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So I had some raw data, and it looked like there was a square root relation. I plotted graphs of $y=\sqrt{x}$

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They look kind of straight. So doing the algebra and taking the ln of both sides, we get $\ln y=0.5 \ln x+\ln k$

I then plotted the graphs of the ln values, but they weren't that straight. Clearly, there is a problem here. What exactly can be done about it?

enter image description here

Jim
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  • Did you have a particularly reason to think it should be a square-root relation? In general, I find it's a bad idea to 'guess' a functional form empirically. (On the other hand, guessing from theory is usually a good idea.) – Semiclassical Aug 04 '14 at 18:22
  • @Semiclassical there's actually not a lot of quantitative theory available but from what I have found, the relation is a square root one. My raw data looks like it too.. – Jim Aug 04 '14 at 18:48
  • Hmm. Certainly there's a small but obvious deviation from square-root behavior. But the presence of that deviation is all the math can really say. The "why" of it is something to do with the model or the experimental conditions, i.e. the context of the data. We can't really help with that. – Semiclassical Aug 04 '14 at 18:51

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