Question

I have a confusion about Lec 16 videos. How is the error calculated "vertically" instead of at an angle ... If p is projected on the line, b would be a little to the left and not directly above p, correct?

Answer 1

The error is *not* (defined) as the the "shortest distance" from a point to the line.
Rather, the idea is
you find m and b so that we can predict y:
y_predicted= m x_input + b

and the squared error is *defined* to be (y_actual - y_predicted)^2

You could define the error the way you are thinking, but the math is probably more ugly.