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I'd like to predict number of schools by state in the US based on each state's population. Here's what I know:

  1. Population of all states in the US
  2. The number of schools in 10 of the 50 states in the US
  3. The total number of schools in the US

I'm thinking I can establish a linear regression between population and number of schools in my sample of 10, then use this coefficient and slope to predict the other 40 states. However, I know the total number of schools in the US (let the variable x represent this value).

My questions:

  1. How do I predict schools in the other 40 states and ensure that the total number of schools in these 40 states plus my known sample of 10 states comes to x?
  2. Is there a better way to approach this problem?
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