Is it possible for more than one "linear regression" line to fit a given set of points? (i.e.... "least squares" is minimised equally in both cases)
I'm assuming a simple one-variable regression in which we have a single "dependent" variable for a given x-value. It may be that regression is forced "through the origin" for the purpose of the Q (if that matters), so, I know it wouldn't be a great fit.
Or is there something intrinsic about a regression line that means it is unique? I am interested in a 'proof' (could be just an intuitive proof) if it exists, that a regression line must be unique.