\begin{equation} \label{eq:ris1}
\hat{\beta}^{\text{c-ridge}} =  \underset{\beta}{\operatorname{argmin}}  \left\{ \sum_{i=1}^{n} \Big((y^c_i - \beta_0 - \sum_{j=1}^{p} x^c_{ij} \beta_j \Big)^2 + \lambda \sum_{j=1}^{p} \beta_j^2 \right\}. 
\end{equation}
