data points to the regression line. In this case, denote each observation as a point zj in the complex plane (i.e., the point (xj, yj) is written as zj = xj + iyj where i is the imaginary unit). Denote as Z the sum of the squared differences of the data points from the centroid (also denoted in complex coordinates), which is the point whose horizontal and vertical locations are the averages of those of the data points. Then: If Z = 0, then every line through the centroid is a line of best orthogonal fit. If Z ≠ 0, the orthogonal regression line goes through the centroid and is parallel to the vector from the origin to . A trigonometric representation of the orthogonal regression line was given by Coolidge in 1913. Application In the case of three non-collinear points in the plane, the triangle with these points as its vertices has a unique Steiner inellipse that is tangent to the triangle's sides at their midpoints. The major axis of this ellipse falls on the orthogonal regression line for the three vertices. The quantification of a biological cell's intrinsic cellular noise can be quantified upon applying Deming regression to the observed behavior of a two reporter synthetic biological circuit. See also Line fitting References Notes Bibliography Curve fitting Regression analysis