Question:

Implement Linear regression using NumPy. You should implement your code in the provided linear$\_$regression.py file. This python file takes a csv file and a list of features as input. From these list of features, the last feature will be the target label and the remaining ones will be your training inputs. For example, in the following usage scenario, $$linear$.$csv$$ is the csv file and $$Writing$$ is the target label, while $$Math$$ and $$Reading$$ are training inputs.

$python$3$ linear$\_$regression.py linear.csv Math Reading Writing

Output the RMSE score of prediction.

$-$provided linear$\_$regression.py file,is as follow:

import numpy as np

import pandas as pd

import math

import sys

import os

#Todo : define necessary functions

def compute$\_$weights$($X$,$ y$)$:

$"""$

Compute linear regression weights using the normal equation.

X: input features with a column of ones $($bias term$).$

y: target variable.

$"""$

# Normal equation: $($X$^$T $*$ X$)^-1*$ X$^$T $*$ y

weights $=$ np$.$linalg.inv$($X$.$T$.$dot$($X$)).$dot$($X$.$T$).$dot$($y$)$

return weights

def predict$($X$,$ weights$)$:

$"""$

Predict the target variable using the linear model.

X: input features with a column of ones $($bias term$).$

weights: weights of the linear model.

$"""$

predictions $=$ X$.$dot$($weights$)$

return predictions

def rmse$($predictions$,$ targets$)$:

$"""$

Calculate the root mean squared error.

predictions: predicted values.

targets: actual values.

$"""$

return np$.$sqrt$((($predictions $-$ targets$)**2).$mean$())$

def linear$\_$regression$($data$)$:

$"""$

data: input data matrix

return: rmse value

$"""$

#Todo : fill code here

# Extract the features and target variable

features $=$ data.iloc$[$:$,$ :$-1]$

target $=$ data.iloc$[$:$,-1]$

# Add a column of ones to the features $($for the intercept term$)$

features $=$ np$.$hstack$([$np$.$ones$(($features$.$shape$[0],1)),$ features$])$

# Compute weights

weights $=$ compute$\_$weights$($features$,$ target$)$

# Predict the target variable

predictions $=$ predict$($features$,$ weights$)$

# Calculate and return RMSE

return rmse$($predictions$,$ target$)$

# do not modify this function

def load$\_$data$()$:

filename $=$ sys$.$argv$[1]$

feature$\_$matrix $=$ pd$.$read$\_$csv$($filename$)$

feature$\_$matrix $=$ feature$\_$matrix.dropna$()$

features $=$ sys$.$argv$[2$:$]$

#print$($feature$\_$matrix$[$features$])$

return feature$\_$matrix

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

data $=$ load$\_$data$()$

RMSE$\_$SCORE $=$ linear$\_$regression$($data$)$

print$("$RMSE score is : $",$ RMSE$\_$SCORE$)$

$-$linear$.$csv$$contains in the following format: Math, Reading, Writing. There are $1001$ lines of data structured in this way.Math, Reading, Writing. There are $1001$ lines of data structured in this way.im attaching the image of csv file