.. _sphx_glr_api_gallery_numerical_analysis_regression:

Least-squares regression
-------------------------

Polynomial least-squares regression via the normal equations, and how the
fit's numerical conditioning worsens as the polynomial degree grows.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbcontainer" tooltip="PolynomialRegression fits a degree-``d`` polynomial by solving the normal equations V^T V c = V^T y. This script fits noisy cubic data, checks the R^2 and residuals, and then shows the fit&#x27;s condition number (estimated via power iteration on the normal-equations matrix) growing sharply with degree -- squaring the design matrix&#x27;s own condition number is exactly why the normal-equations approach is eventually replaced by a QR-based least-squares solve in mathematicskit.linalg.">

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  .. image:: /api/gallery/numerical_analysis/regression/images/thumb/sphx_glr_plot_01_polynomial_regression_thumb.png
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  :doc:`/api/gallery/numerical_analysis/regression/plot_01_polynomial_regression`

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      <div class="sphx-glr-thumbnail-title">Least-squares polynomial regression and its conditioning</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/numerical_analysis/regression/plot_01_polynomial_regression