.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/linear_model/plot_logistic.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_logistic.py>`
        to download the full example code or to run this example in your browser via JupyterLite or Binder

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

.. _sphx_glr_auto_examples_linear_model_plot_logistic.py:


=========================================================
Logistic function
=========================================================

Shown in the plot is how the logistic regression would, in this
synthetic dataset, classify values as either 0 or 1,
i.e. class one or two, using the logistic curve.

.. GENERATED FROM PYTHON SOURCE LINES 11-67



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_logistic_001.png
   :alt: plot logistic
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_logistic_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    # Code source: Gael Varoquaux
    # License: BSD 3 clause

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.special import expit

    from sklearn.linear_model import LinearRegression, LogisticRegression

    # Generate a toy dataset, it's just a straight line with some Gaussian noise:
    xmin, xmax = -5, 5
    n_samples = 100
    np.random.seed(0)
    X = np.random.normal(size=n_samples)
    y = (X > 0).astype(float)
    X[X > 0] *= 4
    X += 0.3 * np.random.normal(size=n_samples)

    X = X[:, np.newaxis]

    # Fit the classifier
    clf = LogisticRegression(C=1e5)
    clf.fit(X, y)

    # and plot the result
    plt.figure(1, figsize=(4, 3))
    plt.clf()
    plt.scatter(X.ravel(), y, label="example data", color="black", zorder=20)
    X_test = np.linspace(-5, 10, 300)

    loss = expit(X_test * clf.coef_ + clf.intercept_).ravel()
    plt.plot(X_test, loss, label="Logistic Regression Model", color="red", linewidth=3)

    ols = LinearRegression()
    ols.fit(X, y)
    plt.plot(
        X_test,
        ols.coef_ * X_test + ols.intercept_,
        label="Linear Regression Model",
        linewidth=1,
    )
    plt.axhline(0.5, color=".5")

    plt.ylabel("y")
    plt.xlabel("X")
    plt.xticks(range(-5, 10))
    plt.yticks([0, 0.5, 1])
    plt.ylim(-0.25, 1.25)
    plt.xlim(-4, 10)
    plt.legend(
        loc="lower right",
        fontsize="small",
    )
    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.104 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_logistic.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_logistic.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/linear_model/plot_logistic.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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


.. include:: plot_logistic.recommendations


.. only:: html

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

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