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.