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I have done this analysis before but want to open it up to the community because I have not considered alternative methods.

I essentially am trying to "score" ZIP codes for how much a ZIP code demands private school and related goods and services. I have data for each ZIP code on...

  1. Household income (e.g., % of families earning above certain thresholds
  2. Level of education attainment (e.g., % of families earning bachelors, doctorates, etc.
  3. Level of private school enrollment (e.g., # and X% of the ZIP code is enrolled in PS
  4. Number of high quality public school alternatives

I would like to be able to create a function so that I can enter the values of each ZIP code and then have a result that returns and says demand is X%ile along a curve, but the problem is I don't have a Y variable that is just "private school demand". I can and in the past have used private school enrollment as a proxy, but I am wondering what you all think I should do here.

Thanks very much.

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If you don't have the $y$, then you can't learn a function which gives you $\mathbb{E}(y\vert x)$, plain and simple. Using a proxy measure, as you've done, is probably the next best thing but you open yourself up to problems without knowing how and when the proxy is a bad proxy for the outcome.

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