/Statsmodels

# Statsmodels

`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.

## Minimal Examples

Since version `0.5.0` of `statsmodels`, you can use R-style formulas together with `pandas` data frames to fit your models. 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, 28 Feb 2017   Prob (F-statistic):           1.90e-08
Time:                        21:38:05   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.
==============================================================================

Warnings:
[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:                       0.260
Model:                            OLS   Adj. R-squared:                  0.245
Method:                 Least Squares   F-statistic:                     17.06
Date:                Tue, 28 Feb 2017   Prob (F-statistic):           4.49e-07
Time:                        21:38:05   Log-Likelihood:                -23.039
No. Observations:                 100   AIC:                             52.08
Df Residuals:                      97   BIC:                             59.89
Df Model:                           2
Covariance Type:            nonrobust
==============================================================================
coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          1.3622      0.088     15.521      0.000       1.188       1.536
x1             0.2220      0.112      1.973      0.051      -0.001       0.445
x2             0.6277      0.112      5.585      0.000       0.405       0.851
==============================================================================
Omnibus:                       38.171   Durbin-Watson:                   1.957
Prob(Omnibus):                  0.000   Jarque-Bera (JB):                6.373
Skew:                           0.079   Prob(JB):                       0.0413
Kurtosis:                       1.773   Cond. No.                         5.71
==============================================================================

Warnings:
[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

When using statsmodels in scientific publication, please consider using the following citation:

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},
}
```

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/index.html