使用 statsmodels.formula.api package ols ZC1C425268E68385D1AB5074C17A94F13BDD2565DDDFCZEBEE7B43 时单个变量的重复列

Question

我正在尝试使用 statsmodels.formula.api package 中的 python 执行多元线性回归，并在下面列出了我用来执行此回归的代码。

auto_1= pd.read_csv("Auto.csv")
formula = 'mpg ~ ' + " + ".join(auto_1.columns[1:-1])
results = smf.ols(formula, data=auto_1).fit()
print(results.summary())

数据包含以下变量 - mpg、气缸、排量、马力、重量、加速度、年份、产地和名称。 当打印结果出现时，显示多行马力列，回归结果也不正确。 我不确定为什么？

重复行的屏幕截图

Answer 1

这可能是因为horsepower列的数据类型。 如果它的值是类别或只是字符串，model 将默认为它们使用处理（虚拟）编码，产生您所看到的结果。 检查数据类型（运行auto_1.dtypes ）并将列转换为数字类型（最好在第一次使用read_csv()方法的 dtype dtype=参数读取 csv 文件时执行此操作。

这是一个示例，其中具有数值的列被强制转换（即转换）为字符串（或类别）：

import numpy as np
import pandas as pd
import statsmodels.formula.api as smf

df = pd.DataFrame(
    {
        'mpg': np.random.randint(20, 40, 50),
        'horsepower': np.random.randint(100, 200, 50)
    }
)
# convert integers to strings (or categories)
df['horsepower'] = (
    df['horsepower'].astype('str')  # same result with .astype('category')
)

formula = 'mpg ~ horsepower'

results = smf.ols(formula, df).fit()
print(results.summary())

Output（虚拟编码）：

OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.778
Model:                            OLS   Adj. R-squared:                 -0.207
Method:                 Least Squares   F-statistic:                    0.7901
Date:                Sun, 18 Sep 2022   Prob (F-statistic):              0.715
Time:                        20:17:51   Log-Likelihood:                -110.27
No. Observations:                  50   AIC:                             302.5
Df Residuals:                       9   BIC:                             380.9
Df Model:                          40                                         
Covariance Type:            nonrobust                                         
=====================================================================================
                        coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------
Intercept            32.0000      5.175      6.184      0.000      20.294      43.706
horsepower[T.103]    -4.0000      7.318     -0.547      0.598     -20.555      12.555
horsepower[T.112]    -1.0000      7.318     -0.137      0.894     -17.555      15.555
horsepower[T.116]    -9.0000      7.318     -1.230      0.250     -25.555       7.555
horsepower[T.117]     6.0000      7.318      0.820      0.433     -10.555      22.555
horsepower[T.118]     2.0000      7.318      0.273      0.791     -14.555      18.555
horsepower[T.120]    -4.0000      6.338     -0.631      0.544     -18.337      10.337

etc.

现在，将字符串转换回整数：

df['horsepower'] = pd.to_numeric(df.horsepower)
# or df['horsepower'] = df['horsepower'].astype('int')

results = smf.ols(formula, df).fit()
print(results.summary())

Output（如预期）：

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.011
Model:                            OLS   Adj. R-squared:                 -0.010
Method:                 Least Squares   F-statistic:                    0.5388
Date:                Sun, 18 Sep 2022   Prob (F-statistic):              0.466
Time:                        20:24:54   Log-Likelihood:                -147.65
No. Observations:                  50   AIC:                             299.3
Df Residuals:                      48   BIC:                             303.1
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     31.7638      3.663      8.671      0.000      24.398      39.129
horsepower    -0.0176      0.024     -0.734      0.466      -0.066       0.031
==============================================================================
Omnibus:                        3.529   Durbin-Watson:                   1.859
Prob(Omnibus):                  0.171   Jarque-Bera (JB):                1.725
Skew:                           0.068   Prob(JB):                        0.422
Kurtosis:                       2.100   Cond. No.                         834.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.