I'm trying to show that $\hat\sigma^2 =\frac{\sum\hat\epsilon^2}{n-2}$ is an estimator without biais and I started with:
$$\hat\epsilon_i=y_i-\hat y_i$$
and my teacher suggested me to use the formula I gave in the title, which works to demonstrate what I am looking for, but which I don't understand.
Thus why is $\hat y_i= \hat\beta_1-\hat\beta_2x_i$?
what frustrates me the more is why does the $x_i$ doesn't have an hat, like its little friend $y_i$?