python中的单变量回归

Question

需要在 python 中在数据框中的一列和同一数据框中的其他几列之间运行多个单因素（单变量）回归模型

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所以基于图像，我想在 x1 & dep、x2 & dep 等之间运行回归模型，以此类推

想要输出 - beta、截距、R-sq、p-value、SSE、AIC、BIC、残差正态性检验等

Answer 1

您可以在此处使用两个选项。一个是流行的scikit-learn 库。使用如下

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...

您可以在 scikit 中使用的其他统计信息并不多。

另一个选项是statsmodels，它为模型的统计数据提供了更丰富的细节

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 统计量等。