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 .