Equation with condition

Question

I'd like to create the following equation:

Could you please give me a solution? Thank you.

Answer 1

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
   \hat{y}_i= \begin{cases} 
        y_i, & \text{if}\ i\notin I\\ 
        (x\hat{\beta})_i, & \text{if}\ i \in I \end{cases}
\]
\end{document}