The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.
This mean that x and y are non linear correlated, but them are correlated.
For this type of data is used a non linear correlation technique know it as logarithm correlation.
Option III is incorrect because random patterns have a correlation value close to 0, which is not the case.
