# Chi-squared confidence intervals for big measurments

Let's say I have some observational data. For example: in a certain wavelength interval I measure the flux, 10 000 points, and I have the uncertainty for each one of them. For example:

Wavelength Flux Sigma_flux
5000.00    0.988  0.00012
5001.00    0.986  0.00013
...


And I have a grid of parameters that, for four different inputs give me a simulated data in the same wavelengths. For example:

Wv-simul Flux-simul
5000.00  0.991
5001.00  0.989
...


For the 10000 points.

Now I can calculate the chi-squared and see which model better fits the data. First basic question, should I calculate using:

$\chi&space;^{2}=&space;\sum&space;\frac{(O_i&space;-&space;E_i)^2}{dO_i^2}$

or

$\chi&space;^{2}=&space;\sum&space;\frac{(O_i&space;-&space;E_i)^2}{E_i}$

And after I calculate my chi-squared, let's say I fix all the parameters except one. In that way I can see how the chi squared varies for that parameter, and I have some kind of parabola where I can identify where the minimum is. I'm not really sure of the method to calculate the confidence interval. From what I read I could use a relation that says that

$\sigma_j^2&space;=&space;2\left&space;(\frac{\partial&space;\chi^2}{\partial&space;a_j^2}\right&space;)^{-1}$.

Or I could add +1 to the minimum chi-squared and see at which values the intersection with the "parabola" would happen (+1 because I'm working with 1 parameter), or even if I should add all the value equivalent to all the degrees of freedom, that I'm guessing in includes the N data points.

I'm kind of lost, thank you for the help!