
.. 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

        Click :ref:`here <sphx_glr_download_auto_examples_linear_model_plot_ols.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_linear_model_plot_ols.py:


=========================================================
Linear Regression Example
=========================================================
This example uses the only the first feature of the `diabetes` dataset, in
order to illustrate a two-dimensional plot of this regression technique. 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, the residual sum of squares and the coefficient
of determination are also calculated.

.. GENERATED FROM PYTHON SOURCE LINES 19-71



.. 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

 Out:

 .. code-block:: none


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






|

.. code-block:: default

    print(__doc__)


    # Code source: Jaques Grobler
    # License: 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  0.039 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_ols.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_ols.py <plot_ols.py>`



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

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


.. only:: html

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

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