.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/linear_model/plot_ols.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_linear_model_plot_ols.py>`
        to download the full example code. or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_linear_model_plot_ols.py:


=========================================================
Linear Regression Example
=========================================================
The example below uses only the first feature of the `diabetes` dataset,
in order to illustrate the data points within the two-dimensional plot.
The straight line can be seen in the plot, showing how linear regression
attempts to draw a straight line that will best minimize the
residual sum of squares between the observed responses in the dataset,
and the responses predicted by the linear approximation.

The coefficients, residual sum of squares and the coefficient of
determination are also calculated.

.. GENERATED FROM PYTHON SOURCE LINES 16-64



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_ols_001.png
   :alt: plot ols
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_ols_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Coefficients: 
     [938.23786125]
    Mean squared error: 2548.07
    Coefficient of determination: 0.47






|

.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn import datasets, linear_model
    from sklearn.metrics import mean_squared_error, r2_score

    # Load the diabetes dataset
    diabetes_X, diabetes_y = datasets.load_diabetes(return_X_y=True)

    # Use only one feature
    diabetes_X = diabetes_X[:, np.newaxis, 2]

    # Split the data into training/testing sets
    diabetes_X_train = diabetes_X[:-20]
    diabetes_X_test = diabetes_X[-20:]

    # Split the targets into training/testing sets
    diabetes_y_train = diabetes_y[:-20]
    diabetes_y_test = diabetes_y[-20:]

    # Create linear regression object
    regr = linear_model.LinearRegression()

    # Train the model using the training sets
    regr.fit(diabetes_X_train, diabetes_y_train)

    # Make predictions using the testing set
    diabetes_y_pred = regr.predict(diabetes_X_test)

    # The coefficients
    print("Coefficients: \n", regr.coef_)
    # The mean squared error
    print("Mean squared error: %.2f" % mean_squared_error(diabetes_y_test, diabetes_y_pred))
    # The coefficient of determination: 1 is perfect prediction
    print("Coefficient of determination: %.2f" % r2_score(diabetes_y_test, diabetes_y_pred))

    # Plot outputs
    plt.scatter(diabetes_X_test, diabetes_y_test, color="black")
    plt.plot(diabetes_X_test, diabetes_y_pred, color="blue", linewidth=3)

    plt.xticks(())
    plt.yticks(())

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.033 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_ols.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_ols.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_ols.recommendations


.. only:: html

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

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