
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/tree/plot_tree_regression.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_tree_plot_tree_regression.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_tree_plot_tree_regression.py:


========================
Decision Tree Regression
========================
In this example, we demonstrate the effect of changing the maximum depth of a
decision tree on how it fits to the data. We perform this once on a 1D regression
task and once on a multi-output regression task.

.. GENERATED FROM PYTHON SOURCE LINES 9-13

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 14-29

Decision Tree on a 1D Regression Task
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Here we fit a tree on a 1D regression task.

The :ref:`decision trees <tree>` is
used to fit a sine curve with addition noisy observation. As a result, it
learns local linear regressions approximating the sine curve.

We can see that if the maximum depth of the tree (controlled by the
`max_depth` parameter) is set too high, the decision trees learn too fine
details of the training data and learn from the noise, i.e. they overfit.

Create a random 1D dataset
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 29-36

.. code-block:: Python

    import numpy as np

    rng = np.random.RandomState(1)
    X = np.sort(5 * rng.rand(80, 1), axis=0)
    y = np.sin(X).ravel()
    y[::5] += 3 * (0.5 - rng.rand(16))








.. GENERATED FROM PYTHON SOURCE LINES 37-40

Fit regression model
--------------------
Here we fit two models with different maximum depths

.. GENERATED FROM PYTHON SOURCE LINES 40-47

.. code-block:: Python

    from sklearn.tree import DecisionTreeRegressor

    regr_1 = DecisionTreeRegressor(max_depth=2)
    regr_2 = DecisionTreeRegressor(max_depth=5)
    regr_1.fit(X, y)
    regr_2.fit(X, y)






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      --sklearn-color-unfitted-level-1: #f6e4d2;
      --sklearn-color-unfitted-level-2: #ffe0b3;
      --sklearn-color-unfitted-level-3: chocolate;
      /* Definition of color scheme for fitted estimators */
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      --sklearn-color-fitted-level-1: #d4ebff;
      --sklearn-color-fitted-level-2: #b3dbfd;
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    #sk-container-id-13 div.sk-dashed-wrapped {
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         but bootstrap.min.css set `[hidden] { display: none !important; }`
         so we also need the `!important` here to be able to override the
         default hidden behavior on the sphinx rendered scikit-learn.org.
         See: https://github.com/scikit-learn/scikit-learn/issues/21755 */
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    div.sk-parallel-item,
    div.sk-serial,
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    #sk-container-id-13 div.sk-parallel-item:only-child::after {
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    /* Serial-specific style estimator block */

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      padding-right: 1em;
      padding-left: 1em;
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    /* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is
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    */

    /* Pipeline and ColumnTransformer style (default) */

    #sk-container-id-13 div.sk-toggleable {
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    }

    /* Toggleable label */
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      cursor: pointer;
      display: flex;
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      margin-bottom: 0;
      padding: 0.5em;
      box-sizing: border-box;
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      align-items: center;
      justify-content: center;
      gap: 0.5em;
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      font-weight: lighter;
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    #sk-container-id-13 div.sk-toggleable__content.fitted {
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      background-color: var(--sklearn-color-unfitted-level-2);
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    /* Estimator-specific style */

