# Correlation and dependency of two variables

Lets say I am interested in finding the correlation of the following two metrics. They are aggregations and include the same input A in their formula.

Is it possible to talk about correlation of these metrics? With a satisfactory r-squared value, is it possible to use metric#1 as predictor of metric#2? Should I also be looking for normality?

metric#1 = A/B
metric#2 = A/C

• Are B and C independent ,correlated to some degree or linear? Jun 18, 2014 at 14:15
• Yes it would be correlated. Jun 18, 2014 at 14:21

You have a non-linearity (independent-variable in the divisor) in there, that the most common analysis tools cannot handle, so you could first linearize it with log:

log metric#1 = log A - log B
log metric#2 = log A - log C


Now you are with a almost textbook example of multiple linear regression.

You can view the correlation of log metric#1 to log metric#2 and see if they are related. You also could remove the A dependency and do this:

log metric#1 - log metric#2 = log C - log B


to view the relationship of one metric to another. In order to use the numbers in your system you would need to reverse the logs, doing base 10 exponentiation.

Look for the normality of the log of the variables, in this case, if true, they are said to be lognormal distributed.

• Log-linearization makes sense! However it really surprised me. When I apply lm(log10(B)~log10(C)) I get r^2 = .7 but when I apply lm((log10(A) - log10(B)) ~ (log10(A) - log10(C))) I get a correlation of .35?! Jun 18, 2014 at 16:23
• I just modified my formula with lm( I(log10(A) - log10(B)) ~ I(log10(A) - log10(C))) and worked out fine. Thanks very much! Jun 18, 2014 at 17:03