<story><title>Everything Is Correlated</title><url>https://www.gwern.net/Everything</url></story><parent_chain><item><author>ajuc</author><text>When the correlation is close to 0 it&amp;#x27;s often because of a feedback loop.&lt;p&gt;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&amp;#x27;s because central bank adjusts interest rates to counter other variables so that inflation remains near the target.&lt;p&gt;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 :)</text></item></parent_chain><comment><author>gwern</author><text>That&amp;#x27;s a good point. Another one I forgot to make: given the established empirical reality of &amp;#x27;everything is correlated&amp;#x27;, if you find a variable which does in fact seem to be independent of most or everything else, that alone makes that variable suspicious - it suggests that it may be a pseudo-variable, composed largely or entirely of measurement error&amp;#x2F;randomness, or perhaps afflicted by a severe selection bias or other problem (such as range restriction or Berkson&amp;#x27;s paradox eliminating the real correlation).&lt;p&gt;Somewhat similarly, because &amp;#x27;everything is heritable&amp;#x27;, if you run into a human trait which is &lt;i&gt;not&lt;/i&gt; heritable at all and is precisely estimated at h^2~0, that cast considerable doubt on whether you have a real trait at all. (I&amp;#x27;ve seen this happen to a few latent variables extracted by factor analysis: they have near-zero heritability in a twin study and on further investigation, turn out to have been just sampling error or bad factor analysis in the first place, and don&amp;#x27;t replicate or predict anything or satisfy any of the criteria you might use to decide if a trait is &amp;#x27;real&amp;#x27;.)</text></comment>
<story><title>Everything Is Correlated</title><url>https://www.gwern.net/Everything</url></story><parent_chain><item><author>ajuc</author><text>When the correlation is close to 0 it&amp;#x27;s often because of a feedback loop.&lt;p&gt;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&amp;#x27;s because central bank adjusts interest rates to counter other variables so that inflation remains near the target.&lt;p&gt;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 :)</text></item></parent_chain><comment><author>tcgv</author><text>That&amp;#x27;s very interesting. In the car driving example we can define three variables: 1) Throttle 2) Speed 3) Elevation derivative&lt;p&gt;If &amp;quot;3&amp;quot; is constant (ex: flat terrain) then &amp;quot;1&amp;quot; and &amp;quot;2&amp;quot; will have strong correlation. However if &amp;quot;2&amp;quot; is constant (ex: cruise control) as in your example, &amp;quot;1&amp;quot; and &amp;quot;3&amp;quot; will have strong correlation.&lt;p&gt;In the economic example, however, this kind of analisys should be much more complex and take plenty of variables into account.</text></comment>