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I am using thie χ^{2}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!

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# Chi^2 test with dominating x-errors

Can you offer guidance or do you also need help?

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