    /* Colorize estimator box */
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      /* unfitted */
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      /* fitted */
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      /* unfitted */
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    #sk-container-id-13 div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
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    /* on hover */
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      /* unfitted */
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    .sk-estimator-doc-link,
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    a:visited.sk-estimator-doc-link {
      float: right;
      font-size: smaller;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-unfitted-level-0);
      border-radius: 1em;
      height: 1em;
      width: 1em;
      text-decoration: none !important;
      margin-left: 0.5em;
      text-align: center;
      /* unfitted */
      border: var(--sklearn-color-unfitted-level-3) 1pt solid;
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    .sk-estimator-doc-link.fitted,
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      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3) 1pt solid;
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    .sk-estimator-doc-link.fitted:hover,
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      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-fitted-level-0);
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    /* Span, style for the box shown on hovering the info icon */
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      display: none;
      z-index: 9999;
      position: relative;
      font-weight: normal;
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      padding: .5ex;
      margin: .5ex;
      width: min-content;
      min-width: 20ex;
      max-width: 50ex;
      color: var(--sklearn-color-text);
      box-shadow: 2pt 2pt 4pt #999;
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      float: right;
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      background-color: var(--sklearn-color-unfitted-level-0);
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      width: 1rem;
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      /* unfitted */
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    .estimator-table .parameters-table tr:nth-child(even) {
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        `table td`is set in notebook with right text-align.
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    .user-set td.value {
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        padding: .5ex;
        margin-left: 1.5em;
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        box-shadow: .3em .3em .4em #999;
        width: max-content;
        text-align: left;
        max-height: 10em;
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        /* unfitted */
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        /* fitted */
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        background-repeat: no-repeat;
        background-size: 14px 14px;
        background-position: 0;
        display: inline-block;
        width: 14px;
        height: 14px;
        cursor: pointer;
    }
    </style><body><div id="sk-container-id-13" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>DecisionTreeRegressor(max_depth=5)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-40" type="checkbox" checked><label for="sk-estimator-id-40" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>DecisionTreeRegressor</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html">?<span>Documentation for DecisionTreeRegressor</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted" data-param-prefix="">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('criterion',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=criterion,-%7B%22squared_error%22%2C%20%22friedman_mse%22%2C%20%22absolute_error%22%2C%20%20%20%20%20%20%20%20%20%20%20%20%20%22poisson%22%7D%2C%20default%3D%22squared_error%22">
                criterion
                <span class="param-doc-description">criterion: {"squared_error", "friedman_mse", "absolute_error",             "poisson"}, default="squared_error"<br><br>The function to measure the quality of a split. Supported criteria<br>are "squared_error" for the mean squared error, which is equal to<br>variance reduction as feature selection criterion and minimizes the L2<br>loss using the mean of each terminal node, "friedman_mse", which uses<br>mean squared error with Friedman's improvement score for potential<br>splits, "absolute_error" for the mean absolute error, which minimizes<br>the L1 loss using the median of each terminal node, and "poisson" which<br>uses reduction in the half mean Poisson deviance to find splits.<br><br>.. versionadded:: 0.18<br>   Mean Absolute Error (MAE) criterion.<br><br>.. versionadded:: 0.24<br>    Poisson deviance criterion.</span>
            </a>
        </td>
                <td class="value">&#x27;squared_error&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('splitter',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=splitter,-%7B%22best%22%2C%20%22random%22%7D%2C%20default%3D%22best%22">
                splitter
                <span class="param-doc-description">splitter: {"best", "random"}, default="best"<br><br>The strategy used to choose the split at each node. Supported<br>strategies are "best" to choose the best split and "random" to choose<br>the best random split.</span>
            </a>
        </td>
                <td class="value">&#x27;best&#x27;</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_depth',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=max_depth,-int%2C%20default%3DNone">
                max_depth
                <span class="param-doc-description">max_depth: int, default=None<br><br>The maximum depth of the tree. If None, then nodes are expanded until<br>all leaves are pure or until all leaves contain less than<br>min_samples_split samples.<br><br>For an example of how ``max_depth`` influences the model, see<br>:ref:`sphx_glr_auto_examples_tree_plot_tree_regression.py`.</span>
            </a>
        </td>
                <td class="value">5</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_samples_split',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_samples_split,-int%20or%20float%2C%20default%3D2">
                min_samples_split
