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

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#k

$=$

$5$

$$and rmse

$=$

$68890\mathrm{.}19$

for k

$=$

$5$

$,$

$$the rmse