.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/LinearModels/LinearRegressionConfidenceIntervals.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_LinearModels_LinearRegressionConfidenceIntervals.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_LinearModels_LinearRegressionConfidenceIntervals.py:


Linear Regression with confidence intervals
==============================================

This script performs linear regression on a synthetic dataset using the 
LinearRegression class from the DLL library. It also computes and visualizes 
the 95% confidence interval for the regression line.

.. GENERATED FROM PYTHON SOURCE LINES 9-46



.. image-sg:: /auto_examples/LinearModels/images/sphx_glr_LinearRegressionConfidenceIntervals_001.png
   :alt: Linear Regression with 95% Confidence Interval
   :srcset: /auto_examples/LinearModels/images/sphx_glr_LinearRegressionConfidenceIntervals_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import torch
    import matplotlib.pyplot as plt
    from scipy.stats import t

    from DLL.MachineLearning.SupervisedLearning.LinearModels import LinearRegression


    x = torch.linspace(0, 10, 100)
    y = 2.5 * x + 3 + 5 * torch.randn(len(x))
    x = x.unsqueeze(1)

    model = LinearRegression()
    model.fit(x, y)
    y_pred = model.predict(x)
    x = x.squeeze()

    n = len(x)
    dof = n - 2
    s_err = torch.sqrt(torch.sum(model.residuals ** 2) / dof)

    t_crit = t.ppf(0.975, dof)
    x_mean = torch.mean(x)
    sum_sq_x = torch.sum((x - x_mean)**2)
    conf_margin = t_crit * s_err * torch.sqrt(1/n + (x - x_mean)**2 / sum_sq_x)

    y_upper = y_pred + conf_margin
    y_lower = y_pred - conf_margin

    plt.figure(figsize=(8, 8))
    plt.scatter(x.numpy(), y.numpy(), s=10, label="Data", alpha=0.6)
    plt.plot(x.numpy(), y_pred.numpy(), color="red", label="Regression Line")
    plt.fill_between(x.numpy(), y_lower.numpy(), y_upper.numpy(), color="red", alpha=0.2, label="95% CI")

    plt.xlabel("X")
    plt.ylabel("Y")
    plt.title("Linear Regression with 95% Confidence Interval")
    plt.legend()
    plt.show()

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

   **Total running time of the script:** (0 minutes 0.086 seconds)


.. _sphx_glr_download_auto_examples_LinearModels_LinearRegressionConfidenceIntervals.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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