wls - optim_doc
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### 2.6 Statistics for weighted least squares

The backends for `objf_type == "wls"` (currently the only supported type of objective function) compute `covd` (due to user request or as a prerequisite for `covp` and `corp`) as a diagonal matrix by assuming that the variances of data points are proportional to the reciprocal of the squared `weights` and guessing the factor of proportionality from the residuals. If `covp` is not defined (e.g. because the Jacobian has no full rank), an attempt is made to still compute its uniquely defined elements, if any. In `corp`, interdependent parameters can cause elements of `1` or `-1`, which in this case are not the real coefficients of correlation, but rather indicate the direction of parameter interdependence. To be consistent with this, an attempt is made (often not successful) to identify parameter interdependence and mark it with elements of `1` or `-1` in `corp` even if the respective elements of `covp` can not be computed.