The OLS statistical formula

Summary

• Setup:
• a sample $X,y$
• a linear regression model $y=Xβ+ε$
• $b={\left( X'X \right)}^{-1}X'y$ is the OLS estimator of $β$
• Result:

$$b=β+{\left( X'X \right)}^{-1}X'ε$$

• This is called the OLS statistical formula .