I am working on a project that looks at the relationship between an indicator (economic/social/health) (x) and an outcome (teen pregnancy/infant mortality) (y). I ran linear regression on the variables and it returned coefficients for the equation. The data is at the neighborhood level.
The purpose of the project is to develop short statements about the relationship between the indicator and the outcome. The statements were to be written in this type of fashion:
"Neighborhoods with the highest number of (Indicator) have more than twice the rate of teen pregnancy than neighborhoods with the least number."
To make such a statement, I ranked the indicator (x) values from highest to lowest and divided the indicator data into thirds. I then took the average of each third and entered that number into the linear regression equation.
My question is: When I enter the average value of x into a linear regression equation, do I get the average value of the outcome (teen pregnancy)? How would I write a statement based on entering the average value of the indicator (x)?