Dear all,
I have an experimental data set in which two variables coming from normally distributed populations are correlated. The correlation, from theoretical models, follows a power law, i.e. y=a*x^b.
With a NLS method, I found an R-squared of 0.89. When log-transforming the data and using Pearson correlation, the Pearson coefficient is -0.74. It is clear that data are correlated, but which method is the most correct to present the results?
Pearsons correlation describes the linear correlation, i.e. the correlation based on a linear relationship between the variables. This linear relationship has the form y = a + bx.
It's obvious that the power law is not linear (but it may be approximately so for a relatively "small" interval of x).
If you now log the equation of the power law, what do you get?
Dear Jochen,
when taking the log of the power equation, a linear correlation subsists, see image
log(y) = log(a)+b*log(x), yes of course!
Sorry for the mistake, I changed the axis label to upload the figure and I forgot log(x)
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