least squares error ellipse

I'm doing a least squares computation in C and it's mostly pushing matrices
around and combing them in different ways according to a recipe that I just
copied without trying to understand it, it works great, but now I've been
asked to add an error ellipse to each point I locate

( I solve the equations and get best fit coordinates for point in 2-space)

I understand an error ellipse to be the two dimensional cousin of the
confidence interval I learnt about in stat101. the problem is the only
algorithm I've found to generate the ellipse uses a function I've never
heard of and can't identify.

here's an exceprt from the documentation I found using google:

<http://www.orbitals.com/self/least/least.htm#Error>

..
..To determine the error to a specific confidence level, the length of the
..semi-axis is multiplied by a confidence factor based on the Fisher
..distribution using the formula
..
.. S_axis% = S_axis sqrt( 2 * Fisher( 1 - confidence, numOfUnknowns , r ) )
..
..where the confidence is a number from 0 to 1, with 1 being complete
..confidence, and r is the number of degrees of freedom. The Fisher
..distribution is determined from the equation


the eigenvectors had me worried for a while until I realised I only had to
do it for a 2x2 matrix so that bit is solved. my problem is I can't figure
out how to compute the Fisher Function,

I tried Google but it gave me a bunch of hits on different sorts of fisher
distributions and functions that seemed to have different numbers and/or
ordering of their arguments.

If someone can point me to a website that tells me how to compute this
fisher function on an ordinary spread***, or a scientific calculator,
or in a computer language like C, Pascal, or BASIC that'd be great.

--

Bye.
Jasen
.

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