python中的单变量回归

Question

需要在python的一个数据帧中的列与同一数据帧中的其他几列之间运行多个单因素（单变量）回归模型

-

所以基于图像，我想在x1和dep，x2和dep等之间运行回归模型，依此类推

想要输出-beta，截距，R-sq，p值，SSE，AIC，BIC，残差的正态性检验等

Answer 1

您可以在此处使用两个选项。一种是流行的scikit-learn库。用途如下

from sklearn.linear_model import LinearRegression
model = LinearRegression()
model.fit(X, y)  # where X is your feature data and y is your target
reg.score(X, y)  # R^2 value
>>> 0.87
reg.coef_  # slope coeficients
>>> array([1.45, -9.2])
reg.intercept_  # intercept
>>> 6.1723...

您可以使用scikit进行其他统计。

另一个选择是statsmodels，它为模型的统计信息提供了更为丰富的细节

import numpy as np
import statsmodels.api as sm

# generate some synthetic data
nsample = 100
x = np.linspace(0, 10, 100)
X = np.column_stack((x, x**2))
beta = np.array([1, 0.1, 10])
e = np.random.normal(size=nsample)

X = sm.add_constant(X)
y = np.dot(X, beta) + e

# fit the model and get a summary of the statistics
model = sm.OLS(y, X)
results = model.fit()
print(results.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       1.000
Model:                            OLS   Adj. R-squared:                  1.000
Method:                 Least Squares   F-statistic:                 4.020e+06
Date:                Mon, 08 Jul 2019   Prob (F-statistic):          2.83e-239
Time:                        02:07:22   Log-Likelihood:                -146.51
No. Observations:                 100   AIC:                             299.0
Df Residuals:                      97   BIC:                             306.8
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          1.3423      0.313      4.292      0.000       0.722       1.963
x1            -0.0402      0.145     -0.278      0.781      -0.327       0.247
x2            10.0103      0.014    715.745      0.000       9.982      10.038
==============================================================================
Omnibus:                        2.042   Durbin-Watson:                   2.274
Prob(Omnibus):                  0.360   Jarque-Bera (JB):                1.875
Skew:                           0.234   Prob(JB):                        0.392
Kurtosis:                       2.519   Cond. No.                         144.
==============================================================================

您可以看到statsmodels提供了更多详细信息，例如AIC，BIC，t统计等。