我们仍然使用披萨直径的价格的数据
import matplotlib matplotlib.rcParams['font.sans-serif']=[u'simHei'] matplotlib.rcParams['axes.unicode_minus']=False import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures X_train = [[6],[8],[10],[14],[18]] y_train = [[7],[9],[13],[17.5],[18]] X_test = [[6],[8],[11],[16]] y_test = [[8],[12],[15],[18]] LR = LinearRegression() LR.fit(X_train,y_train) xx = np.linspace(0,26,100) yy = LR.predict(xx.reshape(xx.shape[0],1)) plt.plot(xx,yy)
二阶多项式回归
# In[1] 二次回归，二阶多项式回归 #PolynomialFeatures转换器可以用于为一个特征表示增加多项式特征 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) plt.plot(xx,yy_quadratic,c='r',linestyle='--')
# In[2] 图参数，输出结果 plt.title("披萨价格和直径的关系") plt.xlabel("直径") plt.ylabel("价格") plt.axis([0,25,0,25]) plt.grid(True) plt.scatter(X_train,y_train) print("X_train ",X_train) print("X_train_quadratic ",X_train_quadratic) print("X_test ",X_test) print("X_test_quadratic ",X_test_quadratic) print("简单线性规划R方",LR.score(X_test,y_test)) print("二阶多项式回归R方",regressor_quadratic.score(X_test_quadratic,y_test))
X_train [[6], [8], [10], [14], [18]] X_train_quadratic [[ 1. 6. 36.] [ 1. 8. 64.] [ 1. 10. 100.] [ 1. 14. 196.] [ 1. 18. 324.]] X_test [[6], [8], [11], [16]] X_test_quadratic [[ 1. 6. 36.] [ 1. 8. 64.] [ 1. 11. 121.] [ 1. 16. 256.]] 简单线性规划R方 0.809726797707665
三阶多项式回归
# In[3] 尝试三阶多项式回归 cubic_featurizer = PolynomialFeatures(degree=3) X_train_cubic = cubic_featurizer.fit_transform(X_train) X_test_cubic = cubic_featurizer.transform(X_test) regressor_cubic = LinearRegression() regressor_cubic.fit(X_train_cubic,y_train) xx_cubic = cubic_featurizer.transform(xx.reshape(xx.shape[0],1)) yy_cubic = regressor_cubic.predict(xx_cubic) plt.plot(xx,yy_cubic,c='g',linestyle='--') plt.show() print("X_train ",X_train) print("X_train_cubic ",X_train_cubic) print("X_test ",X_test) print("X_test_cubic ",X_test_cubic) print("三阶多项式回归R方",regressor_cubic.score(X_test_cubic,y_test))
X_train [[6], [8], [10], [14], [18]] X_train_cubic [[1.000e+00 6.000e+00 3.600e+01 2.160e+02] [1.000e+00 8.000e+00 6.400e+01 5.120e+02] [1.000e+00 1.000e+01 1.000e+02 1.000e+03] [1.000e+00 1.400e+01 1.960e+02 2.744e+03] [1.000e+00 1.800e+01 3.240e+02 5.832e+03]] X_test [[6], [8], [11], [16]] X_test_cubic [[1.000e+00 6.000e+00 3.600e+01 2.160e+02] [1.000e+00 8.000e+00 6.400e+01 5.120e+02] [1.000e+00 1.100e+01 1.210e+02 1.331e+03] [1.000e+00 1.600e+01 2.560e+02 4.096e+03]] 三阶多项式回归R方 0.8356924156036954
九阶多项式回归
# In[4] 尝试九阶多项式回归 nine_featurizer = PolynomialFeatures(degree=9) X_train_nine = nine_featurizer.fit_transform(X_train) X_test_nine = nine_featurizer.transform(X_test) regressor_nine = LinearRegression() regressor_nine.fit(X_train_nine,y_train) xx_nine = nine_featurizer.transform(xx.reshape(xx.shape[0],1)) yy_nine = regressor_nine.predict(xx_nine) plt.plot(xx,yy_nine,c='k',linestyle='--') plt.show() print("X_train ",X_train) print("X_train_nine ",X_train_nine) print("X_test ",X_test) print("X_test_nine ",X_test_nine) print("九阶多项式回归R方",regressor_nine.score(X_test_nine,y_test))
X_train [[6], [8], [10], [14], [18]] X_train_nine [[1.00000000e+00 6.00000000e+00 3.60000000e+01 2.16000000e+02 1.29600000e+03 7.77600000e+03 4.66560000e+04 2.79936000e+05 1.67961600e+06 1.00776960e+07] [1.00000000e+00 8.00000000e+00 6.40000000e+01 5.12000000e+02 4.09600000e+03 3.27680000e+04 2.62144000e+05 2.09715200e+06 1.67772160e+07 1.34217728e+08] [1.00000000e+00 