$(16$ points$)$ Use the data chart below to answer the following questions without using any ML R functions $($like kmeans, hclust, or

$k).$ Feel free to use any basic utilities $R$ functions to calculate your answers. For each part, you must include all the work needed to

justify and obtain your answers in order to receive full credit.

$($a$)$ Use the $3-$nearest neighbor algorithm with the Manhattan metric to calculate the

predicted target $($color$)$ of the point $(5,5,4).$ Make sure to indicate which of the

points are the $3$ nearest neighbors.

$($b$)$ Suppose that P$1$ and P$3$ are randomly selected as centroids for the $2-$means

clustering algorithm $($with the Euclidean metric$).$

$($i$)$ For the other four points, indicate for each which cluster they get assigned to $($call

P$1\text{'}$s cluster as "cluster #$1"$ and P$3\text{'}$s as "cluster #$2")$

$($ii$)$ Compute the new centroids of the clusters after $($i$)$ has been completed.

NOTE: There will be little or no partial credit for this problem, so please triple

check your work.