Investigating the Correlation between the Gini Coefficient and 'At Risk of Poverty' Rates in High GNI European Countries

This investigation explores the relationship between income inequality, measured by the Gini coefficient, and the "at risk of poverty" rate across eight high-GNI European nations.

The methodology involves constructing Lorenz Curves for each country using income quintile data. Mathematical modeling is achieved through quadratic regression, derived via partial derivatives and the least squares method, with cubic regression applied where necessary. Definite integrals are utilized to calculate the area under the curves to determine Gini coefficients.

The study identifies a strong positive correlation (R² = 0.728) between the two variables. Key strengths include a rigorous mathematical approach to regression and a thoughtful evaluation of model limitations, such as the necessity for constrained regression to ensure curves pass through the origin.