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For those unfamiliar with census geography, census tracts are made up of multiple block groups.

Suppose I have three data tables (all categorical):

  • Block Group Geography x Home Value
  • Block Group Geography x Household Income
  • Census Tract Geography x Home Value x Household Income

Would I be able to use Bayes' Theorem and the information I know about the census tract and block group to calculate the probability of a home's value being in a particular category (i.e. 100k-200k) given that the person owning the home has a certain household income and lives within a particular block group?

If so, is this the correct way to do it:

  • p = P(Home Value [T] | Household Income [T]) where [T] indicates census tract
  • q = Total owner-occupied housing units with a particular home value [BG]/Total owner-occupied housing units [BG] where [BG] indicates block group

P(Home Value [BG] | Household Income [BG]) = $\frac{pq}{\sum_{p,q} pq}$

Thanks for any help!

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