$[KNN+CV]longrightarrow$ Considering the dataset with two real$-$valued inputs $x1$ and $x2$ and one binary output $y$ in the table below. Each data point will be referred using the first column $"$ID$"$ in the following. You will use KNN with Euclidean distance to predict $y.$

Write code in Python to perform the following tasks; if needed, you are allowed to use scipy, sklearn, and numpy packages. Please submit one code file via the NCSU GitHub repository you have been given. Show your work. Show steps for reaching the answer.

$\backslash$table$[[$ID$,$x $1,$x $2,$y$],[1,-3\mathrm{.}44,1\mathrm{.}0,**],[2,-6\mathrm{.}48,5\mathrm{.}0,**],[3,0\mathrm{.}93,-2\mathrm{.}0,**],[4,0\mathrm{.}2,2\mathrm{.}0,**],[5,-6\mathrm{.}69,13\mathrm{.}0,**],[6,-5\mathrm{.}85,4\mathrm{.}0,**],[7,3\mathrm{.}0,0\mathrm{.}0,**],[8,-0\mathrm{.}36,0\mathrm{.}0,**],[9,1\mathrm{.}68,-3\mathrm{.}0,**],[10,-0\mathrm{.}45,-3\mathrm{.}0,**]]$

$($a$)(4$ points$)$ What is the leave$-$one$-$out cross$-$validation error of $1$ NN on this dataset?

$($b$)(2$ points$)$ What are the $3$ nearest neighbors for data points $2$ and $8$ respectively.

$($c$)(5$ points$)$ What is the $3-$folded cross$-$validation error of $3$NN on this dataset? For the $i$ th fold, the testing dataset is composed of all the data points whose $($ID mod $3=i-1.$

$($d$)(5$ points$)$ Based on the results of $($a$)$ and $($c$),$ can we determine which is a better classifier, $1$NN or $3$NN$?$ Why? $($Answers without a correct justification will get zero points.$)$