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→Applications: changed statement about use of log-log lines and limited validity for estimating power laws |
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Log–log regression can also be used to estimate the [[fractal dimension]] of a naturally occurring [[fractal]].
However, going in the other direction – observing that data appears as an approximate line on a log–log scale and concluding that the data follows a power law – is
In fact, many other functional forms appear approximately linear on the log–log scale, and simply evaluating the [[goodness of fit]] of a [[linear regression]] on logged data using the [[coefficient of determination]] (''R''<sup>2</sup>) may be invalid, as the assumptions of the linear regression model, such as Gaussian error, may not be satisfied; in addition, tests of fit of the log–log form may exhibit low [[statistical power]], as these tests may have low likelihood of rejecting power laws in the presence of other true functional forms. While simple log–log plots may be instructive in detecting possible power laws, and have been used dating back to [[Vilfredo Pareto|Pareto]] in the 1890s, validation as a power laws requires more sophisticated statistics.<ref name=clauset/>
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