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Chi^2 test with dominating x-errors

  1. Sep 13, 2012 #1
    Hi,

    I am using thie χ2 test to fit a dataset in order to calibrate a sensor.

    [itex]\chi^{2} = \sum_{i}{{\left(y_{i} - (a_{0}+a_{1}*x_{i}+a_{2}*x_{i}^{2})\right)^2 \over \sigma_i^2}}[/itex]

    The sensor delivers raw data [itex]x_{i}[/itex] and the reference values [itex]y_{i}[/itex] are measured with an instrument of far greater precision than the sensor that is calibrated.

    The coefficients [itex]a_0, a_1, a_2 [/itex] have to be determined with the test.


    The uncertainty in the [itex]x_{i}[/itex] and the [itex]y_{i}[/itex] are known. Unfortunately the [itex]x_{i}[/itex] uncertainties cannot be neglected.

    Could anyone tell me how I can calculate the [itex]\sigma_i[/itex] values?

    Thank you very much!
     
  2. jcsd
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