I need to extract the uncertainty from a two-dimensional chi square minimization contour plot between the three variables (x, y, and z). Basically, I plotted the two physical parameters on the x and y axes and the chi square on the z axis. I obtained a closed contour (chi square minimization condition). Now, based on that closed contour, I want to extract the uncertainty in two physical parameters (x and y). How do I extract it? Please let me know if anyone has any ideas.

I think @moneta and @jonas will be able to help you. In principle, what you are after is a “section” along 2 directions of the 2D shape of your chi2 I believe…

From the contours of the chi2 function you can get the confidence interval regions of your two variables x and y. If you want the separate uncertainty in x and y you should do a profile likelihood scan (or MINOS error analysis). See for example this note and any statistical book for HEP, such as this one (see chapter 2).