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