The correlation is not perfect, but a number of research papers on energy poverty have noted the correlation.
Last year I ran a couple of regressions:
Cost = (.014 x %Penetration) + 0.077
p-value = 0.0011
Is the slope significantly different from zero? Yes.
And for solar penetration:
For the same 20 largest GDP countries the slope of cost versus solar penetration is twice as steep.
Cost = (.028 x %Penetration) + 0.046
DB2