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I have a non-linear reglationship and I want to find the best way to determine the value for the exponent $\gamma$ in the following regression:

$y = \beta x ^ \gamma$

I would preferably like to do this in R.

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It depends on what you mean by "best" and on the nature of your data. For example, if $y$ is measured with additive error then really $y = \beta x^\gamma + \varepsilon$, which is nonlinear, but if $y$ is measured with multiplicative error then $\log(y) = \log(\beta) + \gamma \log(x) + \delta$ is actually a linear model. The two models are not the same: typically they will produce (slightly) different estimates of $\gamma$ and different standard errors. If also $x$ is measured with error, both models get substantially more complicated and yield yet two more estimates. – whuber♦ Jan 16 at 16:24

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