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

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

.. _sphx_glr_packages_statistics_auto_examples_solutions_plot_brain_size.py:


Relating Gender and IQ
=======================

Going back to the brain size + IQ data, test if the VIQ of male and
female are different after removing the effect of brain size, height and
weight.

Notice that here 'Gender' is a categorical value. As it is a non-float
data type, statsmodels is able to automatically infer this.




.. code-block:: python

    import pandas
    from statsmodels.formula.api import ols

    data = pandas.read_csv('../brain_size.csv', sep=';', na_values='.')

    model = ols('VIQ ~ Gender + MRI_Count + Height', data).fit()
    print(model.summary())

    # Here, we don't need to define a contrast, as we are testing a single
    # coefficient of our model, and not a combination of coefficients.
    # However, defining a contrast, which would then be a 'unit contrast',
    # will give us the same results
    print(model.f_test([0, 1, 0, 0]))





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

 Out:

 .. code-block:: none

    OLS Regression Results                            
    ==============================================================================
    Dep. Variable:                    VIQ   R-squared:                       0.246
    Model:                            OLS   Adj. R-squared:                  0.181
    Method:                 Least Squares   F-statistic:                     3.809
    Date:                Thu, 18 Aug 2022   Prob (F-statistic):             0.0184
    Time:                        10:40:21   Log-Likelihood:                -172.34
    No. Observations:                  39   AIC:                             352.7
    Df Residuals:                      35   BIC:                             359.3
    Df Model:                           3                                         
    Covariance Type:            nonrobust                                         
    ==================================================================================
                         coef    std err          t      P>|t|      [0.025      0.975]
    ----------------------------------------------------------------------------------
    Intercept        166.6258     88.824      1.876      0.069     -13.696     346.948
    Gender[T.Male]     8.8524     10.710      0.827      0.414     -12.890      30.595
    MRI_Count          0.0002   6.46e-05      2.615      0.013    3.78e-05       0.000
    Height            -3.0837      1.276     -2.417      0.021      -5.674      -0.494
    ==============================================================================
    Omnibus:                        7.373   Durbin-Watson:                   2.109
    Prob(Omnibus):                  0.025   Jarque-Bera (JB):                2.252
    Skew:                           0.005   Prob(JB):                        0.324
    Kurtosis:                       1.823   Cond. No.                     2.40e+07
    ==============================================================================

    Warnings:
    [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
    [2] The condition number is large, 2.4e+07. This might indicate that there are
    strong multicollinearity or other numerical problems.
    <F test: F=array([[0.68319608]]), p=0.4140878441244722, df_denom=35, df_num=1>


Here we plot a scatter matrix to get intuitions on our results.
This goes beyond what was asked in the exercise



.. code-block:: python


    # This plotting is useful to get an intuitions on the relationships between
    # our different variables

    from pandas.tools import plotting
    import matplotlib.pyplot as plt

    # Fill in the missing values for Height for plotting
    data['Height'].fillna(method='pad', inplace=True)

    # The parameter 'c' is passed to plt.scatter and will control the color
    # The same holds for parameters 'marker', 'alpha' and 'cmap', that
    # control respectively the type of marker used, their transparency and
    # the colormap
    plotting.scatter_matrix(data[['VIQ', 'MRI_Count', 'Height']],
                            c=(data['Gender'] == 'Female'), marker='o',
                            alpha=1, cmap='winter')

    fig = plt.gcf()
    fig.suptitle("blue: male, green: female", size=13)

    plt.show()



.. image:: /packages/statistics/auto_examples/solutions/images/sphx_glr_plot_brain_size_001.png
    :class: sphx-glr-single-img




**Total running time of the script:** ( 0 minutes  0.328 seconds)


.. _sphx_glr_download_packages_statistics_auto_examples_solutions_plot_brain_size.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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