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 not always valid. 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 (R2) 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 Pareto in the 1890s, validation as a power laws requires more sophisticated statistics. These graphs are also extremely useful when data are gathered by varying the control variable along an exponential function, in which case the control variable x is more naturally represented on a log scale, so that the data points are evenly spaced, rather than compressed at the low end. The output variable y can either be represented linearly, yielding a lin–log graph (log x, y), or its logarithm can also be taken, yielding the log–log graph (log x, log y). Bode plot (a graph of the frequency response of a system) is also log–log plot. See also Semi-log plot (lin–log or log–lin) Power law Zipf law References External links Non-Newtonian calculus website Logarithmic scales of measurement Statistical charts and diagrams Non-Newtonian calculus de:Logarithmenpapier#Doppeltlogarithmisches Papier