.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_packages_statistics_auto_examples_plot_iris_analysis.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_packages_statistics_auto_examples_plot_iris_analysis.py:


Analysis of Iris petal and sepal sizes
=======================================

Ilustrate an analysis on a real dataset:

- Visualizing the data to formulate intuitions
- Fitting of a linear model
- Hypothesis test of the effect of a categorical variable in the presence
  of a continuous confound




.. code-block:: python

    import matplotlib.pyplot as plt

    import pandas
    from pandas.tools import plotting

    from statsmodels.formula.api import ols

    # Load the data
    data = pandas.read_csv('iris.csv')







Plot a scatter matrix



.. code-block:: python


    # Express the names as categories
    categories = pandas.Categorical(data['name'])

    # The parameter 'c' is passed to plt.scatter and will control the color
    plotting.scatter_matrix(data, c=categories.codes, marker='o')

    fig = plt.gcf()
    fig.suptitle("blue: setosa, green: versicolor, red: virginica", size=13)




.. image:: /packages/statistics/auto_examples/images/sphx_glr_plot_iris_analysis_001.png
    :class: sphx-glr-single-img




Statistical analysis



.. code-block:: python


    # Let us try to explain the sepal length as a function of the petal
    # width and the category of iris

    model = ols('sepal_width ~ name + petal_length', data).fit()
    print(model.summary())

    # Now formulate a "contrast", to test if the offset for versicolor and
    # virginica are identical

    print('Testing the difference between effect of versicolor and virginica')
    print(model.f_test([0, 1, -1, 0]))
    plt.show()




.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    OLS Regression Results                            
    ==============================================================================
    Dep. Variable:            sepal_width   R-squared:                       0.478
    Model:                            OLS   Adj. R-squared:                  0.468
    Method:                 Least Squares   F-statistic:                     44.63
    Date:                Thu, 18 Aug 2022   Prob (F-statistic):           1.58e-20
    Time:                        10:40:00   Log-Likelihood:                -38.185
    No. Observations:                 150   AIC:                             84.37
    Df Residuals:                     146   BIC:                             96.41
    Df Model:                           3                                         
    Covariance Type:            nonrobust                                         
    ======================================================================================
                             coef    std err          t      P>|t|      [0.025      0.975]
    --------------------------------------------------------------------------------------
    Intercept              2.9813      0.099     29.989      0.000       2.785       3.178
    name[T.versicolor]    -1.4821      0.181     -8.190      0.000      -1.840      -1.124
    name[T.virginica]     -1.6635      0.256     -6.502      0.000      -2.169      -1.158
    petal_length           0.2983      0.061      4.920      0.000       0.178       0.418
    ==============================================================================
    Omnibus:                        2.868   Durbin-Watson:                   1.753
    Prob(Omnibus):                  0.238   Jarque-Bera (JB):                2.885
    Skew:                          -0.082   Prob(JB):                        0.236
    Kurtosis:                       3.659   Cond. No.                         54.0
    ==============================================================================

    Warnings:
    [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
    Testing the difference between effect of versicolor and virginica
    <F test: F=array([[3.24533535]]), p=0.07369058781700064, df_denom=146, df_num=1>


**Total running time of the script:** ( 0 minutes  0.387 seconds)


.. _sphx_glr_download_packages_statistics_auto_examples_plot_iris_analysis.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_iris_analysis.py <plot_iris_analysis.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_iris_analysis.ipynb <plot_iris_analysis.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_