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:


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


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!


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