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I have two datasets of schoolchildren performance by height in cm, one for each school. I was wondering how to best visualize how the differences in the performance between the schools vary by grade. I was thinking of creating a regression for both school's performances, and graphing the differences between the two lines, but I'm not sure how rigorous or informative that would be.

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You question is really abstract... I'd propose to try different visualizations and try to decide what exactly you want to show.

I leave here a small example that could be converted, as I think, to your needs (color = school, price = performance, carat = grade):

ggplot(data = diamonds, aes(carat, price, color = color))+
  geom_point()+
  geom_smooth(method = "lm", se = FALSE)

enter image description here

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