.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/statistics/regression/plot_01_ols_diagnostics.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_statistics_regression_plot_01_ols_diagnostics.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_statistics_regression_plot_01_ols_diagnostics.py:


OLS regression with residual diagnostics
================================================

Fits a noisy linear relationship and inspects the fit: coefficient
standard errors/p-values, R^2, and a residuals-vs-fitted-values plot.

.. GENERATED FROM PYTHON SOURCE LINES 10-15

.. code-block:: Python

    import numpy as np

    from mathematicskit.statistics import linear_regression
    from mathematicskit.statistics.visualizers.plots import plot_regression_fit, plot_residuals








.. GENERATED FROM PYTHON SOURCE LINES 16-18

Simulate noisy linear data and fit
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 18-28

.. code-block:: Python


    rng = np.random.default_rng(0)
    x = np.linspace(0.0, 10.0, 60)
    y = 3.0 * x + 5.0 + rng.normal(0.0, 2.0, x.shape)

    result = linear_regression(x, y)
    print(f"intercept = {result.coefficients[0]:.3f} (se={result.standard_errors[0]:.3f}, p={result.p_values[0]:.4f})")
    print(f"slope     = {result.coefficients[1]:.3f} (se={result.standard_errors[1]:.3f}, p={result.p_values[1]:.4f})")
    print(f"R^2 = {result.r_squared:.4f}, adjusted R^2 = {result.adjusted_r_squared:.4f}")





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

 .. code-block:: none

    intercept = 4.608 (se=0.458, p=0.0000)
    slope     = 3.109 (se=0.079, p=0.0000)
    R^2 = 0.9639, adjusted R^2 = 0.9633




.. GENERATED FROM PYTHON SOURCE LINES 29-31

Plot the fit and residual diagnostics
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 31-34

.. code-block:: Python


    plot_regression_fit(x, y, result)
    plot_residuals(result)



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /api/gallery/statistics/regression/images/sphx_glr_plot_01_ols_diagnostics_001.png
         :alt: Linear regression fit
         :srcset: /api/gallery/statistics/regression/images/sphx_glr_plot_01_ols_diagnostics_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /api/gallery/statistics/regression/images/sphx_glr_plot_01_ols_diagnostics_002.png
         :alt: Residuals vs. fitted values
         :srcset: /api/gallery/statistics/regression/images/sphx_glr_plot_01_ols_diagnostics_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <Axes: title={'center': 'Residuals vs. fitted values'}, xlabel='fitted values', ylabel='residuals'>




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

   **Total running time of the script:** (0 minutes 0.045 seconds)


.. _sphx_glr_download_api_gallery_statistics_regression_plot_01_ols_diagnostics.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_ols_diagnostics.ipynb <plot_01_ols_diagnostics.ipynb>`

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

      :download:`Download Python source code: plot_01_ols_diagnostics.py <plot_01_ols_diagnostics.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_ols_diagnostics.zip <plot_01_ols_diagnostics.zip>`


.. only:: html

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

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