Total Least Squares
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High Quality Content by WIKIPEDIA articles! Total least squares, also known as errors in variables, rigorous least squares, or orthogonal regression, is 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 can be applied to both linear and non-linear models. In short, total least squares does not have the property of units-invariance (it is not scale invariant). For a meaningful model we require this property to hold. A way forward is to realise that residuals (...
High Quality Content by WIKIPEDIA articles! Total least squares, also known as errors in variables, rigorous least squares, or orthogonal regression, is 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 can be applied to both linear and non-linear models. In short, total least squares does not have the property of units-invariance (it is not scale invariant). For a meaningful model we require this property to hold. A way forward is to realise that residuals (distances) measured in different units can be combined if multiplication is used instead of addition. Consider fitting a line: for each data point the product of the vertical and horizontal residuals equals twice the area of the triangle formed by the residual lines and the fitted line.
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