statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. An extensive list of result statistics are available for each estimator. The results are tested against existing statistical packages to ensure that they are correct. The package is released under the open source Modified BSD (3-clause) license. The online documentation is hosted at statsmodels.org.
Introduction¶
statsmodels supports specifying models using R-style formulas and pandas DataFrames.
Here is a simple example using ordinary least squares:
In [1]: import numpy as np
In [2]: import statsmodels.api as sm
In [3]: import statsmodels.formula.api as smf
# Load data
In [4]: dat = sm.datasets.get_rdataset("Guerry", "HistData").data
# Fit regression model (using the natural log of one of the regressors)
In [5]: results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=dat).fit()
# Inspect the results
In [6]: print(results.summary())
OLS Regression Results
==============================================================================
Dep. Variable: Lottery R-squared: 0.348
Model: OLS Adj. R-squared: 0.333
Method: Least Squares F-statistic: 22.20
Date: Tue, 02 Feb 2021 Prob (F-statistic): 1.90e-08
Time: 07:07:09 Log-Likelihood: -379.82
No. Observations: 86 AIC: 765.6
Df Residuals: 83 BIC: 773.0
Df Model: 2
Covariance Type: nonrobust
===================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------
Intercept 246.4341 35.233 6.995 0.000 176.358 316.510
Literacy -0.4889 0.128 -3.832 0.000 -0.743 -0.235
np.log(Pop1831) -31.3114 5.977 -5.239 0.000 -43.199 -19.424
==============================================================================
Omnibus: 3.713 Durbin-Watson: 2.019
Prob(Omnibus): 0.156 Jarque-Bera (JB): 3.394
Skew: -0.487 Prob(JB): 0.183
Kurtosis: 3.003 Cond. No. 702.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
You can also use numpy arrays instead of formulas:
In [7]: import numpy as np
In [8]: import statsmodels.api as sm
# Generate artificial data (2 regressors + constant)
In [9]: nobs = 100
In [10]: X = np.random.random((nobs, 2))
In [11]: X = sm.add_constant(X)
In [12]: beta = [1, .1, .5]
In [13]: e = np.random.random(nobs)
In [14]: y = np.dot(X, beta) + e
# Fit regression model
In [15]: results = sm.OLS(y, X).fit()
# Inspect the results
In [16]: print(results.summary())
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.241
Model: OLS Adj. R-squared: 0.225
Method: Least Squares F-statistic: 15.36
Date: Tue, 02 Feb 2021 Prob (F-statistic): 1.60e-06
Time: 07:07:09 Log-Likelihood: -13.384
No. Observations: 100 AIC: 32.77
Df Residuals: 97 BIC: 40.58
Df Model: 2
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 1.4839 0.067 22.000 0.000 1.350 1.618
x1 0.1966 0.096 2.046 0.043 0.006 0.387
x2 0.4322 0.093 4.653 0.000 0.248 0.617
==============================================================================
Omnibus: 9.795 Durbin-Watson: 2.016
Prob(Omnibus): 0.007 Jarque-Bera (JB): 3.512
Skew: 0.018 Prob(JB): 0.173
Kurtosis: 2.083 Cond. No. 4.72
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Have a look at dir(results) to see available results. Attributes are described in results.__doc__ and results methods have their own docstrings.
Citation¶
Please use following citation to cite statsmodels in scientific publications:
Seabold, Skipper, and Josef Perktold. “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference. 2010.
Bibtex entry:
@inproceedings{seabold2010statsmodels,
title={statsmodels: Econometric and statistical modeling with python},
author={Seabold, Skipper and Perktold, Josef},
booktitle={9th Python in Science Conference},
year={2010},
}