"KevinW" wrote:

Just to be clear, I am -not- trying to find the 'best fit' for a plot
of scattered data. Rather, I am trying to find an equation to describe
an existing line. I scanned and digitized a Larson-Miller curve I will
be using extensively for my thesis. The data points are very close
together. I'd like to be able to enter a value and return the
corresponding value from the curve. As long as the answer is the same
as the original curve, then I'm happy with the equation for the line.

Jon Peltier (a PhD metalurgist) might be able to add more, but what I have
seen of Larson-Miller curves (based on a Google search) they are smooth
monotonic curves that may not be fit well by a single low-order polynomial
over the entire range.

You might do better with local interpolation. y = (a+b*x)/(1+c*x) is a
simple function that you can fit with 3 observations for local monotonic
interpolation. Linear interpolation (c=0) is a special case.

To fit the function, you would need 3 points bracketing your desired point,
all having distinct x-values and distinct y-values. Given the discreteness
of your observations, I would tend to use the median x-value for a given
y-value, ... You might compare or even average the results from 3 points
with 2 of them to the left of the desired point and 3 poitns with 2 of them
to the right of the desired point.

Jerry