Q$6.$ a$)$ For a given predictor matrix $x=[x_1,x_2,$cdots$]($say$,$ students scores list$),$ and

the binary response vector $y($students enrolled to college or not$),$ if we transform

every column vector $x_i$ in $x$ to a normalized new vector

$z_i=\frac{x_i-\text{m}\text{e}\text{a}\text{n}(x_i)}{standard\text{d}\text{e}\text{v}\text{i}\text{a}\text{t}\text{i}\text{o}\text{n}of(x_i)}$

Does this normalization will change the AUC performance of logistic regression

results? If yes, specify what the changes are? If not, explain why not?

b$)$ For the same data in part a$),$ if we reform each column vector $x_i$ as

$y_i=e^{x_i}$

Does this transform will change the AUC performance of logistic regression re$-$

sults? Justify your answer.