Model vs Fitted Line

Our regression model is given by

In this context we will call and the model parameters. We are trying to calculate these - they are unknowns. In trying to calculate the model parameters, we generated estimated parameters, and , which are known values (they are known because we generated them). We use these estimated parameters to produce a specific fitted line:

This fitted line produces a specific predicted value given an specific observed value x;

Note that we can use this fitted line to make reverse predictions as well. If we have a specific y, we can calculate an estimated .