8-1 什么是多项式回归

Notbook 示例

Notbook 源码

 1 [1]
 2 import numpy as np
 3 import matplotlib.pyplot as plt
 4 [2]
 5 x = np.random.uniform(-3, 3, size=100)
 6 X = x.reshape(-1,1)
 7 [3]
 8 y = 0.5 * x**2 + x + 2 + np.random.normal(0, 1, size=100)
 9 [4]
10 plt.scatter(x,y)
11 <matplotlib.collections.PathCollection at 0x1c6b9056910>
12 
13 [5]
14 from sklearn.linear_model import LinearRegression
15 
16 lin_reg = LinearRegression()
17 lin_reg.fit(X,y)
18 LinearRegression()
19 [6]
20 y_predict = lin_reg.predict(X)
21 [7]
22 plt.scatter(X, y)
23 plt.plot(x, y_predict, color='r')
24 [<matplotlib.lines.Line2D at 0x1c6bba7a4c0>]
25 
26 解决方案， 添加一个特征
27 [8]
28 (X**2).shape
29 (100, 1)
30 [9]
31 X2 = np.hstack([X,X**2])
32 [10]
33 X2.shape
34 (100, 2)
35 [11]
36 lin_reg2 = LinearRegression()
37 lin_reg2.fit(X2,y)
38 y_predict2 = lin_reg2.predict(X2)
39 [12]
40 plt.scatter(X, y)
41 plt.plot(x, y_predict2, color='r')
42 [<matplotlib.lines.Line2D at 0x1c6bbaeaaf0>]
43 
44 [13]
45 plt.scatter(X, y)
46 plt.plot(np.sort(x), y_predict2[np.argsort(x)], color='r')
47 [<matplotlib.lines.Line2D at 0x1c6bbb5d580>]
48 
49 [14]
50 lin_reg2.coef_
51 array([1.20691609, 0.45458127])
52 [15]
53 lin_reg2.intercept_
54 2.0128010763968693