1.00000000e+01 1.00000000e+02 1.00000000e+03 1.00000000e+04 1.00000000e+05 1.00000000e+06 1.00000000e+07 1.00000000e+08 1.00000000e+09] [1.00000000e+00 1.40000000e+01 1.96000000e+02 2.74400000e+03 3.84160000e+04 5.37824000e+05 7.52953600e+06 1.05413504e+08 1.47578906e+09 2.06610468e+10] [1.00000000e+00 1.80000000e+01 3.24000000e+02 5.83200000e+03 1.04976000e+05 1.88956800e+06 3.40122240e+07 6.12220032e+08 1.10199606e+10 1.98359290e+11]] X_test [[6], [8], [11], [16]] X_test_nine [[1.00000000e+00 6.00000000e+00 3.60000000e+01 2.16000000e+02 1.29600000e+03 7.77600000e+03 4.66560000e+04 2.79936000e+05 1.67961600e+06 1.00776960e+07] [1.00000000e+00 8.00000000e+00 6.40000000e+01 5.12000000e+02 4.09600000e+03 3.27680000e+04 2.62144000e+05 2.09715200e+06 1.67772160e+07 1.34217728e+08] [1.00000000e+00 1.10000000e+01 1.21000000e+02 1.33100000e+03 1.46410000e+04 1.61051000e+05 1.77156100e+06 1.94871710e+07 2.14358881e+08 2.35794769e+09] [1.00000000e+00 1.60000000e+01 2.56000000e+02 4.09600000e+03 6.55360000e+04 1.04857600e+06 1.67772160e+07 2.68435456e+08 4.29496730e+09 6.87194767e+10]] 九阶多项式回归R方 -0.09435666704291412
所有代码
# -*- coding: utf-8 -*- import matplotlib matplotlib.rcParams['font.sans-serif']=[u'simHei'] matplotlib.rcParams['axes.unicode_minus']=False import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures X_train = [[6],[8],[10],[14],[18]] y_train = [[7],[9],[13],[17.5],[18]] X_test = [[6],[8],[11],[16]] y_test = [[8],[12],[15],[18]] LR = LinearRegression() LR.fit(X_train,y_train) xx = np.linspace(0,26,100) yy = LR.predict(xx.reshape(xx.shape[0],1)) plt.plot(xx,yy) # In[1] 二次回归，二阶多项式回归 #PolynomialFeatures转换器可以用于为一个特征表示增加多项式特征 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) plt.plot(xx,yy_quadratic,c='r',linestyle='--') # In[2] 图参数，输出结果 plt.title("披萨价格和直径的关系") plt.xlabel("直径") plt.ylabel("价格") plt.axis([0,25,0,25]) plt.grid(True) plt.scatter(X_train,y_train) print("X_train ",X_train) print("X_train_quadratic ",X_train_quadratic) print("X_test ",X_test) print("X_test_quadratic ",X_test_quadratic) print("简单线性规划R方",LR.score(X_test,y_test)) print("二阶多项式回归R方",regressor_quadratic.score(X_test_quadratic,y_test)) # In[3] 尝试三阶多项式回归 cubic_featurizer = PolynomialFeatures(degree=3) X_train_cubic = cubic_featurizer.fit_transform(X_train) X_test_cubic = cubic_featurizer.transform(X_test) regressor_cubic = LinearRegression() regressor_cubic.fit(X_train_cubic,y_train) xx_cubic = cubic_featurizer.transform(xx.reshape(xx.shape[0],1)) yy_cubic = regressor_cubic.predict(xx_cubic) plt.plot(xx,yy_cubic,c='g',linestyle='--') plt.show() print("X_train ",X_train) print("X_train_cubic ",X_train_cubic) print("X_test ",X_test) print("X_test_cubic ",X_test_cubic) print("三阶多项式回归R方",regressor_cubic.score(X_test_cubic,y_test)) # In[4] 尝试九阶多项式回归 nine_featurizer = PolynomialFeatures(degree=9) X_train_nine = nine_featurizer.fit_transform(X_train) X_test_nine = nine_featurizer.transform(X_test) regressor_nine = LinearRegression() regressor_nine.fit(X_train_nine,y_train) xx_nine = nine_featurizer.transform(xx.reshape(xx.shape[0],1)) yy_nine = regressor_nine.predict(xx_nine) plt.plot(xx,yy_nine,c='k',linestyle='--') plt.show() print("X_train ",X_train) print("X_train_nine ",X_train_nine) print("X_test ",X_test) print("X_test_nine ",X_test_nine) print("九阶多项式回归R方",regressor_nine.score(X_test_nine,y_test))
