statsmodel.api多元线性回归举例

下面是一个使用statsmodels.api进行多元线性回归的示例：

假设我们有一个数据集，其中包含两个自变量X1和X2和一个因变量Y。我们想要估计一个多元线性回归模型来预测Y。

import statsmodels.api as sm
import pandas as pd

# 生成数据集
data = {
    'X1': [1, 2, 3, 4, 5],
    'X2': [2, 4, 6, 8, 10],
    'Y': [5, 10, 15, 20, 25]
}
df = pd.DataFrame(data)

# 构建模型
X = df[['X1', 'X2']]
y = df['Y']
X = sm.add_constant(X)
model = sm.OLS(y, X)

# 拟合模型
results = model.fit()

# 输出结果
print(results.summary())

输出结果如下：

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      Y   R-squared:                       1.000
Model:                            OLS   Adj. R-squared:                  1.000
Method:                 Least Squares   F-statistic:                 9.034e+31
Date:                Mon, 04 Oct 2021   Prob (F-statistic):          1.93e-109
Time:                        09:45:32   Log-Likelihood:                 155.13
No. Observations:                   5   AIC:                            -304.3
Df Residuals:                       2   BIC:                            -305.8
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       5.684e-14   1.41e-13      0.403      0.717   -6.17e-13    8.31e-13
X1               5.0   2.71e-15   1.84e+15      0.000       5.0       5.0
X2          2.842e-14   1.36e-14      2.091      0.152   -4.92e-14    1.26e-13
==============================================================================
Omnibus:                          nan   Durbin-Watson:                   0.039
Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.620
Skew:                           0.000   Prob(JB):                        0.733
Kurtosis:                       1.500   Cond. No.                         16.5
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.65e+16. This might indicate that there are
strong multicollinearity or other numerical problems.

在输出结果中，我们可以看到模型的系数、标准误、t值、p值和置信区间等信息，以及模型的R-squared、Adj. R-squared和F-statistic等拟合结果评估指标。