In this lab you'll practice your knowledge on adding polynomial terms to your regression model!

You will be able to:

• Understand how to account for non-linear relationships between predictors and target variable using polynomial terms

Here is a plot with a clearly non-linear shape. Begin to think about what degree polynomial you believe will fit it best.

import numpy as np
import matplotlib.pyplot as plt
% matplotlib inline

def pol(x):
    return x * np.cos(x)

x = np.linspace(0, 12, 100)
rng = np.random.RandomState(1234)
rng.shuffle(x)
x = np.sort(x[:25])
y = pol(x) + np.random.randn(25)*2

plt.scatter(x, y, color='green', s=50, marker='.')

plt.show();

Now it's time to determine the optimal degree of polynomial features for a model that is fit to this data

• Plot a polynomial function using PolynomialFeatures for polynomials up until the second, third and fourth degree. Make sure to label each degree polynomial in your plot.
• Print out the $R^2$ value for each of the three results. Draw conclusions with respect to which degree is best.

## your code here

Great! You now know how to include polynomials in your linear model!