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

Here, “distance” means the difference between the observed value and the estimated value, not the length of the shortest line segment that passes through the point and intersects the line. The latter definition is fine for geometry, but the former is more useful for modeling.