Richard Jackson wrote:
Another question you may also ask is, why we are using the vertical distance as error and not the horizontal one or, even better, the perpendicular one (guess this would be fun when we include units). Think the answer is - because its easier!
The assumption is that there is an independent variable and a dependent variable, and the independent variable has no error. By convention the independent variable is plotted on the abscissa, so the errors are "vertical".
Yes, its a matter of what one would like to use the fitted line for and the appraoch you sketch sure is the most common one in technical statistics.
I was drawn away by a pure geometrical point of view where perpendicular distance would be the only true correct (whatever that should mean in that context) appraoch. Its hard to define anyway what the meaning of "this line fits the data points best" should mean and so we define that its exactly that what we calculate (sum of squared "distance", or sum of absolute values of the same or whatever). Which result fits your needs best may be a completely different question and may depend on your application, your data itself, your willingness to manually remoce outliers before, etc.
I have a nice example worksheet (not written by me) of a parametric least squares fit to an ellipse, in which the errors are always perpendicular to the ellipse.
Sounds interesting.
Are you referring to this one?: http://communities.ptc.com/message/219565#219565