$3.$ Here we explore the maximal margin classifier on a toy data set.

$($a$)$ We are given n $=8$ observations in p $=2$ dimensions. For each observation, there is an associated class label.

Obs. X$1$ X$2$ Y

$114$ Blue

$234$ Red

$343$ Red

$422$ Blue

$542$ Red

$644$ Red

$712$ Blue

$813$ Blue

Sketch the observations.

$($b$)$ Sketch the optimal separating hyperplane, and provide the equation for this hyperplane $($of the form $(9\mathrm{.}1)$ from the book pdf$).$

$($c$)$ Describe the classification rule for the maximal margin classifier. It should be something along the lines of $$Classify to Red if $\backslash$beta $0+\backslash$beta $1$X$1+\backslash$beta $2$X$2>0,$ and classify to Blue otherwise.$$ Provide the values for $\backslash$beta $0,\backslash$beta $1,$ and $\backslash$beta $2.$

$($d$)$ On your sketch, indicate the margin for the maximal margin hyperplane.

$($e$)$ Indicate the support vectors for the maximal margin classifier.

$($f$)$ Argue that a slight movement of the seventh observation would not affect the maximal margin hyperplane.

$($g$)$ Sketch a hyperplane that is not the optimal separating hyperplane, and provide the equation for this hyperplane.

$($h$)$ Draw an additional observation o

please label each part of the question from a$-$h to avoid confusion and clear and legible graphs