                <span class="param-doc-description">min_samples_split: int or float, default=2<br><br>The minimum number of samples required to split an internal node:<br><br>- If int, then consider `min_samples_split` as the minimum number.<br>- If float, then `min_samples_split` is a fraction and<br>  `ceil(min_samples_split * n_samples)` are the minimum<br>  number of samples for each split.<br><br>.. versionchanged:: 0.18<br>   Added float values for fractions.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_samples_leaf',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_samples_leaf,-int%20or%20float%2C%20default%3D1">
                min_samples_leaf
                <span class="param-doc-description">min_samples_leaf: int or float, default=1<br><br>The minimum number of samples required to be at a leaf node.<br>A split point at any depth will only be considered if it leaves at<br>least ``min_samples_leaf`` training samples in each of the left and<br>right branches.  This may have the effect of smoothing the model,<br>especially in regression.<br><br>- If int, then consider `min_samples_leaf` as the minimum number.<br>- If float, then `min_samples_leaf` is a fraction and<br>  `ceil(min_samples_leaf * n_samples)` are the minimum<br>  number of samples for each node.<br><br>.. versionchanged:: 0.18<br>   Added float values for fractions.</span>
            </a>
        </td>
                <td class="value">1</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_weight_fraction_leaf',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_weight_fraction_leaf,-float%2C%20default%3D0.0">
                min_weight_fraction_leaf
                <span class="param-doc-description">min_weight_fraction_leaf: float, default=0.0<br><br>The minimum weighted fraction of the sum total of weights (of all<br>the input samples) required to be at a leaf node. Samples have<br>equal weight when sample_weight is not provided.</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_features',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=max_features,-int%2C%20float%20or%20%7B%22sqrt%22%2C%20%22log2%22%7D%2C%20default%3DNone">
                max_features
                <span class="param-doc-description">max_features: int, float or {"sqrt", "log2"}, default=None<br><br>The number of features to consider when looking for the best split:<br><br>- If int, then consider `max_features` features at each split.<br>- If float, then `max_features` is a fraction and<br>  `max(1, int(max_features * n_features_in_))` features are considered at each<br>  split.<br>- If "sqrt", then `max_features=sqrt(n_features)`.<br>- If "log2", then `max_features=log2(n_features)`.<br>- If None, then `max_features=n_features`.<br><br>Note: the search for a split does not stop until at least one<br>valid partition of the node samples is found, even if it requires to<br>effectively inspect more than ``max_features`` features.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('random_state',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=random_state,-int%2C%20RandomState%20instance%20or%20None%2C%20default%3DNone">
                random_state
                <span class="param-doc-description">random_state: int, RandomState instance or None, default=None<br><br>Controls the randomness of the estimator. The features are always<br>randomly permuted at each split, even if ``splitter`` is set to<br>``"best"``. When ``max_features < n_features``, the algorithm will<br>select ``max_features`` at random at each split before finding the best<br>split among them. But the best found split may vary across different<br>runs, even if ``max_features=n_features``. That is the case, if the<br>improvement of the criterion is identical for several splits and one<br>split has to be selected at random. To obtain a deterministic behaviour<br>during fitting, ``random_state`` has to be fixed to an integer.<br>See :term:`Glossary <random_state>` for details.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_leaf_nodes',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=max_leaf_nodes,-int%2C%20default%3DNone">
                max_leaf_nodes
                <span class="param-doc-description">max_leaf_nodes: int, default=None<br><br>Grow a tree with ``max_leaf_nodes`` in best-first fashion.<br>Best nodes are defined as relative reduction in impurity.<br>If None then unlimited number of leaf nodes.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_impurity_decrease',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_impurity_decrease,-float%2C%20default%3D0.0">
                min_impurity_decrease
                <span class="param-doc-description">min_impurity_decrease: float, default=0.0<br><br>A node will be split if this split induces a decrease of the impurity<br>greater than or equal to this value.<br><br>The weighted impurity decrease equation is the following::<br><br>    N_t / N * (impurity - N_t_R / N_t * right_impurity<br>                        - N_t_L / N_t * left_impurity)<br><br>where ``N`` is the total number of samples, ``N_t`` is the number of<br>samples at the current node, ``N_t_L`` is the number of samples in the<br>left child, and ``N_t_R`` is the number of samples in the right child.<br><br>``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,<br>if ``sample_weight`` is passed.<br><br>.. versionadded:: 0.19</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('ccp_alpha',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=ccp_alpha,-non-negative%20float%2C%20default%3D0.0">
                ccp_alpha
                <span class="param-doc-description">ccp_alpha: non-negative float, default=0.0<br><br>Complexity parameter used for Minimal Cost-Complexity Pruning. The<br>subtree with the largest cost complexity that is smaller than<br>``ccp_alpha`` will be chosen. By default, no pruning is performed. See<br>:ref:`minimal_cost_complexity_pruning` for details. See<br>:ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py`<br>for an example of such pruning.<br><br>.. versionadded:: 0.22</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('monotonic_cst',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=monotonic_cst,-array-like%20of%20int%20of%20shape%20%28n_features%29%2C%20default%3DNone">
                monotonic_cst
                <span class="param-doc-description">monotonic_cst: array-like of int of shape (n_features), default=None<br><br>Indicates the monotonicity constraint to enforce on each feature.<br>  - 1: monotonic increase<br>  - 0: no constraint<br>  - -1: monotonic decrease<br><br>If monotonic_cst is None, no constraints are applied.<br><br>Monotonicity constraints are not supported for:<br>  - multioutput regressions (i.e. when `n_outputs_ > 1`),<br>  - regressions trained on data with missing values.<br><br>Read more in the :ref:`User Guide <monotonic_cst_gbdt>`.<br><br>.. versionadded:: 1.4</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
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.. GENERATED FROM PYTHON SOURCE LINES 48-51

