SF’s housing costs are 3.3x higher than the US average. Plotting it on this line,
This feels dubious to me. I think there’s no a priori reason to assume the correlation is similar for cities as for states.
A full-on Simpson’s paradox with reversed correlation seems unlikely, since I guess rich cities are typically in rich states. But I could easily imagine something like: “the housing costs of the state are basically irrelevant, the housing costs of the city matters a lot. When you bin cities into states, you’re introducing noise that makes the correlation seem weaker than it is”. And I wouldn’t be completely shocked by something the other way around, where the housing costs of the state matter a lot more than the housing costs of the city. In which case SF would only get the same multiplier here as anywhere else in California.
Still, if this is the data you had, plotting it on this line seems clearly better than not doing so.
This feels dubious to me. I think there’s no a priori reason to assume the correlation is similar for cities as for states.
A full-on Simpson’s paradox with reversed correlation seems unlikely, since I guess rich cities are typically in rich states. But I could easily imagine something like: “the housing costs of the state are basically irrelevant, the housing costs of the city matters a lot. When you bin cities into states, you’re introducing noise that makes the correlation seem weaker than it is”. And I wouldn’t be completely shocked by something the other way around, where the housing costs of the state matter a lot more than the housing costs of the city. In which case SF would only get the same multiplier here as anywhere else in California.
Still, if this is the data you had, plotting it on this line seems clearly better than not doing so.