# Chi^2 test with dominating x-errors

1. Sep 13, 2012

### egon ll

Hi,

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

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

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

The coefficients $a_0, a_1, a_2$ have to be determined with the test.

The uncertainty in the $x_{i}$ and the $y_{i}$ are known. Unfortunately the $x_{i}$ uncertainties cannot be neglected.

Could anyone tell me how I can calculate the $\sigma_i$ values?

Thank you very much!