I'd like to predict number of schools by state in the US based on each state's population. Here's what I know:
- Population of all states in the US
- The number of schools in 10 of the 50 states in the US
- 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).
- 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?
- Is there a better way to approach this problem?