Suppose you trained a logistic regression classifier and attained the following model

$f(x,)=({}_0+{}_{1}x+{}_2{x}^2),$

where ${}_0=4,{}_1=-5,$ and ${}_2=1.$

$($a$)(6$ points$)$ For which values of $x$ will the classifier predict a value of $1.$

$($b$)(6$ points$)$ Assume each feature is shifted $2-$upwards $($add $2$ to each sample each feature$).$ Compute the new range of values of $x$ that predict $1.$

$($c$)(6$ points$)$ Predict the label for the following testing samples

$\backslash$table$[[x,0\mathrm{.}5,1\mathrm{.}5,3,6,2\mathrm{.}5,2\mathrm{.}7,7,3\mathrm{.}3]]$

$2$

$($d$)(6$ points$)$ Assume that the Sigmoid function is replaced by the following function

$(z)=\frac{e^{-z}}{1+e^{-z}}.$

How will your predictions in the part $($c$)$ change?

$2.$ Suppose you trained a simple logistic regression model and attained the following

hat$(y)={}_0+{}_{1}x,$

where ${}_0=2\mathrm{.}5$ and ${}_1=1\mathrm{.}5.$

$(12$ points$)$ Assume that for each sample $(($:$x_i,y_i\}$ we doubled the label $($i$.$e$.$ updated samples $(x_i,2y_i)).$ Show that the optimal linear regression model for the updated data will be

hat$(y)=5+3{}_1,$

Suppose you are given the following $2-$class data where $+$ represents positive class and $-$ represents negative class. The dataset is given in the table below.

$\backslash$table$[[x_1,x_2,$Label$],[1,1,=$