On weighted total least-squares adjustment for linear regression

The weighted total least-squares solution (WTLSS) is presented for an errors-in-variables model with fairly general variance-covariance matrices. In particular, the observations can be heteroscedastic and correlated, but the variance-covariance matrix of the dependent variables needs to have a certain block structure. An algorithm for the computation of the WTLSS is presented and applied to a straight-line fit problem where the data have been observed with different precision, and to a multiple regression problem from recently published climate change research.