Consider a binary classification problem with $n$ input features $(x_1,x_2,$cdots,$x_n)$ and bi$-$

nary outputs yin$\{0,1\}.$ After training a Logistic Regression model, one obtains opti$-$

mal parameters:

hat$()=(hat({)}_0,$hat$({)}_1,$hat$({)}_2,$cdots,hat$({)}_n)$

Let hat$(OR)$:$R^n(0,)$ be the function that computes, according to the model, the odds

ratio that an input $v=(x_1,x_2,cdots{x}_n)$ belongs to class $y=1.$ Prove that:

$log(hat(OR))=$hat$({)}_0+$hat$({)}_1*x_1+$hat$({)}_2*x_2+$hat$({)}_3*x_3+$cdots$+$hat$({)}_n*x_n$