It is well known that school results are mostly explained by socioeconomic status (I read somewhere up to 75% of the variance can be explained that way). So if you don't take into account other factors that graph doesn't prove anything other than people who can afford private schools and homescholing are on average richer. My guess is that the rest of the data can be explained by smaller class sizes and better resources.

If you want more research this [0] article has a good bibliography on the effects of socioeconomic diversity in schools

[0] https://repository.law.umich.edu/cgi/viewcontent.cgi?article...