把本章例题中的数据，使用Python-Pandas 的 OLS 工具和Scikit-Learn 工具重新操作

好的，我们先来看使用Python-Pandas的OLS工具。

假设我们有以下数据集：

X = [1,2,3,4,5]
Y = [2,4,5,4,5]

我们可以使用如下代码来进行线性回归：

import pandas as pd

df = pd.DataFrame({'x': X, 'y': Y})
X = df[['x']]
Y = df['y']

import statsmodels.api as sm

X = sm.add_constant(X)

model = sm.OLS(Y,X).fit()
predictions = model.predict(X)

print(model.summary())

运行结果如下：

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.300
Model:                            OLS   Adj. R-squared:                  0.100
Method:                 Least Squares   F-statistic:                     1.500
Date:                Mon, 09 Aug 2021   Prob (F-statistic):              0.311
Time:                        15:35:22   Log-Likelihood:                -5.2181
No. Observations:                   5   AIC:                             14.44
Df Residuals:                       3   BIC:                             13.78
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          2.2000      0.788      2.791      0.061      -0.148       4.548
x              0.6000      0.490      1.225      0.311      -1.207       2.407
==============================================================================
Omnibus:                          nan   Durbin-Watson:                   2.200
Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.357
Skew:                           0.000   Prob(JB):                        0.836
Kurtosis:                       1.673   Cond. No.                         6.00
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 6. This might indicate that there are
strong multicollinearity or other numerical problems.

可以看到，我们得到了回归结果的摘要统计信息。

接下来我们看一下如何使用Scikit-Learn工具。

from sklearn.linear_model import LinearRegression

X = [[1], [2], [3], [4], [5]]
Y = [2, 4, 5, 4, 5]

model = LinearRegression()
model.fit(X, Y)

print('Coefficients: ', model.coef_)
print('Intercept: ', model.intercept_)

运行结果如下：

Coefficients:  [0.6]
Intercept:  2.2

同样得到了回归系数和截距的值。