Ok, everything I wrote in Post # 12 is wrong. I'm going to try an entirely different approach: rotations. We start with a simple North-South hyperbola, which we can write as

Here

are the slopes of the asymptotes.

Here is a plot, where

What we would like to do is rotate this figure counter-clockwise through some angle such that the

asymptote lines up with the x axis, and the

asymptote becomes the slope of the line corresponding to your data. It turns out that the hyperbola to start with such that when you rotate it through a certain angle, you get one asymptote to be the x axis, and the other the line

is the following:

Next, we rotate the coordinates counter-clockwise through the angle

Define

and

Then our new coordinates become

Plugging this into our hyperbola equation yields

Finally, to translate the hyperbola to the right by

units, we simply replace

by

to obtain

Solving for y yields the upper sheet equation of

So this is the equation to which you're going to fit your data. It has three parameters: the slope

the x-intercept

and an arbitrary parameter

that measures how close the hyperbola gets to the intersection of its two asymptotes.

I have plotted this equation, and it looks right to me.

That's all for now. Next step: least-squares fit!