Predict
-------
Get predictions on the test set

.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: Python

    X_test = np.arange(0.0, 5.0, 0.01)[:, np.newaxis]
    y_1 = regr_1.predict(X_test)
    y_2 = regr_2.predict(X_test)








.. GENERATED FROM PYTHON SOURCE LINES 56-58

Plot the results
----------------

.. GENERATED FROM PYTHON SOURCE LINES 58-70

.. code-block:: Python

    import matplotlib.pyplot as plt

    plt.figure()
    plt.scatter(X, y, s=20, edgecolor="black", c="darkorange", label="data")
    plt.plot(X_test, y_1, color="cornflowerblue", label="max_depth=2", linewidth=2)
    plt.plot(X_test, y_2, color="yellowgreen", label="max_depth=5", linewidth=2)
    plt.xlabel("data")
    plt.ylabel("target")
    plt.title("Decision Tree Regression")
    plt.legend()
    plt.show()




.. image-sg:: /auto_examples/tree/images/sphx_glr_plot_tree_regression_001.png
   :alt: Decision Tree Regression
   :srcset: /auto_examples/tree/images/sphx_glr_plot_tree_regression_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 71-76

As you can see, the model with a depth of 5 (yellow) learns the details of the
training data to the point that it overfits to the noise. On the other hand,
the model with a depth of 2 (blue) learns the major tendencies in the data well
and does not overfit. In real use cases, you need to make sure that the tree
is not overfitting the training data, which can be done using cross-validation.

.. GENERATED FROM PYTHON SOURCE LINES 78-89

Decision Tree Regression with Multi-Output Targets
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Here the :ref:`decision trees <tree>`
is used to predict simultaneously the noisy `x` and `y` observations of a circle
given a single underlying feature. As a result, it learns local linear
regressions approximating the circle.

We can see that if the maximum depth of the tree (controlled by the
`max_depth` parameter) is set too high, the decision trees learn too fine
details of the training data and learn from the noise, i.e. they overfit.

.. GENERATED FROM PYTHON SOURCE LINES 91-93

Create a random dataset
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 93-98

.. code-block:: Python

    rng = np.random.RandomState(1)
    X = np.sort(200 * rng.rand(100, 1) - 100, axis=0)
    y = np.array([np.pi * np.sin(X).ravel(), np.pi * np.cos(X).ravel()]).T
    y[::5, :] += 0.5 - rng.rand(20, 2)








.. GENERATED FROM PYTHON SOURCE LINES 99-101

Fit regression model
--------------------

.. GENERATED FROM PYTHON SOURCE LINES 101-108

.. code-block:: Python

    regr_1 = DecisionTreeRegressor(max_depth=2)
    regr_2 = DecisionTreeRegressor(max_depth=5)
    regr_3 = DecisionTreeRegressor(max_depth=8)
    regr_1.fit(X, y)
    regr_2.fit(X, y)
    regr_3.fit(X, y)






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      color: var(--sklearn-color-text);
    }

    /* Toggleable content - dropdown */

    #sk-container-id-14 div.sk-toggleable__content {
      display: none;
      text-align: left;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-14 div.sk-toggleable__content.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-14 div.sk-toggleable__content pre {
      margin: 0.2em;
      border-radius: 0.25em;
      color: var(--sklearn-color-text);
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-14 div.sk-toggleable__content.fitted pre {
      /* unfitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-14 input.sk-toggleable__control:checked~div.sk-toggleable__content {
      /* Expand drop-down */
      display: block;
      width: 100%;
      overflow: visible;
    }

    #sk-container-id-14 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {
      content: "▾";
    }

