Republic of the| 700| 50,02|
16. Costa Rica| 9100| 76,43|
17. Croatia| 10600| 74,37|
18. Cuba| 2900| 76,08|
19. Czech Republic| 15700| 75,18|
20. Denmark| 31100| 77,01|
21. Dominican Republic| 6000| 67,96|
22. Ecuador| 3300| 71,89|
23. Egypt| 4000| 70,41|
24. El Salvador| 4800| 70,62|
25. Estonia| 12300| 70,31|
26. Finland| 27400| 77,92|
27. France| 27600| 79,28|
28. Georgia| 2500| 64,76|
29. Germany| 27600| 78,42|
30. Ghana| 2200| 56,53|
31. Greece| 20000| 78,89|
32. Guatemala| 4100| 65,23|
33. Guinea| 2100| 49,54|
34. Haiti| 1600| 51,61|
35. Hong Kong| 28800| 79,93|
36. Hungary| 13900| 72,17|
37. India| 2900| 63,62|
38. Indonesia| 3200| 68,94|
39. Iraq| 1500| 67,81|
40. Israel| 19800| 79,02|
41. Italy| 26700| 79,04|
42. Jamaica| 3900| 75,85|
43. Japan| 28200| 80,93|
44. Jordan| 4300| 77,88|
45. South Africa| 10700| 46,56|
46. Turkey| 6700| 71,08|
47. United Kingdom| 27700| 78,16|
48. United States| 37800| 77,14|

Table1: GDP per capita and Life Expectancy at birth in 48 countries in 2003 (source:...
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