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

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

.. _sphx_glr_packages_scikit-learn_auto_examples_plot_polynomial_regression.py:


Plot fitting a 9th order polynomial
====================================

Fits data generated from a 9th order polynomial with model of 4th order
and 9th order polynomials, to demonstrate that often simpler models are
to be prefered



.. code-block:: python


    import numpy as np
    from matplotlib import pyplot as plt
    from matplotlib.colors import ListedColormap

    from sklearn import linear_model

    # Create color maps for 3-class classification problem, as with iris
    cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
    cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])


    rng = np.random.RandomState(0)
    x = 2*rng.rand(100) - 1

    f = lambda t: 1.2 * t**2 + .1 * t**3 - .4 * t **5 - .5 * t ** 9
    y = f(x) + .4 * rng.normal(size=100)

    x_test = np.linspace(-1, 1, 100)







The data



.. code-block:: python

    plt.figure(figsize=(6, 4))
    plt.scatter(x, y, s=4)




.. image:: /packages/scikit-learn/auto_examples/images/sphx_glr_plot_polynomial_regression_001.png
    :class: sphx-glr-single-img




Fitting 4th and 9th order polynomials

For this we need to engineer features: the n_th powers of x:



.. code-block:: python

    plt.figure(figsize=(6, 4))
    plt.scatter(x, y, s=4)

    X = np.array([x**i for i in range(5)]).T
    X_test = np.array([x_test**i for i in range(5)]).T
    regr = linear_model.LinearRegression()
    regr.fit(X, y)
    plt.plot(x_test, regr.predict(X_test), label='4th order')

    X = np.array([x**i for i in range(10)]).T
    X_test = np.array([x_test**i for i in range(10)]).T
    regr = linear_model.LinearRegression()
    regr.fit(X, y)
    plt.plot(x_test, regr.predict(X_test), label='9th order')

    plt.legend(loc='best')
    plt.axis('tight')
    plt.title('Fitting a 4th and a 9th order polynomial')




.. image:: /packages/scikit-learn/auto_examples/images/sphx_glr_plot_polynomial_regression_002.png
    :class: sphx-glr-single-img




Ground truth



.. code-block:: python

    plt.figure(figsize=(6, 4))
    plt.scatter(x, y, s=4)
    plt.plot(x_test, f(x_test), label="truth")
    plt.axis('tight')
    plt.title('Ground truth (9th order polynomial)')

    plt.show()



.. image:: /packages/scikit-learn/auto_examples/images/sphx_glr_plot_polynomial_regression_003.png
    :class: sphx-glr-single-img




**Total running time of the script:** ( 0 minutes  0.047 seconds)


.. _sphx_glr_download_packages_scikit-learn_auto_examples_plot_polynomial_regression.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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