Python 使用 Pandas 数据框运行 OLS 回归
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Run an OLS regression with Pandas Data Frame
提问by Michael
I have a pandasdata frame and I would like to able to predict the values of column A from the values in columns B and C. Here is a toy example:
我有一个pandas数据框，我希望能够从 B 列和 C 列中的值预测 A 列的值。这是一个玩具示例：
import pandas as pd
df = pd.DataFrame({"A": [10,20,30,40,50],
"B": [20, 30, 10, 40, 50],
"C": [32, 234, 23, 23, 42523]})
Ideally, I would have something like ols(A ~ B + C, data = df)but when I look at the examplesfrom algorithm libraries like scikit-learnit appears to feed the data to the model with a list of rows instead of columns. This would require me to reformat the data into lists inside lists, which seems to defeat the purpose of using pandas in the first place. What is the most pythonic way to run an OLS regression (or any machine learning algorithm more generally) on data in a pandas data frame?
理想情况下，我会有类似的东西，ols(A ~ B + C, data = df)但是当我查看算法库中的示例时，scikit-learn它似乎将数据提供给带有行列表而不是列的模型。这将需要我将数据重新格式化为列表内的列表，这似乎首先违背了使用熊猫的目的。对 Pandas 数据框中的数据运行 OLS 回归（或更一般的任何机器学习算法）的最pythonic 方法是什么？
回答by DSM
I think you can almost do exactly what you thought would be ideal, using the statsmodelspackage which was one of pandas' optional dependencies before pandas' version 0.20.0 (it was used for a few things in pandas.stats.)
我认为您几乎可以完全按照您认为的理想操作，使用statsmodels包，该包是0.20.0 版pandas之前的“可选依赖项pandas”之一（它在pandas.stats.
>>> import pandas as pd
>>> import statsmodels.formula.api as sm
>>> df = pd.DataFrame({"A": [10,20,30,40,50], "B": [20, 30, 10, 40, 50], "C": [32, 234, 23, 23, 42523]})
>>> result = sm.ols(formula="A ~ B + C", data=df).fit()
>>> print(result.params)
Intercept 14.952480
B 0.401182
C 0.000352
dtype: float64
>>> print(result.summary())
OLS Regression Results
==============================================================================
Dep. Variable: A R-squared: 0.579
Model: OLS Adj. R-squared: 0.158
Method: Least Squares F-statistic: 1.375
Date: Thu, 14 Nov 2013 Prob (F-statistic): 0.421
Time: 20:04:30 Log-Likelihood: -18.178
No. Observations: 5 AIC: 42.36
Df Residuals: 2 BIC: 41.19
Df Model: 2
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept 14.9525 17.764 0.842 0.489 -61.481 91.386
B 0.4012 0.650 0.617 0.600 -2.394 3.197
C 0.0004 0.001 0.650 0.583 -0.002 0.003
==============================================================================
Omnibus: nan Durbin-Watson: 1.061
Prob(Omnibus): nan Jarque-Bera (JB): 0.498
Skew: -0.123 Prob(JB): 0.780
Kurtosis: 1.474 Cond. No. 5.21e+04
==============================================================================
Warnings:
[1] The condition number is large, 5.21e+04. This might indicate that there are
strong multicollinearity or other numerical problems.
回答by Roman Pekar
Note:pandas.statshas been removedwith 0.20.0
It's possible to do this with pandas.stats.ols:
可以通过以下方式做到这一点pandas.stats.ols：
>>> from pandas.stats.api import ols
>>> df = pd.DataFrame({"A": [10,20,30,40,50], "B": [20, 30, 10, 40, 50], "C": [32, 234, 23, 23, 42523]})
>>> res = ols(y=df['A'], x=df[['B','C']])
>>> res
-------------------------Summary of Regression Analysis-------------------------
Formula: Y ~ <B> + <C> + <intercept>
Number of Observations: 5
Number of Degrees of Freedom: 3
R-squared: 0.5789
Adj R-squared: 0.1577
Rmse: 14.5108
F-stat (2, 2): 1.3746, p-value: 0.4211
Degrees of Freedom: model 2, resid 2
-----------------------Summary of Estimated Coefficients------------------------
Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%
--------------------------------------------------------------------------------
B 0.4012 0.6497 0.62 0.5999 -0.8723 1.6746
C 0.0004 0.0005 0.65 0.5826 -0.0007 0.0014
intercept 14.9525 17.7643 0.84 0.4886 -19.8655 49.7705
---------------------------------End of Summary---------------------------------
Note that you need to have statsmodelspackage installed, it is used internally by the pandas.stats.olsfunction.
