How do Igor's CurveFit and FuncFit operations calculate W_sigma?

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Wed, 07/22/2015 - 12:38 pm

I've been trying to better understand how W_sigma is calculated, and have found the following snippet in the "Curve Fitting" help topic:

"Igor automatically calculates the estimated error (standard deviation) for each of the coefficients in a curve fit. When you perform a curve fit, it creates a wave called W_sigma. Each point of W_sigma is set to the estimated error of the corresponding coefficients in the fit. The estimated errors are also indicated in the history area, along with the other results from the fit. If you don't provide a weighting wave, the sigma values are estimated from the residuals. This implicitly assumes that the errors are normally distributed with zero mean and constant variance and that the fit function is a good description of the data."

Is there a more complete reference explaining (with equations, perhaps) how these estimated errors are calculated? I'm trying to fill in some gaps in my knowledge of what the least-squares fit is. From what I've been reading in Igor's help literature, the relevant quantity seems to be something called the covariance matrix, and there seem to be some important aspects related to normalization, but this is about as far as I understand.

Thanks!