Yes, that's the whole point of the saying. If you notice a pattern, don't automatically assume that a causes b, when it might be that both are triggered by some additional variable c that is not immediately apparent without further investigation.

Silver is not gold, but that doesn't mean that silver has no value.

Nice. I was missing comment sections written by ai

Determining causation is often stymied by little things like ethics. This is where correlation becomes the "best guess" to avoid ethical quagmires.

For example much of our medical science often starts out based upon correlation studies. Eventually indirect evidence can be used to confirm partial causation.

Attention yes, but only as a clue to put more effort into understanding.

I try.

What's the deal with your username?

Correlation doesn’t equal causation—but then again, nothing else does either.

Causality is an emergent property, like entropy: it’s not in the physical world, it’s in our mental model of it. And that model is built on correlations.

Correlation does not equal causation but causation always involves correlation.

Yes, when there's a causation link between things there's also a correlation between them. But correlation does not imply causation means the link doesn't go the other way. It's like, every dog is an animal, but not every animal is a dog.

Correlations might be useful to figure out common causes, for example the correlation between student height and reading skills, could mean taller people are more educated, or, more likely, that your students are young enough that age is an important factor at play.

And finally, correlation might be just a fluke of chance, for example the amount of automotive recalls related to AirBags correlates almost perfectly with the popularity of the first name Killian: https://www.tylervigen.com/spurious/correlation/2599_popularity-of-the-first-name-killian_correlates-with_automotive-recalls-for-issues-with-the-air-bags that site has other similar examples.

So yeah, correlation might be important, but they might be nothing at all, so don't just assume that a correlation implies causation.