# How to estimate the goodness of a 2D fit using the chi-square distribution?

I have measured a quantity $b$ as a function of two variables, let's say $x$ and $y$. Then I fitted a 2D polynomial of the shape $$b(x,y) = \sum c_{j,i} x^i y^j$$ to the data (which is of 2nd order).

To estimate the goodness of the fit, I calculated the $\chi^2$ value as $$\chi^2 = \sum_i\frac{\left(O_i-E_i\right)^2}{E_i},$$ where $O_i$ are the observed (measured) values and $E_i$ are the expected (fitted) values.

I have 30 points in parameter space, that is 30 different combinations of $x$ and $y$ and the resulting $b$ values. If I understand it correctly, the degrees of freedom are $$\mbox{DF} = 30 - 1 = 29.$$

Using some calculator or tabulated values and using a significance level of 0.05 (a confidence-level of 95 %), I allow for $\chi^2 \lesssim 18$ to say "That fit is good."

Is that a reasonable statement to estimate the goodness of a 2D fit or is that completely non-sense ?