#参考网址http://www.statsmodels.org

statsmodels有多个api这里我们只介绍statsmodels.api，statsmodels.formula.api 用不同的api估计模型，语法是不一样的

import numpy as np

import statsmodels.api as sm

import statsmodels.formula.api as smf

#准备一些数据

data=pd.DataFrame(np.random.randint(3,10,(10,3)),columns=["y","x1","x2"])

#------------------------首先介绍用statsmodels.api实现OLS线性回归

#设定模型因变量自变量

model = sm.OLS(data["y"], data.loc[:,["x1","x2"]])

#估计模型

results = model.fit()

#查看模型估计结果

print(results.summary()) #这个结果报告表格比sklearn库更接近统计学软件的报告表格

OLS Regression Results

=======================================================================================

Dep. Variable: y R-squared (uncentered): 0.752

Model: OLS Adj. R-squared (uncentered): 0.690

Method: Least Squares F-statistic: 12.12

Date: Fri, 27 Nov 2020 Prob (F-statistic): 0.00379

Time: 19:30:18 Log-Likelihood: -24.375

No. Observations: 10 AIC: 52.75

Df Residuals: 8 BIC: 53.35

Df Model: 2

Covariance Type: nonrobust

==============================================================================

coef std err t P>|t| [0.025 0.975]

------------------------------------------------------------------------------

x1 0.0033 0.443 0.007 0.994 -1.018 1.025

x2 0.8768 0.468 1.873 0.098 -0.203 1.956

==============================================================================

Omnibus: 1.234 Durbin-Watson: 0.858

Prob(Omnibus): 0.540 Jarque-Bera (JB): 0.186

Skew: -0.333 Prob(JB): 0.911

Kurtosis: 3.066 Cond. No. 5.05

==============================================================================

#results对象还有predict,resid,ssr等很多方法属性

#------------------------然后介绍用statsmodels.formula.api实现OLS线性回归

我们还可以用更接近R的语法实现上面的回归结果如下：

model2 = smf.ols('y ~ x1 + np.log(x2)', data=data).fit()

print(model2.summary())

用过R的人，应该会更喜欢用这个语法来做回归。而且可以直接用数学表达式来表示一个变量，而不用真正生成这么一个变量