Minimum distance regression

Question

Hi,
Why is the minimum distance parallel to the y-axis and not from the point directly towards the red line?
There could be angle if it not parallel to the y-axis

Answer 1

Because the X is fixed, that's your input. The Y is your output and what you are trying to optimize. So you compare your actual Y with the Y you predicted with the corresponding X.

Comments

I am not sure this answers my question. The distance you minimize is always parallel to the y-axis. that is what you showed.
But I saw recently an example where people went from the points not parallel in y toward the slope from each point, but under an angle in comparison to y