| ▲ | CGMthrowaway 3 days ago | |
That makes sense. Why does least squares skew the line downwards though (Vs some other direction)? Seems arbitrary | ||
| ▲ | mr_toad 3 days ago | parent | next [-] | |
The Pythagorean distance would assume that some of the distance (difference) is on the x axis, and some on the y axis, and the total distance is orthogonal to the fitted line. OLS assumes that x is given, and the distance is entirely due to the variance in y, (so parallel to the y axis). It’s not the line that’s skewed, it’s the space. | ||
| ▲ | sega_sai 3 days ago | parent | prev [-] | |
I think it has to do with the ratio of \Sigma_xx, \Sigma_yy. I don't have time to verify that, but it should be easy to check analytically. | ||