    /* Pipeline/ColumnTransformer-specific style */

    #sk-container-id-14 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-14 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator-specific style */

    /* Colorize estimator box */
    #sk-container-id-14 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-14 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    #sk-container-id-14 div.sk-label label.sk-toggleable__label,
    #sk-container-id-14 div.sk-label label {
      /* The background is the default theme color */
      color: var(--sklearn-color-text-on-default-background);
    }

    /* On hover, darken the color of the background */
    #sk-container-id-14 div.sk-label:hover label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    /* Label box, darken color on hover, fitted */
    #sk-container-id-14 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator label */

    #sk-container-id-14 div.sk-label label {
      font-family: monospace;
      font-weight: bold;
      line-height: 1.2em;
    }

    #sk-container-id-14 div.sk-label-container {
      text-align: center;
    }

    /* Estimator-specific */
    #sk-container-id-14 div.sk-estimator {
      font-family: monospace;
      border: 1px dotted var(--sklearn-color-border-box);
      border-radius: 0.25em;
      box-sizing: border-box;
      margin-bottom: 0.5em;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-14 div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    /* on hover */
    #sk-container-id-14 div.sk-estimator:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-14 div.sk-estimator.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Specification for estimator info (e.g. "i" and "?") */

    /* Common style for "i" and "?" */

    .sk-estimator-doc-link,
    a:link.sk-estimator-doc-link,
    a:visited.sk-estimator-doc-link {
      float: right;
      font-size: smaller;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-unfitted-level-0);
      border-radius: 1em;
      height: 1em;
      width: 1em;
      text-decoration: none !important;
      margin-left: 0.5em;
      text-align: center;
      /* unfitted */
      border: var(--sklearn-color-unfitted-level-3) 1pt solid;
      color: var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted,
    a:link.sk-estimator-doc-link.fitted,
    a:visited.sk-estimator-doc-link.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3) 1pt solid;
      color: var(--sklearn-color-fitted-level-3);
    }

    /* On hover */
    div.sk-estimator:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover,
    div.sk-label-container:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-unfitted-level-0);
      text-decoration: none;
    }

    div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover,
    div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-fitted-level-0);
      text-decoration: none;
    }

    /* Span, style for the box shown on hovering the info icon */
    .sk-estimator-doc-link span {
      display: none;
      z-index: 9999;
      position: relative;
      font-weight: normal;
      right: .2ex;
      padding: .5ex;
      margin: .5ex;
      width: min-content;
      min-width: 20ex;
      max-width: 50ex;
      color: var(--sklearn-color-text);
      box-shadow: 2pt 2pt 4pt #999;
      /* unfitted */
      background: var(--sklearn-color-unfitted-level-0);
      border: .5pt solid var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted span {
      /* fitted */
      background: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3);
    }

    .sk-estimator-doc-link:hover span {
      display: block;
    }

    /* "?"-specific style due to the `<a>` HTML tag */

    #sk-container-id-14 a.estimator_doc_link {
      float: right;
      font-size: 1rem;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-unfitted-level-0);
      border-radius: 1rem;
      height: 1rem;
      width: 1rem;
      text-decoration: none;
      /* unfitted */
      color: var(--sklearn-color-unfitted-level-1);
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
    }

    #sk-container-id-14 a.estimator_doc_link.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

    /* On hover */
    #sk-container-id-14 a.estimator_doc_link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    #sk-container-id-14 a.estimator_doc_link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
    }

    .estimator-table {
        font-family: monospace;
    }

    .estimator-table summary {
        padding: .5rem;
        cursor: pointer;
    }

    .estimator-table summary::marker {
        font-size: 0.7rem;
    }

    .estimator-table details[open] {
        padding-left: 0.1rem;
        padding-right: 0.1rem;
        padding-bottom: 0.3rem;
    }

    .estimator-table .parameters-table {
        margin-left: auto !important;
        margin-right: auto !important;
        margin-top: 0;
    }

    .estimator-table .parameters-table tr:nth-child(odd) {
        background-color: #fff;
    }

    .estimator-table .parameters-table tr:nth-child(even) {
        background-color: #f6f6f6;
    }

    .estimator-table .parameters-table tr:hover {
        background-color: #e0e0e0;
    }

    .estimator-table table td {
        border: 1px solid rgba(106, 105, 104, 0.232);
    }

