.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_02_calibration_line.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_plot_02_calibration_line.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_02_calibration_line.py:


Calibration line
================

A thermocouple voltage is calibrated against reference temperatures. The model is a
straight line; each voltage reading has its own uncertainty.

.. GENERATED FROM PYTHON SOURCE LINES 10-22

.. code-block:: Python

    import numpy as np

    import fitwise as fw

    rng = np.random.default_rng(2)
    temperature = np.array([0.0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200])  # °C
    u_volt = 0.010 + 0.0002 * temperature  # mV, larger at high temperatures
    voltage = 0.0410 * temperature - 0.02 + rng.normal(0, u_volt)

    result = fw.fit(fw.models.linear, temperature, voltage, yerr=u_volt)
    print(result)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Model:      linear(x; slope, intercept)
    Method:     Linear least squares (direct) (auto: linear in the parameters)
    Converged:  yes (3 evals)
    Data:       11 points, yerr given (absolute)
    Start:      slope, intercept: not needed (linear model)

    Parameter     Value   ± Std.Err     Rel.   Bounds
    slope       0.04110     0.00012    0.3 %   –
    intercept   -0.0247      0.0080   32.2 %   –

    χ²/ndf = 1.38 (9 dof, p = 0.19)    R² = 0.99989    AIC = 5.3
    Correlations > 0.5:  slope–intercept (-0.62)
    Warnings:   none




.. GENERATED FROM PYTHON SOURCE LINES 23-26

The slope is the sensitivity of the thermocouple in mV/°C. Note the strong negative
correlation between slope and intercept, listed in the report: both are estimated from the
same points, so their errors are not independent.

.. GENERATED FROM PYTHON SOURCE LINES 26-30

.. code-block:: Python

    fig, axes = result.plot(show_params=True)
    axes[0].set_ylabel("voltage (mV)")
    axes[1].set_xlabel("temperature (°C)")




.. image-sg:: /auto_examples/images/sphx_glr_plot_02_calibration_line_001.png
   :alt: plot 02 calibration line
   :srcset: /auto_examples/images/sphx_glr_plot_02_calibration_line_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 18.503588541666666, 'temperature (°C)')



.. GENERATED FROM PYTHON SOURCE LINES 31-33

Because the uncertainties were given, χ²/ndf tests whether they are realistic. A value near
1 means the line describes the data within their errors.

.. GENERATED FROM PYTHON SOURCE LINES 33-34

.. code-block:: Python

    print(f"χ²/ndf = {result.redchi:.2f}, p = {result.pvalue:.2f}")




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    χ²/ndf = 1.38, p = 0.19





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

   **Total running time of the script:** (0 minutes 0.131 seconds)


.. _sphx_glr_download_auto_examples_plot_02_calibration_line.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_02_calibration_line.ipynb <plot_02_calibration_line.ipynb>`

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

      :download:`Download Python source code: plot_02_calibration_line.py <plot_02_calibration_line.py>`

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

      :download:`Download zipped: plot_02_calibration_line.zip <plot_02_calibration_line.zip>`


.. only:: html

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

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