.. _sphx_glr_api_gallery_analytical_calibration:

Calibration curves
--------------------

Least-squares calibration lines, and the limits of detection and
quantitation derived from their residual scatter.


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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="The method of least squares picks the straight line that minimizes the sum of squared residuals S(m,b)=\sum_i(y_i-mx_i-b)^2. fit_calibration performs exactly that fit for a set of calibration standards; here we check that its slope sits at the bottom of the S(m) parabola, and that the residuals it leaves behind scatter around zero.">

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  .. image:: /api/gallery/analytical/calibration/images/thumb/sphx_glr_plot_01_least_squares_calibration_thumb.png
    :alt:

  :doc:`/api/gallery/analytical/calibration/plot_01_least_squares_calibration`

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      <div class="sphx-glr-thumbnail-title">Legendre and Gauss's least squares: fitting a calibration line</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Long and Winefordner argued that a detection limit should be tied to the calibration&#x27;s own residual scatter s_{y/x} and slope m. lod and loq use the widely adopted calibration-based convention \text{LOD}=3.3\,s_{y/x}/m and \text{LOQ}=10\,s_{y/x}/m. A noisier method has proportionally higher limits.">

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  .. image:: /api/gallery/analytical/calibration/images/thumb/sphx_glr_plot_02_limits_of_detection_and_quantitation_thumb.png
    :alt:

  :doc:`/api/gallery/analytical/calibration/plot_02_limits_of_detection_and_quantitation`

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      <div class="sphx-glr-thumbnail-title">Limits of detection and quantitation from a calibration curve</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/analytical/calibration/plot_01_least_squares_calibration
   /api/gallery/analytical/calibration/plot_02_limits_of_detection_and_quantitation