HW$1$: K$-$NN Implementation

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

$(2)(10$ points$)$

$-$ Create a function used to calculate the average price of k$-$NNs 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 $=5$#

$10$ points define a function which is used to find k$-$NN$\text{'}$s average pricethe formula to calculate the Scipy's Euclidean distance of sample $1$ and sample $2$:def find$\_$kNNmean$\_$price$($X$,$ y$,$ selected, k$)$:

$""!"$

for any selected sample, find its K$-$NN neighbors' average price

input:

X: the training dataframe,

y: the training data price,

selected: any row of the testing dataframe,

k: the number of neighbors in the training dataframe. k is int and larger than $0$

return:

k$\_$nn$\text{'}$s average price, floating point

$"\text{'}""$A sample outputsample $=0$: the real price $245300\mathrm{.}0$For a single sample, the k$-$NN prediction:This step will take about $2$ minutes in my case

def root$\_$mse$($X$,$ y$,$ X$\_$test$\_1$k$,$ y$\_$test$\_1$k$,$ k$)$:

$"!",$

For a given k$,$ collect their kNN$\_$average price, then find the rsme

Input:

X$\_$test$\_$copy: dataframe of all testing samples

y$\_$test$\_$copy: data series of all testing sample prices

k: the number of neighbors, int.

Return:

rmse: the root mean square erros, floating point type$-------------------------$

#k $=5$ and rmse $=68890\mathrm{.}19$

for k $=5,$ the rmse $=68890\mathrm{.}19$