Implement linear regression to predict Yscore $.$ Use batch gradient descent as your optimization technique with the Least Mean Square objective function. Use a learning rate of r$=103$ and train for a maximum of T$=10$ epochs. Report your final LMS error on the test data, and provide a plot of the training error computed at each epoch. Initialze your parameters randomly from a normal distribution wi$$N$(0,1).$ You will need to implement linear regression with no regularization, l$1$ regularization, and l$2$ regularizaiton.

First, modify the function below to initialize parameters by drawing from the normal distribution.

$[]$

# MODIFY THIS

def initialize$\_$parameters$($n$)$:

$"""$

This function initializes the parameters by drawing from a normal distribution.

args:

n$\_$features $-$ the number of features to return a vector for

output:

w $-($ feature x $1$ column vector $)-$ vector of randomly initialized parameters"""

return np$.$random.normal$(0,1,($n$\_$features, $1))$