    /*
        `table td`is set in notebook with right text-align.
        We need to overwrite it.
    */
    .estimator-table table td.param {
        text-align: left;
        position: relative;
        padding: 0;
    }

    .user-set td {
        color:rgb(255, 94, 0);
        text-align: left !important;
    }

    .user-set td.value {
        color:rgb(255, 94, 0);
        background-color: transparent;
    }

    .default td {
        color: black;
        text-align: left !important;
    }

    .user-set td i,
    .default td i {
        color: black;
    }

    /*
        Styles for parameter documentation links
        We need styling for visited so jupyter doesn't overwrite it
    */
    a.param-doc-link,
    a.param-doc-link:link,
    a.param-doc-link:visited {
        text-decoration: underline dashed;
        text-underline-offset: .3em;
        color: inherit;
        display: block;
        padding: .5em;
    }

    /* "hack" to make the entire area of the cell containing the link clickable */
    a.param-doc-link::before {
        position: absolute;
        content: "";
        inset: 0;
    }

    .param-doc-description {
        display: none;
        position: absolute;
        z-index: 9999;
        left: 0;
        padding: .5ex;
        margin-left: 1.5em;
        color: var(--sklearn-color-text);
        box-shadow: .3em .3em .4em #999;
        width: max-content;
        text-align: left;
        max-height: 10em;
        overflow-y: auto;

        /* unfitted */
        background: var(--sklearn-color-unfitted-level-0);
        border: thin solid var(--sklearn-color-unfitted-level-3);
    }

    /* Fitted state for parameter tooltips */
    .fitted .param-doc-description {
        /* fitted */
        background: var(--sklearn-color-fitted-level-0);
        border: thin solid var(--sklearn-color-fitted-level-3);
    }

