1.最小二乘法数学表达式：

 

使经验函数风险最小化 = 损失函数（平方损失）

2.示例

1 from sklearn import linear_model
2 reg = linear_model.LinearRegression()
3 reg.fit ([[0, 0], [1, 1], [2, 2]], [0, 1, 2])
4 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)
5 reg.coef_
6 array([ 0.5,  0.5])

模型参数 coef = w 相关系数 intercept = w0 截距 在fit_intercept = Flase的时候将会返回0

　　copy_x  是否对x值进行复制保存

　　fit_intercept 是否显示截距 即b的值
　　n_jobs  运算时电脑几核运行
　　normalize  在进行最小二乘法运算时x是否先标准化，当_fit_intercep_t为False时该参数默认取消

3.官方案例

 1 import matplotlib.pyplot as plt
 2 import numpy as np
 3 from sklearn import datasets, linear_model
 4 from sklearn.metrics import mean_squared_error, r2_score
 5 
 6 # Load the diabetes dataset
 7 diabetes_X, diabetes_y = datasets.load_diabetes(return_X_y=True)
 8 print(diabetes_y)
 9 # Use only one feature
10 diabetes_X = diabetes_X[:, np.newaxis, 2]
11 
12 
13 # Split the data into training/testing sets
14 diabetes_X_train = diabetes_X[:-20]
15 diabetes_X_test = diabetes_X[-20:]
16 
17 # Split the targets into training/testing sets
18 diabetes_y_train = diabetes_y[:-20]
19 diabetes_y_test = diabetes_y[-20:]
20 
21 # Create linear regression object
22 regr = linear_model.LinearRegression()
23 
24 # Train the model using the training sets
25 regr.fit(diabetes_X_train, diabetes_y_train)
26 
27 # Make predictions using the testing set
28 diabetes_y_pred = regr.predict(diabetes_X_test)
29 
30 # The coefficients
31 print('Coefficients: \n', regr.coef_)
32 # The mean squared error  #残差平方和
33 print('Mean squared error: %.2f'
34       % mean_squared_error(diabetes_y_test, diabetes_y_pred))
35 # The coefficient of determination: 1 is perfect prediction
36 print('Coefficient of determination: %.2f'
37       % r2_score(diabetes_y_test, diabetes_y_pred))
38 
39 # Plot outputs
40 plt.scatter(diabetes_X_test, diabetes_y_test,  color='black')
41 plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=3)
42 
43 plt.xticks(())
44 plt.yticks(())