Is there a derivation of the linear regression equation from statistical principles? Let us say that we have the equation $y = ax + b$ where $a = \frac{rs_{x}}{s_{y}}$ and $b = \bar{y} - a\bar{x}$. Where does $a$ and $b$ come from? How do statisticians reason their "derivation" if there is one?
See Ordinary Least Squares and Simple Linear Regression at Wikipedia.
See Ordinary Least Squares and Simple Linear Regression at Wikipedia.