These two tables show values of R2 coupled to the best fits of data sets LMi,y versus Γi,y for all the countries considered and for several choices of binning; the case with 30 bins is the one shown in Fig 1.

As for Italy, whatever the level of resolution we fix (i.e., whatever the amount of bins we use), the best fit considering the country as a whole is always significantly worst than the one obtained considering Northern and Southern regions separately.