<story><title>How to Think about Correlation?</title><url>https://statmodeling.stat.columbia.edu/2020/12/03/how-to-think-about-correlation-its-the-slope-of-the-regression-when-x-and-y-have-been-standardized/</url></story><parent_chain></parent_chain><comment><author>Geminidog</author><text>Correlations are a profound part of our universe.&lt;p&gt;When observing the universe, humans can never prove any facts about the universe. We can only establish correlations. Correlations between events that occur in our universe is the furthest &amp;quot;truth&amp;quot; we can establish about the universe short of a full on proof.&lt;p&gt;What this means is that nothing in the physical universe can be proven. Proof is the domain of maths and logic, correlations is the domain of science. Science cannot prove anything, it can only establish correlations and causations.&lt;p&gt;The reason this occurs is because at any time in the future one can observe an event that contradicts a hypothesis. You can hypothesize that all birds have wings and observe 2 trillion birds with wings but you never know when one day you&amp;#x27;ll observe a bird without wings disproving your entire hypothesis. That is why nothing can be proven, you can only correlate things through observation.&lt;p&gt;The other interesting part about correlation is what it isn&amp;#x27;t: Causation. People often talk about how correlation is not causation but people never talk about what causation is and how to establish it. If I can&amp;#x27;t empirically use correlation to establish causation how on earth is causation ever formally established? People rarely question this disconnect.&lt;p&gt;The fact is, causation is rarely formally established but a method does exist and it&amp;#x27;s subtle. If I observe that whenever Bob flicks a switch the light comes on then I established that the light coming on is correlated with Bob flipping the switch. This is as far as I can go with just observation. To establish causation I must make myself both an observer and an entity that is part of the system itself. I have to take control and flip the switch randomly and observe that when I don&amp;#x27;t flip the switch nothing happens and when I do flip the switch the lights come on.&lt;p&gt;By doing this I establish causation. To establish causation to higher and higher degrees I need to Cause (keyword) random events and make sure that a cause influences an effect AND absence of a cause and therefore absence of an effect occurs.&lt;p&gt;Also note that establishing causation is not proof. At any point in time in the future I can flip the switch and the light may not come on which is contradictory evidence for causation. Causation in the statistical sense is like correlation, you establish it to a degree of confidence but you can never Prove that A caused B.</text></comment>
<story><title>How to Think about Correlation?</title><url>https://statmodeling.stat.columbia.edu/2020/12/03/how-to-think-about-correlation-its-the-slope-of-the-regression-when-x-and-y-have-been-standardized/</url></story><parent_chain></parent_chain><comment><author>sieste</author><text>There are at least 13 ways to think about correlation&lt;p&gt;Rodgers &amp;amp; Nicewander 1988 &amp;quot;Thirteen ways to look at the correlation coefficient&amp;quot;
&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.jstor.org&amp;#x2F;stable&amp;#x2F;pdf&amp;#x2F;2685263.pdf&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.jstor.org&amp;#x2F;stable&amp;#x2F;pdf&amp;#x2F;2685263.pdf&lt;/a&gt;</text></comment>