.. 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_ridge_variance.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_ridge_variance.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_ridge_variance.py:


=========================================================
普通最小二乘法和岭回归方差
=========================================================
由于每个维度中的点很少，以及线性回归使用直线尽可能地跟随这些点，观测值上的噪声将导致很大的方差，如第一个图所示。由于观测值中引入的噪声，每条线的斜率在每次预测时可能会有很大的变化。

岭回归基本上是最小化一个带惩罚的最小二乘函数。惩罚会“缩小”回归系数的值。尽管每个维度中的数据点很少，但与标准线性回归相比，预测的斜率更加稳定，线本身的方差大大减少。

.. GENERATED FROM PYTHON SOURCE LINES 10-54



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


    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_ols_ridge_variance_001.png
         :alt: ols
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_ols_ridge_variance_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_ols_ridge_variance_002.png
         :alt: ridge
         :srcset: /auto_examples/linear_model/images/sphx_glr_plot_ols_ridge_variance_002.png
         :class: sphx-glr-multi-img





.. code-block:: Python


    # 代码来源：Gaël Varoquaux
    # 由Jaques Grobler修改用于文档
    # SPDX许可证标识符：BSD-3-Clause


    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn import linear_model

    X_train = np.c_[0.5, 1].T
    y_train = [0.5, 1]
    X_test = np.c_[0, 2].T

    np.random.seed(0)

    classifiers = dict(
        ols=linear_model.LinearRegression(), ridge=linear_model.Ridge(alpha=0.1)
    )

    for name, clf in classifiers.items():
        fig, ax = plt.subplots(figsize=(4, 3))

        for _ in range(6):
            this_X = 0.1 * np.random.normal(size=(2, 1)) + X_train
            clf.fit(this_X, y_train)

            ax.plot(X_test, clf.predict(X_test), color="gray")
            ax.scatter(this_X, y_train, s=3, c="gray", marker="o", zorder=10)

        clf.fit(X_train, y_train)
        ax.plot(X_test, clf.predict(X_test), linewidth=2, color="blue")
        ax.scatter(X_train, y_train, s=30, c="red", marker="+", zorder=10)

        ax.set_title(name)
        ax.set_xlim(0, 2)
        ax.set_ylim((0, 1.6))
        ax.set_xlabel("X")
        ax.set_ylabel("y")

        fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.113 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_ols_ridge_variance.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_ridge_variance.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_ols_ridge_variance.recommendations


.. only:: html

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

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