    .param-doc-link:hover .param-doc-description {
        display: block;
    }

    .copy-paste-icon {
        background-image: url(data:image/svg+xml;base64,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);
        background-repeat: no-repeat;
        background-size: 14px 14px;
        background-position: 0;
        display: inline-block;
        width: 14px;
        height: 14px;
        cursor: pointer;
    }
    </style><body><div id="sk-container-id-14" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>DecisionTreeRegressor(max_depth=8)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-41" type="checkbox" checked><label for="sk-estimator-id-41" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>DecisionTreeRegressor</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html">?<span>Documentation for DecisionTreeRegressor</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted" data-param-prefix="">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('criterion',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=criterion,-%7B%22squared_error%22%2C%20%22friedman_mse%22%2C%20%22absolute_error%22%2C%20%20%20%20%20%20%20%20%20%20%20%20%20%22poisson%22%7D%2C%20default%3D%22squared_error%22">
                criterion
                <span class="param-doc-description">criterion: {"squared_error", "friedman_mse", "absolute_error",             "poisson"}, default="squared_error"<br><br>The function to measure the quality of a split. Supported criteria<br>are "squared_error" for the mean squared error, which is equal to<br>variance reduction as feature selection criterion and minimizes the L2<br>loss using the mean of each terminal node, "friedman_mse", which uses<br>mean squared error with Friedman's improvement score for potential<br>splits, "absolute_error" for the mean absolute error, which minimizes<br>the L1 loss using the median of each terminal node, and "poisson" which<br>uses reduction in the half mean Poisson deviance to find splits.<br><br>.. versionadded:: 0.18<br>   Mean Absolute Error (MAE) criterion.<br><br>.. versionadded:: 0.24<br>    Poisson deviance criterion.</span>
            </a>
        </td>
                <td class="value">&#x27;squared_error&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('splitter',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=splitter,-%7B%22best%22%2C%20%22random%22%7D%2C%20default%3D%22best%22">
                splitter
                <span class="param-doc-description">splitter: {"best", "random"}, default="best"<br><br>The strategy used to choose the split at each node. Supported<br>strategies are "best" to choose the best split and "random" to choose<br>the best random split.</span>
            </a>
        </td>
                <td class="value">&#x27;best&#x27;</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_depth',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=max_depth,-int%2C%20default%3DNone">
                max_depth
                <span class="param-doc-description">max_depth: int, default=None<br><br>The maximum depth of the tree. If None, then nodes are expanded until<br>all leaves are pure or until all leaves contain less than<br>min_samples_split samples.<br><br>For an example of how ``max_depth`` influences the model, see<br>:ref:`sphx_glr_auto_examples_tree_plot_tree_regression.py`.</span>
            </a>
        </td>
                <td class="value">8</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_samples_split',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_samples_split,-int%20or%20float%2C%20default%3D2">
                min_samples_split
                <span class="param-doc-description">min_samples_split: int or float, default=2<br><br>The minimum number of samples required to split an internal node:<br><br>- If int, then consider `min_samples_split` as the minimum number.<br>- If float, then `min_samples_split` is a fraction and<br>  `ceil(min_samples_split * n_samples)` are the minimum<br>  number of samples for each split.<br><br>.. versionchanged:: 0.18<br>   Added float values for fractions.</span>
            </a>
        </td>
                <td class="value">2</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_samples_leaf',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_samples_leaf,-int%20or%20float%2C%20default%3D1">
                min_samples_leaf
                <span class="param-doc-description">min_samples_leaf: int or float, default=1<br><br>The minimum number of samples required to be at a leaf node.<br>A split point at any depth will only be considered if it leaves at<br>least ``min_samples_leaf`` training samples in each of the left and<br>right branches.  This may have the effect of smoothing the model,<br>especially in regression.<br><br>- If int, then consider `min_samples_leaf` as the minimum number.<br>- If float, then `min_samples_leaf` is a fraction and<br>  `ceil(min_samples_leaf * n_samples)` are the minimum<br>  number of samples for each node.<br><br>.. versionchanged:: 0.18<br>   Added float values for fractions.</span>
            </a>
        </td>
                <td class="value">1</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_weight_fraction_leaf',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_weight_fraction_leaf,-float%2C%20default%3D0.0">
                min_weight_fraction_leaf
                <span class="param-doc-description">min_weight_fraction_leaf: float, default=0.0<br><br>The minimum weighted fraction of the sum total of weights (of all<br>the input samples) required to be at a leaf node. Samples have<br>equal weight when sample_weight is not provided.</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_features',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=max_features,-int%2C%20float%20or%20%7B%22sqrt%22%2C%20%22log2%22%7D%2C%20default%3DNone">
                max_features
                <span class="param-doc-description">max_features: int, float or {"sqrt", "log2"}, default=None<br><br>The number of features to consider when looking for the best split:<br><br>- If int, then consider `max_features` features at each split.<br>- If float, then `max_features` is a fraction and<br>  `max(1, int(max_features * n_features_in_))` features are considered at each<br>  split.<br>- If "sqrt", then `max_features=sqrt(n_features)`.<br>- If "log2", then `max_features=log2(n_features)`.<br>- If None, then `max_features=n_features`.<br><br>Note: the search for a split does not stop until at least one<br>valid partition of the node samples is found, even if it requires to<br>effectively inspect more than ``max_features`` features.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('random_state',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=random_state,-int%2C%20RandomState%20instance%20or%20None%2C%20default%3DNone">
                random_state
                <span class="param-doc-description">random_state: int, RandomState instance or None, default=None<br><br>Controls the randomness of the estimator. The features are always<br>randomly permuted at each split, even if ``splitter`` is set to<br>``"best"``. When ``max_features < n_features``, the algorithm will<br>select ``max_features`` at random at each split before finding the best<br>split among them. But the best found split may vary across different<br>runs, even if ``max_features=n_features``. That is the case, if the<br>improvement of the criterion is identical for several splits and one<br>split has to be selected at random. To obtain a deterministic behaviour<br>during fitting, ``random_state`` has to be fixed to an integer.<br>See :term:`Glossary <random_state>` for details.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_leaf_nodes',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=max_leaf_nodes,-int%2C%20default%3DNone">
                max_leaf_nodes
                <span class="param-doc-description">max_leaf_nodes: int, default=None<br><br>Grow a tree with ``max_leaf_nodes`` in best-first fashion.<br>Best nodes are defined as relative reduction in impurity.<br>If None then unlimited number of leaf nodes.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('min_impurity_decrease',
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                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=min_impurity_decrease,-float%2C%20default%3D0.0">
                min_impurity_decrease
                <span class="param-doc-description">min_impurity_decrease: float, default=0.0<br><br>A node will be split if this split induces a decrease of the impurity<br>greater than or equal to this value.<br><br>The weighted impurity decrease equation is the following::<br><br>    N_t / N * (impurity - N_t_R / N_t * right_impurity<br>                        - N_t_L / N_t * left_impurity)<br><br>where ``N`` is the total number of samples, ``N_t`` is the number of<br>samples at the current node, ``N_t_L`` is the number of samples in the<br>left child, and ``N_t_R`` is the number of samples in the right child.<br><br>``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,<br>if ``sample_weight`` is passed.<br><br>.. versionadded:: 0.19</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('ccp_alpha',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=ccp_alpha,-non-negative%20float%2C%20default%3D0.0">
                ccp_alpha
                <span class="param-doc-description">ccp_alpha: non-negative float, default=0.0<br><br>Complexity parameter used for Minimal Cost-Complexity Pruning. The<br>subtree with the largest cost complexity that is smaller than<br>``ccp_alpha`` will be chosen. By default, no pruning is performed. See<br>:ref:`minimal_cost_complexity_pruning` for details. See<br>:ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py`<br>for an example of such pruning.<br><br>.. versionadded:: 0.22</span>
            </a>
        </td>
                <td class="value">0.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('monotonic_cst',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.8/modules/generated/sklearn.tree.DecisionTreeRegressor.html#:~:text=monotonic_cst,-array-like%20of%20int%20of%20shape%20%28n_features%29%2C%20default%3DNone">
                monotonic_cst
                <span class="param-doc-description">monotonic_cst: array-like of int of shape (n_features), default=None<br><br>Indicates the monotonicity constraint to enforce on each feature.<br>  - 1: monotonic increase<br>  - 0: no constraint<br>  - -1: monotonic decrease<br><br>If monotonic_cst is None, no constraints are applied.<br><br>Monotonicity constraints are not supported for:<br>  - multioutput regressions (i.e. when `n_outputs_ > 1`),<br>  - regressions trained on data with missing values.<br><br>Read more in the :ref:`User Guide <monotonic_cst_gbdt>`.<br><br>.. versionadded:: 1.4</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
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.. GENERATED FROM PYTHON SOURCE LINES 109-112

