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==Orthogonal regression==
For the case of equal error variances, i.e., when <math>\delta=1</math>, Deming regression becomes '''orthogonal regression''': it minimizes the sum of squared [[distance from a point to a line|perpendicular distances from the data points to the regression line]]. In this case, denote each observation as a point <math>z_j = x_j +i y_j</math> in the complex plane (i.e., the point <math>(x_j, y_j)</math> where <math>i</math> is the [[imaginary unit]]). Denote as <math>S=\sum{(z_j - \overline z)^2}</math> the sum of the squared differences of the data points from the [[centroid]] <math>\overline z = \tfrac{1}{n} \sum z_j</math> (also denoted in complex coordinates), which is the point whose horizontal and vertical locations are the averages of those of the data points. Then:{{sfn|Minda|Phelps|2008|loc=Theorem 2.3}}
*If <math>S=0</math>, then every line through the centroid is a line of best orthogonal fit.
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