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total least squares
Total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models.
The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix.〔I. Markovsky and S. Van Huffel, ''Overview of total least squares methods.'' Signal Processing, vol. 87, pp. 2283-2302, 2007. (preprint )〕
== Linear model ==
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