Just a Little Statistics Refresher

The Wikipedia article on statistical correlation cites this book Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.) Hillsdale, NJ: Lawrence Erlbaum Associates which suggests that, in psychological research, these guidelines apply to interpreting correlation coefficients (i.e., the strength of the relationship between two variables):

Small: +/- 0.1 - 0.3
Medium: +/- 0.3 - 0.5
Large: +/- 0.5 - 1.0

The correlation coefficient is the square root of the coefficient of determination (R-squared), which is the number that appears on each of the graphs I have posted in the two previous posts. So for the following regressions, the correlation coefficients are:

Tax Burden & HDI: +0.432 (Medium)
Tax Burden & GDP/capita: +0.327 (Medium)
Tax Burden & Income Inequality: -0.582 (Strong)
Tax Burden & Absence of Social Mobility: -0.523 (Strong)
Income Inequality & GDP/capita: -0.440 (Medium)
Income Inequality & HDI: -0.422 (Medium)
Income Inequality & Absence of Social Mobility: +0.646 (Strong)

I think it's valid to use the psychology guidelines to help us interpret these results. So a high tax burden is highly correlated with social mobility and income equality and moderately correlated GDP/capita and HDI. Income inequality, in turn, is highly correlated with the lack of social mobility, and moderately negatively correlated with GDP/capita and HDI.

So I may have understated the strength of these relationships. They are actually quite strong.