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

The x value is fixed. It’s the input variable for your model. The y value is what is being predicted. You are measuring the error between the predicted value and the known value.