Predict
-------
Get predictions on the test set

.. GENERATED FROM PYTHON SOURCE LINES 112-117

.. code-block:: Python

    X_test = np.arange(-100.0, 100.0, 0.01)[:, np.newaxis]
    y_1 = regr_1.predict(X_test)
    y_2 = regr_2.predict(X_test)
    y_3 = regr_3.predict(X_test)








.. GENERATED FROM PYTHON SOURCE LINES 118-120

Plot the results
----------------

.. GENERATED FROM PYTHON SOURCE LINES 120-141

.. code-block:: Python

    plt.figure()
    s = 25
    plt.scatter(y[:, 0], y[:, 1], c="yellow", s=s, edgecolor="black", label="data")
    plt.scatter(
        y_1[:, 0],
        y_1[:, 1],
        c="cornflowerblue",
        s=s,
        edgecolor="black",
        label="max_depth=2",
    )
    plt.scatter(y_2[:, 0], y_2[:, 1], c="red", s=s, edgecolor="black", label="max_depth=5")
    plt.scatter(y_3[:, 0], y_3[:, 1], c="blue", s=s, edgecolor="black", label="max_depth=8")
    plt.xlim([-6, 6])
    plt.ylim([-6, 6])
    plt.xlabel("target 1")
    plt.ylabel("target 2")
    plt.title("Multi-output Decision Tree Regression")
    plt.legend(loc="best")
    plt.show()




.. image-sg:: /auto_examples/tree/images/sphx_glr_plot_tree_regression_002.png
   :alt: Multi-output Decision Tree Regression
   :srcset: /auto_examples/tree/images/sphx_glr_plot_tree_regression_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 142-145

As you can see, the higher the value of `max_depth`, the more details of the data
are caught by the model. However, the model also overfits to the data and is
influenced by the noise.


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

   **Total running time of the script:** (0 minutes 0.300 seconds)


.. _sphx_glr_download_auto_examples_tree_plot_tree_regression.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
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        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/tree/plot_tree_regression.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_tree_regression.recommendations


.. only:: html

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

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