test a cloud of 2D points for linearity

[Georg P. Israel]

Dear all,

I am almost ashamed to ask this stupid question,
but with all this wealth of function, i seem to not find the right
stuff. Even thought, I know that it is there, probably just under my
nose.

here my problem:

I have a number of points in a plain (2D points)
This points can have an arbitrary distribution.
I would like to have a function that will fit the line through this
cloud of points.

I expect that one point of this line is the mean of all points plus some
direction vector.

The next thing that I like to have now is the RMS of all the distances
of the points along this line. This is basically a variance as seen
along this line.

Now, I can certainly start to clumsily develop this function, but I am
sure that I am just overlooking the right function.

Hence,
please point my nose this this function ... 

Best regards

Georg P. Israel