Instead of using X:$,2$ as a feature in our second model, we decided to transform

it and use X

$2$

:$,2$

instead. That is$,$ the dataset we use is modified as follows:

Y bias X:$,1$ X

$2$

:$,2$

$-111(-1)2=1$

$31-20$

$2=0$

$4111$

$2=1$

Accordingly, we calculate a single prediction using the new model as specified below:

y

new $=\backslash$theta

new

$0+\backslash$theta

new

$1$ x$1+\backslash$theta

new

$2$ x

$2$

$2$

Is it possible to find a unique optimal solution in this case? If so$,$ compute $\backslash$theta

new and the

corresponding value of MSE. If not, explain why this is not possible. Regardless of which

way you answer, similar to part d$),$ explicitly write out the matrix Xnew for this problem

and show all steps.