Ridge Regression

This is called the $L2-\text{norm}$

Refer to the Lp Norms

$R(B)=\Vert \beta {\Vert }^2={\sum }_j{\beta }_j^2$

Ordinary Least Squares with Penalty

$L(\beta )=\frac{1}{n}||\text{y}-\text{X}\beta |{|}^2+\lambda R(\beta )$

Substituting for $R(\beta )$. We can see that we are using the $L2$ norm. $L(\beta )=\frac{1}{n}||\text{y}-\text{X}\beta |{|}^2+\lambda {\sum }_j{\beta }_j^2$