I want to fit a curve to data using non linear least squares with matrix inversion http://mathworld.wolfram.com/NonlinearLeastSquaresFitting.html

Right now I'm using this, but I'm not sure what algorithm it is using, but I suspect it may not be using non-linear least squares.

z4 = NonlinearModelFit[spectra, a (x + 99)^-2.5 + b (x + 99)^-1.5 + c (x + 99)^-0.5 + d (x + 99)^0.5, {a, b, c, d}, x];

I've tried the "Method -> Option" , but I can't find an option that says nonlinear least squares (regular least squares only allows 2 variables).

I could use some help figuring out what Mathematica is doing and how to get it to using matrix inversion so that I can get a covarience matrix for the fit and not use a method where iterations are done to find the best coefficients.

Thanks in advance, Tom