import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

X = np.array([258.0, 270.0, 294.0, 
              320.0, 342.0, 368.0, 
              396.0, 446.0, 480.0, 586.0])\
             [:, np.newaxis]

y = np.array([236.4, 234.4, 252.8, 
              298.6, 314.2, 342.2, 
              360.8, 368.0, 391.2,
              390.8])

lr = LinearRegression()
pr = LinearRegression()
quadratic = PolynomialFeatures(degree=2)
X_quad = quadratic.fit_transform(X)

# fit linear features
lr.fit(X, y)
X_fit = np.arange(250, 600, 10)[:, np.newaxis]
y_lin_fit = lr.predict(X_fit)

# fit quadratic features
pr.fit(X_quad, y)
y_quad_fit = pr.predict(quadratic.fit_transform(X_fit))

# plot results
plt.scatter(X, y, label='Training points')
plt.plot(X_fit, y_lin_fit, label='Linear fit', linestyle='--')
plt.plot(X_fit, y_quad_fit, label='Quadratic fit')
plt.xlabel('Explanatory variable')
plt.ylabel('Predicted or known target values')
plt.legend(loc='upper left')

plt.tight_layout()
plt.show()

y_lin_pred = lr.predict(X)
y_quad_pred = pr.predict(X_quad)

print('Training MSE linear: %.3f, quadratic: %.3f' % (
        mean_squared_error(y, y_lin_pred),
        mean_squared_error(y, y_quad_pred)))
print('Training R^2 linear: %.3f, quadratic: %.3f' % (
        r2_score(y, y_lin_pred),
        r2_score(y, y_quad_pred)))