Python please!!!I hope you can help me with Problem 6. Thank you!

Here is the data set and code for previous question (Problem 2), which is relevant with Problem 6.

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from sklearn.linear_model import LinearRegression import pandas as pd import pylab as plt import seaborn import numpy.random as nprnd import random

%matplotlib inline

# Import data df = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0) df.head()

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from sklearn.linear_model import LinearRegression from sklearn.model_selection import train_test_split

# Set y to be the sales in df y = df['sales']

# Set X to be just the features described above in df, also create a new column called interecept which is just 1. X = df.drop(['sales'],1)

# Randomly split data into training and testing - 80% training, 20% testing. X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Create linear regression object regr = LinearRegression()

# Train the model using the training sets regr.fit(X_train, y_train)

# The coefficients print('Coefficients: ', regr.coef_) ==============Code Chunk==================

Please provide relevant answers and Python code. (Screenshots of your Jupyter Notebook are okay!!! )

Out [3]: 1 230.1 37.8 2 44.5 39.3 3 17.2 45.9 4 151.5 41.3 5 180.8 10.8 TV radio newspaper sales 69.2 22.1 45.1 10.4 69.3 9.3 58.5 18.5 58.4 12.9 What are the features (variables, covariates, all mean the same thing)? TV: advertising dollars spent on TV for a single product in a given market (in thousands of dollars) Radio: advertising dollars spent on Radio Newspaper: advertising dollars spent on Newspaper . Sales: Number of 1k units sold Goal: Predict the amount of sales in a given market based on the advertising in TV, Radio and Newspaper. Problem 6 : Computing to Problem 2 via gradient descent. Let where (x. y) are as in Problem 2. [10 points] a) Solve VF(B) - 0 for B in terms of X and y and show that the solution is Hint: Use the product rule for inner products afer rewriting [10 points] d) Repeat part c) but for your scaled features. Do you notice that you can obtain convergence with a lower number of iterations and higher learning rate? Explain why rescaling your features could have this impact. from sklearn import preprocessing X_scaledpreprocessing. scale (X) v scaled v np, mean (v) [10 points] e) Finally consider the Lasso regularized OLS FAA : i=1 using the optimal found in Problem 4, rewrite your gradient descent algorithm for this reguarlized norm. Ensure you used your scaled features