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To me the way carry/support is being evaluated is flawed.
Warding might have been easier data to bring up, but damage vs hold share would probably yield a stronger regression. Lo L is super challenging to do statistical analysis with, and not because the models themselves are difficult to run.
The real reason his R is terrible is that he's only analyzing junglers, which is basically the most complex and most nonlinear role in all of Lo L (I bet ADC vs CS/min would be pretty linear).
A lot of the jungler's role depends on EVERYTHING, from your team comp/synergy vs the enemy's, counter comps, your gank path, your team's predictions of the enemy, both jungler's ingenuity at finding something new and unexpected (for example Lee Sin ward hops to areas that avoid commonly warded areas of the enemy).
Specifically: There are definitely variables being omitted here.
Lee Sin comes to mind as building sightstone but being classified as a carry jungler.
I read though most of your paper and although I haven't run the the the regressions myself I think the validity of your statistics are extremely questionable.
All regressions are predicated on assumptions and you need to verify the assumptions are holding.