.. only:: html

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

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

    .. _sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_regression_test.py:


Test samples independence using regression
==========================================

In this example we are going to estimate whether samples are independent using the regression test.

It consists in detecting a linear relation between two scalar samples.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








Generate a sample of dimension 3 with component 0 correlated to component 2


.. code-block:: default

    marginals = [ot.Normal()] * 3
    S = ot.CorrelationMatrix(3)
    S[0, 2] = 0.9
    copula = ot.NormalCopula(S)
    distribution = ot.ComposedDistribution(marginals, copula)
    sample = distribution.getSample(30)








Split it in two samples: firstSample of dimension=2, secondSample of dimension=1


.. code-block:: default

    firstSample = sample[:, :2]
    secondSample = sample[:, 2]








Test independance of each components of firstSample against secondSample


.. code-block:: default

    test_results = ot.LinearModelTest.FullRegression(firstSample, secondSample)
    for i in range(len(test_results)):
        print('Component', i, 'is independent?', test_results[i].getBinaryQualityMeasure(),
              'p-value=%.6g' % test_results[i].getPValue(),
              'threshold=%.6g' % test_results[i].getThreshold())




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

 Out:

 .. code-block:: none

    Component 0 is independent? True p-value=0.998225 threshold=0.05
    Component 1 is independent? False p-value=3.56363e-15 threshold=0.05
    Component 2 is independent? True p-value=0.111968 threshold=0.05





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.003 seconds)


.. _sphx_glr_download_auto_data_analysis_estimate_dependency_and_copulas_plot_regression_test.py:


.. only :: html

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



  .. container:: sphx-glr-download sphx-glr-download-python

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



  .. container:: sphx-glr-download sphx-glr-download-jupyter

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


.. only:: html

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

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