Why in the Ordinary Last Squares method are the distances from the line measured straight up/down?

Question

Hello,

Why does the OLS method minimize the distances from the estimated line that are parallel to the Y axis?

Shouldn’t the distances be minimal if they were at 90° angle to the estimated line?

In: 3

Answer 1

Generally you assume that you have no error (or at least very very little error) in the x-position, and larger error in the y-direction. This means that its super unlikely a point will be to the left/right of a point on your model. It’s much more likely to be directly above/below, so you fit based off of the y-error.

For cases where you actually do have uncertainty in the x position as well, there exist other fitting methods, like Orthogonal Distance Regression that do more like what you’re asking about.