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[tex]r_i == f_i (g,\beta)[/tex]

Where g and [itex]\beta[/itex] are the independent unknown variables and [itex]r_i[/itex] are known experimentally, but have some error associated with them, say something like [itex]4.3 \pm 0.3[/itex] and there are other errors associated with constants inside the [itex]f_i[/itex].

My question is how do I solve for the objectively "best" fit to those two parameters. I remember doing something like this back in prob/stats, I believe I do something like a [itex]\chi^2[/itex] fit but I can't find anything online about it that doesn't concern bins of data points, but rather continuous functions. (Or do I have to simulate data, then fit it)

Can anyone lead me in the right direction? I don't have any of my undergrad books with me.

The equations are all something like :

[tex]

r_1 =\frac{\left(g^2 x+g^2y-\frac{\beta }{3}\right)^2}{g^2 }

[/tex]

with some variations on the form. So nothing with unsolvable functions.

EDIT: Oh and I plan on using Mathematica to do this, but I'd rather understand the mathematics first.