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Relationship between GDP per Capita and Gini Index By: Ms. Bercovitz Probability & Statistics 2/28/2012 STATEMENT OF QUESTION In this report, the relationship between the Gini index and GDP per capita is being investigated. The Gini index measures how equal the distribution of income in a country is. In other words, the Gini index measures how big of an economic or income gap exists between the rich and the poor in a country. A Gini index of 0 represents complete equality; a Gini index of 100 represents complete inequality. GDP per capita is a measure of a country’s total economic output divided by the total number of citizens. GDP per capita is one way in which a country can measure its economic growth, and GDP per capita is often used as a way to compare the economy of one country to another. The essential question being asked in this report is, “Does a relationship exist between the Gini index and GDP per capita, and if so, what is the nature of this relationship?” To gather data for this investigation, Pearson Education’s Infoplease.com website was used as a means to find economic statistics by country. GDP per capita (in thousands) is being used as the explanatory variable, and Gini index is being used as the response variable. This is because I am predicting that GDP, which is a measure of economic success, predicts how fair an economy is. Below are the data and scatterplot for for Gini index and GDP per capita. DATA Chile Honduras Swaziland Norway Namibia Lesotho Sierra Leonne Central African Republic Botswana Bolivia Haitia Colombia Paraguay South Africa Brazil Panama Ecuador El Salvador GDP per capita (in thousands) 11.3 2.9 5 42.3 7 2.5 0.8 1.1 10.5 2.9 1.7 7.9 4.9 12 8.4 7.2 4.3 4.7 Gini Index 54.9 53.8 50.4 25.8 74.3 63.2 62.9 61.3 60.5 60.1 59.2 58.6 58.4 57.8 57 56.1 53.6 52.4 Table 1: Gini Index and GDP per capita (in thousands) for 40 different countries. Gini index is a measure of the economic equality of a country. A Gini index of 0 means perfect economic equality; a Gini index of 100 means perfect economic inequality. Peru Bangladesh Finland Bulgaria Neterlands Mongolia France Canada Slovenia Belgium Japan Germany Romania Hungary Denmark Ukraine Argentina Moldova Slovakia Pakistan Tajikistan 5.9 2.1 30.9 9.6 30.5 1.9 29.9 34 21.6 31.4 31.5 30.4 8.2 16.3 34.6 7.2 13.1 1.8 16.1 2.4 1.2 52 33.4 26.9 29.2 30.9 32.8 32.7 32.6 28.4 33 24.9 28.3 31 26.9 24.7 28.1 51.3 33.2 25.8 30.6 32.6 SCATTER PLOT Graph 1: Relationship between GDP per capita and Gini index, with GDP per capita displayed in thousands. Included are a least-squares regression line and the accompanying regression equation. The correlation value for this relationship is r=-0.58841. Relationship between GDP per capita and Gini Index y = -0.694x + 51.475 70 Gini Index 60 50 40 30 20 10 0 0 10 20 30 GDP per capita (in thousands) 40 50 INTERPRETATION OF DATA The mean GDP per capita is $12.77 thousand, and the standard deviation is $12.17 thousand. This means that, on average, the countries’ GDP per capita values deviated from the mean of $12.77 thousand by $12.17 thousand. Since the standard deviation is nearly as large as the mean, we can say that the GDP per capita values are very widely ranging. The mean Gini index is 43.32, and the standard deviation is 14.94. This means that, on average, the countries’ Gini indexes deviated from the mean of 43.32 by 14.94 units. The relationship between GDP per capita (in thousands) and Gini value is negative and linear with a correlation value of r=-0.58841, indicating a relatively weak relationship. In general, as GDP per capita increases, the Gini value of a country decreases. This means that as a country produces more goods on average per person, their overall economic equality increases. In general, it appears that countries who are experiencing higher levels of economic success and growth have higher levels of economic equality among their citizens. The regression equation for the relationship between GDP per capital (in thousands) and Gini value is y=-0.7224x+52.55, where y represents the Gini value and x represents the GDP per capita. The slope of the regression equation is -0.7224; this means that Gini value decreases by 0.7224 units for every thousand dollar increase in GDP per capita. Since a lower Gini value corresponds to a more equal economy, this negative slope suggests that as GDP per capita increases, economic equality increases. The y-intercept of the regression equation is 52.55. This means that when the Gini value is zero, the GDP per capita of a country would be $52.55 thousand dollars, or $52,500 per person. In other words, if an economy were perfectly equal (which is what a Gini value of zero means), each person would be producing on average $5,255,000 worth of goods each year. The residual plot for the data shows that there is a wide variation in the data, particularly for countries which have low GDP per capita values. The residual plot shows that the regression line is not a particularly good fit for our data. INTERPRETATION OF OUTLIERS There is one unusual point which can be identified as an outlier. Namibia has a GDP per capita of $7 thousand and a Gini index of 74.3. Although we would expect Namibia to have a high Gini index given its low GDP per capita, 74.3 is much higher than the rest of the data points. PREDICTION FROM REGRESSION LINE We could use our regression line to make predictions about unknown data points. We will predict the Gini Index of a country with a GDP per capita of $50 thousand and a GDP per capita of $25 thousand. For a country with a GDP per capita of $50 thousand, the Gini Index would be 13.9, and for a country with a GDP per capita of $25 thousand, the Gini Index would be 33.2. CONCLUSION Overall, our essential question was, “Does a relationship exist between the Gini index and GDP per capita?” It was found that there was a weak negative relationship between GDP per capita and Gini Index. This is likely because as GDP per capita increases, on average more individuals are making more money, which potentially makes an economy more equal. It is important, however, to remember that GDP per capita is an average, meaning that a few very rich individuals could pull the average up and make the GDP appear higher than it actually is.