This may be a naive question, but if I have random variables X and Y and take logs of both, would corr(log X, log Y) be greater than corr(X, Y)? Thank you in advance for your answer.



Does taking logs of two variables increase correlation between the two?
short answer: not necessarily. for example:


let X be a positive random variable with a pdf supported on some non-degenerate interval, 
[0, 1] say. 
let Y = 1 + X. 


then X and Y are perfectly correlated. but U = logX and V = log Y = log (1 + X) = log(1 + e$^U$)
are not linearly related, so their correlation is less than 1.


[X can also be discrete, as long as it assumes at least 3 different values with positive probability.]


this example can be tweaked so that X and Y start out not perfectly correlated, but still
corr(U,V) < corr(X,Y). 


