Looking at that data, have you plotted it on a log scale? However those indices are constructed, the data appears to fit an exponential. Plot log(corruption) vs. HDI and see if it looks linear. It would probably make the outliers on the left side of the chart really stand out.
It could fit a power function, too, though biased. plot log(corruption - about 1.5) vs log(HDI).
It looks to me that as HDI increases, variance in corruption, either above or below the norm gets significantly less.
I just gave it a shot, but I didn’t find it terribly illuminating. The data seems to be equally well fit by both a power law with an offset (the exponent is about 10.1, offset of about 2.55) and an exponential (growth constant of about 8.2, offset of about 2.39.) Of course, this is largely explained by the fact that the ratio of maximum value to minimum value is only about 5 in both cases, which I don’t think is really enough to distinguish between a power law vs. an exponential.
I’ve also added a link to the raw data in the linked blog post above, if anyone else wants to play with it.