The Case of Equal Error Variances
When, Deming regression becomes orthogonal regression: it minimizes the sum of squared perpendicular distances from the 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.
Read more about this topic: Deming Regression
Famous quotes containing the words case, equal and/or error:
“... business training in early life should not be regarded solely as insurance against destitution in the case of an emergency. For from business experience women can gain, too, knowledge of the world and of human beings, which should be of immeasurable value to their marriage careers. Self-discipline, co-operation, adaptability, efficiency, economic management,—if she learns these in her business life she is liable for many less heartbreaks and disappointments in her married life.”
—Hortense Odlum (1892–?)
“If the aristocrat is only valid in fashionable circles, and not with truckmen, he will never be a leader in fashion; and if the man of the people cannot speak on equal terms with the gentleman, so that the gentleman shall perceive that he is already really of his own order, he is not to be feared.”
—Ralph Waldo Emerson (1803–1882)
“What has been the effect of [religious] coercion? To make one half the world fools, and the other half hypocrites. To support roguery and error all over the earth.”
—Thomas Jefferson (1743–1826)