[R] Product of MSE and number of parameters when generating covariance matrix for Nonlinear least squares?

Geoff Loveman geoff at lovemans.co.uk
Sat Feb 15 01:26:41 CET 2014


In 'An Introduction to R', section 11.7 on nonlinear least squares fitting,
the following example is given for obtaining the standard errors of the
estimated parameters:

"To obtain the approximate standard errors (SE) of the estimates we do:
     > sqrt(diag(2*out$minimum/(length(y) - 2) * solve(out$hessian)))
The 2 in the line above represents the number of parameters."

I know the inverted Hessian is multiplied by the mean square error and that
the denominator of the MSE is the degrees of freedom (number of samples -
number of parameters) but why does the numerator of the MSE (which is the
RSS) get multiplied by the number of parameters? I have read through
explanations of the method for obtaining the SE but I don't see where the
MSE gets multiplied by the number of parameters or why this is needed as
shown in the example?

Thanks for any help!

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