I have data (attached) that increases steadily and then levels off. I thought I'd fit it to an exponential trendline but that is concave whereas the data is convex. A Power trendline rises too rapidly. The best fit is a 2nd degree polynomial but that would extrapolate to dropping values and it should stay leveled out. What's the best way to handle data like this?
Last edited by ChemistB; 05-31-2012 at 02:26 PM.
ChemistB
My 2?
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Is the underlying behavior asymptotic? Is the oscillatory behavior noise or phenomenological?
Entia non sunt multiplicanda sine necessitate
The oscillatory behavior is noise. These are averages but not enough points to really smooth out the data.
You could try an exponential fit like a capacitor charging ...
y = y0 + v(1 - exp(-k/x))
where y0 is the initial value, v is the final value, and k is the time constant.
10 data points with oscillating signal noise? And you want to describe second-order behavior from it?
That's... I don't think there's a straightforward solution...
Well, what does "steady increase" mean? Linear behavior?
What does "levels off" mean?
So in materials engineering, steel (well, lots of materials, but the example is steel) will deform in a linear response to a linear loading--until a point, where the behavior changes and it no longer responds linearly. That point is the "yield strength", and usually it's determined numerically as the "2% yield strength"; you take the trend line of the linear portion, and when the real value exceeds 2% difference with the expected value from the trend line, you point at that line-cross and say "there, that's what we're calling the yield strength".
Could you do something similar? Find when it STOPS behaving linearly, and graph it as a slope up to that, then a different line from there?
I guess my feeling is, there's not enough data to describe what you expect with straight-forward numerical methods.
The data I'm presenting is an average. At each time point (the x axis), there are between 15-25 data points. While I'd love to have more data, I think it's enough to get an approximation. What I really want to do (and why this is in the graphing folder) is draw a best fit trendline. None of the Excel default trendlines seem to fit.
The expected behavior is a fairly rapid increase over 12 months (x axis in months) then not so much to 24 months after which it is almost level similar to what might expect in an exponential or power function. The points presented are fairly representative.
See attached.
Last edited by shg; 05-30-2012 at 07:28 PM.
Excellent, that's what I was looking for. I need more practice with Solver. Thanks shg.
Having trouble reproducing the results.
I set up the equations for each y (in your spreadsheet B3:K3), set up the RMS Error and named 3 cells a, b and k.
I set the solver to look at the RMS Error cell, set to minimum and based on cells a,b and k? or on B3:K3? Did you modify any options within solver?
EDIT: Nevermind, figured it out. Had non-negative numbers checked.
Last edited by ChemistB; 05-31-2012 at 02:26 PM.
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