Requirements: Implement K nearest neighbors algorithm to predict the housing median value

$($using sk$-$learn library for verification only, no credit if you submit sk$-$learn k$-$NN $)$

$-$ You are given X$\_$tain, y$\_$train, X$\_$test, and y$\_$test $4$ subsets of data for ML$.$

$-$ You need to complete the following steps:

$(1)(5$ points$)$

$-$ Make a copy of $4$ subsets of data to avoid the sharing address problem.

$-$ To speed up the computation, select the first $5000$ samples from training datasets for training, and first $1000$ sample from testing datasets for testing

$-$ Check $($a$)$ shape, $($b$)$ head$(),$ and $($c$)$ data types of $4$ sampled training and testing subsets;

$(2)(10$ points$)$

$-$ Create a function used to calculate average price of k$-$NN$\text{'}$s in the training subset for any given testing sample and a given k

$-$ Test a sample from the testing subset and compare the k$-$NN price $($k$=5)$ with the sample real price.

$(3)(10$ points$)$

$-$ Create a function used to find root mean squared$-$error for all $1000$ X$\_$test samples with given k $=5$

$(4)(5$ points$)$

$-$ run a loop to find the rmses of all k$\text{'}$s in range$(1,31,5),$ keep them in a list

$**$ This loop will take a while to get outputs.

$(5)(5$ points$)$

$-$ Compare the above rmses $($step $4)$ with the given built$-$in knn model and plot the rmses ~ k

$(6)(5$ points$)$

$-$ run the rest of given code$($Linear$,$ Decision Tree, Random Forest$),$ write a short summary on your observations after comparing your K$-$NN with other $4$ algorithms