Power laws commonly occur as sampling estimates of distributions. This means the inherent errors are on the order of the square root of the number. So small values have proportionately large errors. On a log-log plot they are big near the bottom and small near the top. The fitting algorithm needs to take these errors as inverse measures of the weight. It also matters whether you doing a maximum likelihood fit or a least squares fit or something else. That's why it is best to have a theory of the measurement scatter as well as the underlying relation. Brent On 9/23/2018 11:08 AM, Henry Baker wrote:
At 08:24 AM 9/23/2018, Richard Howard wrote:
If the physics of the problem leads one to suspect a power law (or exponential), it is tempting to fit a straight line on a log-log (or log-linear) plot in Excel.
This does not weight all points (and their uncertainties) properly. I can imagine that the error bounds on measurement errors don't scale properly after taking logs, but if the measurement errors are small compared with the underlying process variation (assuming that it is, indeed, a power law), then the weighting shouldn't be that far off.
Or is there some other issue that I'm missing here?
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