.. _sphx_glr_auto_examples_LinearModels:

Linear Models
====================



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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_LinearRegressionConfidenceIntervals_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_LinearRegressionConfidenceIntervals.py`

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      <div class="sphx-glr-thumbnail-title">Linear Regression with confidence intervals</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates the use of RANSAC (Random Sample Consensus) regression to fit a robust model in the presence of outliers. A quadratic relationship is used to generate inlier data, while a separate set of points acts as outliers. The performance of standard linear regression is compared with RANSAC regression to highlight the latter&#x27;s robustness to noisy data.">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_RANSAC_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_RANSAC.py`

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      <div class="sphx-glr-thumbnail-title">Robust Regression with RANSAC</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates polynomial regression on a 2D dataset using total least squares (TLS). It generates a grid of input points, applies polynomial feature expansion, and fits a linear regression model. Predictions are visualized in 3D, comparing model output (blue) against actual values (red).">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_PolynomialFeatures_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_PolynomialFeatures.py`

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      <div class="sphx-glr-thumbnail-title">Polynomial Surface Regression with Total Least Squares</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script trains a logistic regression model on the Iris dataset using  gradient descent. It supports both binary and multi-class classification.">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_LogisticRegression_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_LogisticRegression.py`

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      <div class="sphx-glr-thumbnail-title">Logistic Regression on the Iris Dataset</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates Locally Weighted Regression (LWR), using a Gaussian kernel  to assign weights to training samples based on their distance from a test  point.">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_LocallyWeightedRegression_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_LocallyWeightedRegression.py`

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      <div class="sphx-glr-thumbnail-title">Locally Weighted Regression on a Sine Function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates the effect of L1 (LASSO), L2 (Ridge), and  ElasticNet regularization on regression coefficients. It generates  a 3D synthetic dataset and fits different models with varying alpha  (regularization strength), tracking the weight paths.">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_LinearRegularisation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_LinearRegularisation.py`

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      <div class="sphx-glr-thumbnail-title">Regularization Path for Ridge, LASSO, and ElasticNet Regression</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates the use of linear regression models and their regularized counterparts (Ridge,  LASSO, and ElasticNet) on synthetic data. The models are fitted to 1D and 2D datasets, and performance  is evaluated through residual analysis, summary statistics, and visualizations.">

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  .. image:: /auto_examples/LinearModels/images/thumb/sphx_glr_LinearModels_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_LinearModels_LinearModels.py`

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      <div class="sphx-glr-thumbnail-title">Linear and Regularized Regression Models on Synthetic Data</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /auto_examples/LinearModels/LinearRegressionConfidenceIntervals
   /auto_examples/LinearModels/RANSAC
   /auto_examples/LinearModels/PolynomialFeatures
   /auto_examples/LinearModels/LogisticRegression
   /auto_examples/LinearModels/LocallyWeightedRegression
   /auto_examples/LinearModels/LinearRegularisation
   /auto_examples/LinearModels/LinearModels