Correlation and covariance
An indication of the accuracy of the fit is displayed in the output under the
names
and
.

where n is the number of degrees of freedom, and
where
are the
diagonal elements of the inverse of the matrix
.
is called the covariance matrix.
The
are called the root mean square statistical errors of estimate.
The
are called the root mean square total errors of estimate, or
standard errors.
The accuracy of the parameters in a linear fit is

In the linear case, for the standard error
to be correct, the weights
wk must be proportional to 1/σk2,
where σk is the standard deviation of the probability distribution of
yk. In the nonlinear case,
does not have the same
statistical significance.
If the \COVMAT qualifier is used, a matrix called
FIT$COVM will be created which
will contain
.
If the \CORRMAT qualifier is used, a matrix with the name
FIT$CORR will be created which will contain the correlation
matrix for the fit. The size of these matrices will be M by M.
If the \E1 qualifier is used, then the root mean square statistical error for each fit
parameter are output into an automatically created vector named FIT$E1
.
If the \E2 qualifier is used, then the root mean square total error of estimate for each
parameter are output into an automatically created vector named FIT$E2
.
The values are stored in these vectors in the order corresponding to the order in which the parameters appeared in the expression. The length of these vectors will be equal to the number of parameters in the fit expression.