most recent 30 from http://mathoverflow.net 2013-05-25T00:18:17Z http://mathoverflow.net/feeds/question/40684 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40684/does-taking-logs-of-two-variables-increase-correlation-between-the-two Buural 2010-09-30T23:46:43Z 2010-10-01T00:41:23Z

<p>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.</p>

http://mathoverflow.net/questions/40684/does-taking-logs-of-two-variables-increase-correlation-between-the-two/40691#40691 ronaf 2010-10-01T00:41:23Z 2010-10-01T00:41:23Z

<p>short answer: not necessarily. for example:</p> <p>let X be a positive random variable with a pdf supported on some non-degenerate interval, [0, 1] say. let Y = 1 + X. </p> <p>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.</p> <p>[X can also be discrete, as long as it assumes at least 3 different values with positive probability.]</p> <p>this example can be tweaked so that X and Y start out not perfectly correlated, but still corr(U,V) &lt; corr(X,Y). </p>