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.

Tolerance
Confidence level of the fit