Everything Is Correlated
When the correlation is close to 0 it's often because of a feedback loop.For example - in economy with central bank trying to hit inflation target - interest rates and inflation will have near 0 correlation (interest rates change but inflation remains constant). That's because central bank adjusts interest rates to counter other variables so that inflation remains near the target.Other example (my favorite, it was mindblowing when my teacher showed it to us on econometrics as a warning :) ) - gas pedal and speed of a car driving on a hilly road. Driver wants to drive near the speed limit, so he adjusts the gas pedal to keep the speed constant. Simplistic conclusion would be - speed is constant despite the gas pedal position changing therefore they are unrelated :)