.. _winescolorlinerst:

===========================
Régression logistique en 2D
===========================


.. only:: html

    **Links:** :download:`notebook <wines_color_line.ipynb>`, :downloadlink:`html <wines_color_line2html.html>`, :download:`PDF <wines_color_line.pdf>`, :download:`python <wines_color_line.py>`, :downloadlink:`slides <wines_color_line.slides.html>`, :githublink:`GitHub|_doc/notebooks/lectures/wines_color_line.ipynb|*`


Prédire la couleur d’un vin à partir de ses composants.

.. code:: ipython3

    %matplotlib inline

.. code:: ipython3

    from papierstat.datasets import load_wines_dataset
    data = load_wines_dataset()
    X = data.drop(['quality', 'color'], axis=1)
    y = data['color']

.. code:: ipython3

    from sklearn.model_selection import train_test_split
    X_train, X_test, y_train, y_test = train_test_split(X, y)

.. code:: ipython3

    from statsmodels.discrete.discrete_model import Logit
    model = Logit(y_train == "white", X_train)
    res = model.fit()


.. parsed-literal::
    Optimization terminated successfully.
             Current function value: 0.044575
             Iterations 11


.. code:: ipython3

    res.summary2()






.. raw:: html

    <table class="simpletable">
    <tr>
            <td>Model:</td>              <td>Logit</td>       <td>No. Iterations:</td>   <td>11.0000</td>
    </tr>
    <tr>
      <td>Dependent Variable:</td>       <td>color</td>      <td>Pseudo R-squared:</td>   <td>0.921</td> 
    </tr>
    <tr>
             <td>Date:</td>        <td>2018-02-08 00:13</td>       <td>AIC:</td>        <td>456.3398</td>
    </tr>
    <tr>
       <td>No. Observations:</td>        <td>4872</td>             <td>BIC:</td>        <td>527.7436</td>
    </tr>
    <tr>
           <td>Df Model:</td>             <td>10</td>         <td>Log-Likelihood:</td>   <td>-217.17</td>
    </tr>
    <tr>
         <td>Df Residuals:</td>          <td>4861</td>           <td>LL-Null:</td>       <td>-2748.5</td>
    </tr>
    <tr>
          <td>Converged:</td>           <td>1.0000</td>           <td>Scale:</td>        <td>1.0000</td> 
    </tr>
    </table>
    <table class="simpletable">
    <tr>
                <td></td>             <th>Coef.</th>  <th>Std.Err.</th>     <th>z</th>     <th>P>|z|</th>  <th>[0.025</th>   <th>0.975]</th> 
    </tr>
    <tr>
      <th>fixed_acidity</th>         <td>-1.4449</td>  <td>0.1519</td>   <td>-9.5141</td> <td>0.0000</td>  <td>-1.7425</td>  <td>-1.1472</td>
    </tr>
    <tr>
      <th>volatile_acidity</th>     <td>-12.0133</td>  <td>0.9940</td>  <td>-12.0857</td> <td>0.0000</td> <td>-13.9615</td> <td>-10.0651</td>
    </tr>
    <tr>
      <th>citric_acid</th>           <td>0.1218</td>   <td>1.1387</td>   <td>0.1070</td>  <td>0.9148</td>  <td>-2.1101</td>  <td>2.3537</td> 
    </tr>
    <tr>
      <th>residual_sugar</th>        <td>0.0780</td>   <td>0.0578</td>   <td>1.3484</td>  <td>0.1775</td>  <td>-0.0354</td>  <td>0.1913</td> 
    </tr>
    <tr>
      <th>chlorides</th>            <td>-33.6942</td>  <td>4.1533</td>   <td>-8.1125</td> <td>0.0000</td> <td>-41.8346</td> <td>-25.5538</td>
    </tr>
    <tr>
      <th>free_sulfur_dioxide</th>   <td>-0.0474</td>  <td>0.0149</td>   <td>-3.1804</td> <td>0.0015</td>  <td>-0.0767</td>  <td>-0.0182</td>
    </tr>
    <tr>
      <th>total_sulfur_dioxide</th>  <td>0.0691</td>   <td>0.0055</td>   <td>12.6272</td> <td>0.0000</td>  <td>0.0584</td>   <td>0.0798</td> 
    </tr>
    <tr>
      <th>density</th>               <td>45.6528</td>  <td>4.4627</td>   <td>10.2299</td> <td>0.0000</td>  <td>36.9061</td>  <td>54.3994</td>
    </tr>
    <tr>
      <th>pH</th>                   <td>-10.0587</td>  <td>1.0255</td>   <td>-9.8086</td> <td>0.0000</td> <td>-12.0687</td>  <td>-8.0488</td>
    </tr>
    <tr>
      <th>sulphates</th>             <td>-9.1971</td>  <td>1.0697</td>   <td>-8.5980</td> <td>0.0000</td> <td>-11.2936</td>  <td>-7.1006</td>
    </tr>
    <tr>
      <th>alcohol</th>               <td>0.5328</td>   <td>0.1284</td>   <td>4.1494</td>  <td>0.0000</td>  <td>0.2811</td>   <td>0.7844</td> 
    </tr>
    </table>



On ne garde que les deux premières.

.. code:: ipython3

    X_train2 = X_train.iloc[:, :2]

.. code:: ipython3

    import pandas
    df = pandas.DataFrame(X_train2.copy())
    df['y'] = y_train
    
    import matplotlib.pyplot as plt
    fig, ax = plt.subplots(1, 1, figsize=(4, 4))
    df[df.y == "white"].plot(x="fixed_acidity", y="volatile_acidity", ax=ax, kind='scatter', label="white")
    df[df.y == "red"].plot(x="fixed_acidity", y="volatile_acidity", ax=ax,
                           kind='scatter', label="red", color="red", s=2)
    ax.set_title("Vins rouges et white selon deux composantes");



.. image:: wines_color_line_8_0.png


.. code:: ipython3

    from sklearn.linear_model import LogisticRegression
    model = LogisticRegression()
    model.fit(X_train2, y_train == "white")




.. parsed-literal::
    LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
              intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
              penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
              verbose=0, warm_start=False)



.. code:: ipython3

    model.coef_, model.intercept_




.. parsed-literal::
    (array([[ -0.92015604, -10.76494765]]), array([11.96976599]))



On trace cette droite sur le graphique.

.. code:: ipython3

    x0 = 3
    y0 = -(model.coef_[0,0] * x0 + model.intercept_) / model.coef_[0,1]
    x1 = 14
    y1 = -(model.coef_[0,0] * x1 + model.intercept_) / model.coef_[0,1]
    x0, y0, x1, y1




.. parsed-literal::
    (3, array([0.85548933]), 14, array([-0.08475829]))



.. code:: ipython3

    import matplotlib.pyplot as plt
    fig, ax = plt.subplots(1, 1, figsize=(4, 4))
    df[df.y == "white"].plot(x="fixed_acidity", y="volatile_acidity", ax=ax, kind='scatter', label="white")
    df[df.y == "red"].plot(x="fixed_acidity", y="volatile_acidity", ax=ax,
                           kind='scatter', label="red", color="red", s=2)
    ax.plot([x0, x1], [y0, y1], 'y--', lw=4, label='frontière trouvée\npar la régression\nlogistique')
    ax.legend()
    ax.set_title("Vins rouges et blancs\nselon deux composantes");



.. image:: wines_color_line_13_0.png