Best fit line using geometric distance (not vertical distance)

Question

There must be a theory of finding the best fit line to a bunch of points in the plane, where "best fit" is defined by the geometric distance, not vertical distance. In other words, we are trying to minimize the sum of the squares of the distances from the points to the line, where the distance is measured along lines that are perpendicular to the best fit. What is this theory called, and where can I learn about it?

Answer 1

You are looking for Deming regression, which is a special (bivariate) case of total least squares aka orthogonal regression.