I'm not a mathematician so I hope I ask this question properly; I apologize for anyone who is annoyed with how I ask it (I will try my best to be precise).
Say I have a point cloud in $\Re^3$. I wish to fit a line through to this point cloud. However - and this is the kicker - I wish to force the line through a specified point in the point cloud; that is, I wish to find a vector through a point I specify which minimizes the distance squared from all the points in the cloud to the line spanned by the vector. Does this make sense?
If I were explaining this to a non-mathematician (like me), I would say I want to "anchor" a line on one of the points and then best fit the line from there.
I understand the notion of ordinary least squares, but this particular spin on the problem doesn't make sense to me.
Thanks in advance, Ben