使用sklearn進行線性回歸和二次回歸的比較

"""
#演示內容：二次回歸和線性回歸的擬合效果的對比
"""
print(__doc__)
 
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from matplotlib.font_manager import FontProperties
font_set = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=20) 
 
def runplt():
    plt.figure()# 定義figure
    plt.title(u'披薩的價格和直徑',fontproperties=font_set)
    plt.xlabel(u'直徑（inch）',fontproperties=font_set)
    plt.ylabel(u'價格（美元）',fontproperties=font_set)
    plt.axis([0, 25, 0, 25])
    plt.grid(True)
    return plt
 
 
#訓練集和測試集數據
X_train = [[6], [8], [10], [14], [18]]
y_train = [[7], [9], [13], [17.5], [18]]
X_test = [[7], [9], [11], [15]]
y_test = [[8], [12], [15], [18]]
 
#畫出橫縱坐標以及若干散點圖
plt1 = runplt()
plt1.scatter(X_train, y_train,s=40)
 
#給出一些點，並畫出線性回歸的曲線
xx = np.linspace(0, 26, 5)
regressor = LinearRegression()
regressor.fit(X_train, y_train)
yy = regressor.predict(xx.reshape(xx.shape[0], 1))
 
plt.plot(xx, yy, label="linear equation")
 
#多項式回歸（本例中為二次回歸）
#首先生成多項式特征
quadratic_featurizer = PolynomialFeatures(degree=2)
X_train_quadratic = quadratic_featurizer.fit_transform(X_train)
 
regressor_quadratic = LinearRegression()
regressor_quadratic.fit(X_train_quadratic, y_train)
 
#numpy.reshape（重塑）給數組一個新的形狀而不改變其數據。在指定的間隔內返回均勻間隔的數字
#給出一些點，並畫出線性回歸的曲線
xx = np.linspace(0, 26, 100)
print (xx.shape)         #(100,)
print (xx.shape[0])      #100
xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1))
print (xx.reshape(xx.shape[0], 1).shape)       #(100,1)
 
plt.plot(xx, regressor_quadratic.predict(xx_quadratic), 'r-',label="quadratic equation")
plt.legend(loc='upper left')
plt.show()
 
X_test_quadratic = quadratic_featurizer.transform(X_test)
print('linear equation  r-squared', regressor.score(X_test, y_test))
print('quadratic equation r-squared', regressor_quadratic.score(X_test_quadratic, y_test))

linear equation r-squared 0.8283656795834485
quadratic equation r-squared 0.9785451046983036

二次回歸的擬合效果更好。