请注意，您需要statsmodels安装包，它由pandas.stats.ols函数内部使用。
回答by Fred Foo
This would require me to reformat the data into lists inside lists, which seems to defeat the purpose of using pandas in the first place.
这将需要我将数据重新格式化为列表内的列表，这似乎首先违背了使用熊猫的目的。
No it doesn't, just convert to a NumPy array:
不，不是，只需转换为 NumPy 数组：
>>> data = np.asarray(df)
This takes constant time because it just creates a viewon your data. Then feed it to scikit-learn:
这需要持续的时间，因为它只是创建了数据视图。然后将其提供给 scikit-learn：
>>> from sklearn.linear_model import LinearRegression
>>> lr = LinearRegression()
>>> X, y = data[:, 1:], data[:, 0]
>>> lr.fit(X, y)
LinearRegression(copy_X=True, fit_intercept=True, normalize=False)
>>> lr.coef_
array([ 4.01182386e-01, 3.51587361e-04])
>>> lr.intercept_
14.952479503953672
回答by 3novak
I don't know if this is new in sklearnor pandas, but I'm able to pass the data frame directly to sklearnwithout converting the data frame to a numpy array or any other data types.
我不知道这是否是新的sklearnor pandas，但我可以将数据帧直接传递给 ，sklearn而无需将数据帧转换为 numpy 数组或任何其他数据类型。
from sklearn import linear_model
reg = linear_model.LinearRegression()
reg.fit(df[['B', 'C']], df['A'])
>>> reg.coef_
array([ 4.01182386e-01, 3.51587361e-04])
回答by vestland
Statsmodelskan build an OLS modelwith column references directly to a pandas dataframe.
Statsmodels 可以构建一个OLS 模型，其中列引用直接指向Pandas 数据框。
Short and sweet:
简短而甜蜜：
model = sm.OLS(df[y], df[x]).fit()
model = sm.OLS(df[y], df[x]).fit()
Code details and regression summary:
代码细节和回归总结：
# imports
import pandas as pd
import statsmodels.api as sm
import numpy as np
# data
np.random.seed(123)
df = pd.DataFrame(np.random.randint(0,100,size=(100, 3)), columns=list('ABC'))
# assign dependent and independent / explanatory variables
variables = list(df.columns)
y = 'A'
x = [var for var in variables if var not in y ]
# Ordinary least squares regression
model_Simple = sm.OLS(df[y], df[x]).fit()
# Add a constant term like so:
model = sm.OLS(df[y], sm.add_constant(df[x])).fit()
model.summary()
Output:
输出：
OLS Regression Results
==============================================================================
Dep. Variable: A R-squared: 0.019
Model: OLS Adj. R-squared: -0.001
Method: Least Squares F-statistic: 0.9409
Date: Thu, 14 Feb 2019 Prob (F-statistic): 0.394
Time: 08:35:04 Log-Likelihood: -484.49
No. Observations: 100 AIC: 975.0
Df Residuals: 97 BIC: 982.8
Df Model: 2
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 43.4801 8.809 4.936 0.000 25.996 60.964
B 0.1241 0.105 1.188 0.238 -0.083 0.332
C -0.0752 0.110 -0.681 0.497 -0.294 0.144
==============================================================================
Omnibus: 50.990 Durbin-Watson: 2.013
Prob(Omnibus): 0.000 Jarque-Bera (JB): 6.905
Skew: 0.032 Prob(JB): 0.0317
Kurtosis: 1.714 Cond. No. 231.
==============================================================================
How to directly get R-squared, Coefficients and p-value:
如何直接得到 R 平方、系数和 p 值：
# commands:
model.params
model.pvalues
model.rsquared
# demo:
In[1]:
model.params
Out[1]:
const 43.480106
B 0.124130
C -0.075156
dtype: float64
In[2]:
model.pvalues
Out[2]:
const 0.000003
B 0.237924
C 0.497400
dtype: float64
Out[3]:
model.rsquared
Out[2]:
0.0190
