$(24$ pts$)$ Given the dataset in Table $3,$ answer the following questions:

$($a$)$ Plot the data using scatter plot.

$($b$)$ What is the hyperplane for SVM and the maximal margin?

$($c$)$ Which points are support vectors?

$($d$)$ Given a new data $(-0\mathrm{.}6,0\mathrm{.}5),$ which class it belongs to$?$

Obs.

X$\_\{1\}$

Y

$+$

$1$

$0$

$-1$

$0$

$-1$

$2$

$-1$

$-1$

$3$

$1$

$0$

$1$

$4$

$5$

$0$

Table $3$

X$\_\{2\}$

$9.(20$ pts$)$ Given the data in Table $3,$ please build a CART model to classify the outcome variable Y based on two input features, X$$ and X$2,$ using the recursive binary splitting algorithm.

a$)$ In the first iteration, find the best split.

b$)$ Repeat step b$)$ until each region is pure.

c$)$ Draw the tree structure$(24$ pts$)$ Given the dataset in Table $3,$ answer the following questions:

$($a$)$ Plot the data using scatter plot.

$($b$)$ What is the hyperplane for SVM and the maximal margin?

$($c$)$ Which points are support vectors?

$($d$)$ Given a new data $(-0\mathrm{.}6,0\mathrm{.}5),$ which class it belongs to$?$

$(20$ pts$)$ Given the data in Table $3,$ please build a CART model to classify the outcome variable $Y$ based

on two input features, $x_1$ and $x_2,$ using the recursive binary splitting algorithm.

a$)$ In the first iteration, find the best split.

b$)$ Repeat step b$)$ until each region is pure.

c$)$ Draw the tree structure.