Polynomial Regression with Scikit-learn

[EngWiPy]

Hello,

I followed an example in a book that compares polynomial regression with linear regression. We have one feature or explanatory variable. The code is the following:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

X_train = np.array([6, 8, 10, 14, 18]).reshape(-1, 1)
Y_train = np.array([7, 9, 13, 17.5, 18])

X_test = np.array([6, 8, 11, 16]).reshape(-1, 1)
Y_test = np.array([8, 12, 15, 18])

regressor_linear = LinearRegression()
regressor_linear.fit(X_train, Y_train)

xx = np.linspace(0, 25, 100)
yy = regressor_linear.predict(xx.reshape(xx.shape[0], 1))

plt.plot(xx, yy)

quadratic_featurizer = PolynomialFeatures(degree = 2)
X_train_quadratic = quadratic_featurizer.fit_transform(X_train)
X_test_quadratic = quadratic_featurizer.transform(X_test)

regressor_quadratic = LinearRegression()
regressor_quadratic.fit(X_train_quadratic, Y_train)

xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1))
yy_quadratic = regressor_quadratic.predict(xx_quadratic)
print(xx_quadratic)

plt.plot(xx_quadratic, yy_quadratic)
plt.title("Polynomial Vs Linear Regression")
plt.xlabel("Pizza diameter")
plt.ylabel("Pizza Price")
plt.scatter(X_train, Y_train)
plt.axis([0, 25, 0, 25])
plt.grid(True)
plt.show()

However, the figure (attached) shows 4 curves not just two. Why? In the book it shows just two.

 

[Mark44]

Hello,

I followed an example in a book that compares polynomial regression with linear regression. We have one feature or explanatory variable. The code is the following:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

X_train = np.array([6, 8, 10, 14, 18]).reshape(-1, 1)
Y_train = np.array([7, 9, 13, 17.5, 18])

X_test = np.array([6, 8, 11, 16]).reshape(-1, 1)
Y_test = np.array([8, 12, 15, 18])

regressor_linear = LinearRegression()
regressor_linear.fit(X_train, Y_train)

xx = np.linspace(0, 25, 100)
yy = regressor_linear.predict(xx.reshape(xx.shape[0], 1))

plt.plot(xx, yy)

quadratic_featurizer = PolynomialFeatures(degree = 2)
X_train_quadratic = quadratic_featurizer.fit_transform(X_train)
X_test_quadratic = quadratic_featurizer.transform(X_test)

regressor_quadratic = LinearRegression()
regressor_quadratic.fit(X_train_quadratic, Y_train)

xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1))
yy_quadratic = regressor_quadratic.predict(xx_quadratic)
print(xx_quadratic)

plt.plot(xx_quadratic, yy_quadratic)
plt.title("Polynomial Vs Linear Regression")
plt.xlabel("Pizza diameter")
plt.ylabel("Pizza Price")
plt.scatter(X_train, Y_train)
plt.axis([0, 25, 0, 25])
plt.grid(True)
plt.show()

However, the figure (attached) shows 4 curves not just two. Why? In the book it shows just two.
View attachment 215921

Are you asking why the vertical line segment (gold) and the sloped segment (red) are plotted? I suspect it's due to the line plt.plot(xx, yy). You could test this by commenting that line out and seeing whether those two lines go away.

 

[EngWiPy]

Are you asking why the vertical line segment (gold) and the sloped segment (red) are plotted? I suspect it's due to the line plt.plot(xx, yy). You could test this by commenting that line out and seeing whether those two lines go away.

Yes, I meant the gold and red ones. They appear along with the green one due to the following line

plt.plot(xx_quadratic, yy_quadratic)

Commenting the above line removes the three mentioned curves. But why do I have 2 extra curves?

 

[EngWiPy]

OK, I discovered my mistake. I must plot

plt.plot(xx, yy_quadratic)

and not

plt.plot(xx_quadratic, yy_quadratic)

The new figure is attached.

Thanks