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I have $x$- and $y$-data, and I want a power-law fit ($y=ax^b$). I always fit $\log(x)$ and $\log(y)$ by $p_1x+p_2$ (Matlab poly1), but when I fit $x$ and $y$ with $p_1x^{p_2}$, I did not get exactly the same result. Why?!

And what is the best way for doing this? First take logs then linear fit??

mehrdad
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  • See 1. https://stats.stackexchange.com/questions/61747/linear-vs-nonlinear-regression. 2. https://stats.stackexchange.com/questions/47870/exponent-for-non-linear-regression-in-r 3. https://stats.stackexchange.com/questions/148638/how-to-tell-the-difference-between-linear-and-non-linear-regression-models 4. https://stats.stackexchange.com/questions/47266/fitting-an-exponential-function-using-least-squares-vs-generalized-linear-model 5. https://stats.stackexchange.com/questions/140706/pitfalls-in-fitting-nonlinear-models-by-transforming-to-linearity - (Re: 4,5: same issue, different model) – Glen_b Dec 04 '18 at 13:27
  • Please review these posts. If you have any remaining questions after reading these, please ask a new question. – Glen_b Dec 04 '18 at 13:35

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