Notes

from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline

def PolynomialRegression(degree=2, **kwargs):
return make_pipeline(PolynomialFeatures(degree), LinearRegression(**kwargs))


import numpy as np

def make_data(N, err=1.0, rseed=1):
#randomly sample the data
rng = np.random.RandomState(rseed)
X = rng.rand(N, 1) ** 2
y= 10 - 1. / (X.ravel() + 0.1)
if err > 0:
y += err * rng.randn(N)
return X, y
X, y = make_data(40)


import numpy as np
import matplotlib.pyplot as plt
import seaborn; seaborn.set() #plot formatting

X_test = np.linspace(-0.1, 1.1, 500)[:, None]

plt.scatter(X.ravel(), y, color='black')
axis = plt.axis()

for degree in [1, 3, 5, 7]:
#for degree in[15]
y_test = PolynomialRegression(degree).fit(X, y).predict(X_test)
plt.plot(X_test.ravel(), y_test, label='degree={0}'.format(degree))

plt.xlim(-0.1, 1,0)
plt.ylim(-2, 12)
plt.legend(loc='best');