Timeline for How would you explain covariance to someone who understands only the mean?
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10 events
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| Jun 25, 2019 at 20:48 | comment | added | whuber♦ | @nbro Covariance is the second central moment of a bivariate random variable. And that returns us to the beginning: how would one convey this precise definition to the proverbial five-year-old? As always, there's a trade-off between economy of expression and accuracy: when the audience doesn't have the concepts or language needed to understand something immediately, somehow you have to weave in an explanation of that background along with your description. Doing it right requires some elaboration. Usually there's no shortcut. | |
| Jun 25, 2019 at 19:47 | comment | added | whuber♦ | @nbro Consider any concrete example: suppose you know the covariance of variables $X$ and $Y$ is $1,$ for instance. Even with the most generous understanding of "variable" and "go up," could you tell from that information alone how much $Y$ goes up when $X$ goes up by a given amount? The answer is no: the only information it gives you is that $Y$ would tend to increase. In this post Peter has confused the covariance with a regression coefficient (of which there are two, by the way, and they usually are different). | |
| Jun 25, 2019 at 19:15 | comment | added | whuber♦ | @nbro The only problem is that it's wrong. (And not just a little bit: this is not a nit-pick.) | |
| Aug 13, 2013 at 20:15 | comment | added | whuber♦ | That's right, Peter, which is why @naught101 made that comment: you description sounds like a rate of change, whose units will therefore be [units of one variable] / [units of the other variable] (if we interpret it like a derivative) or will just be [units of one variable] (if we interpret as a pure difference). Those are neither covariance (whose unit of measure is the product of the units for the two variables) nor correlation (which is unitless). | |
| Feb 28, 2012 at 10:29 | comment | added | Peter Flom | @naught101 Covariance is in the original units, isn't it? | |
| Feb 28, 2012 at 5:44 | comment | added | naught101 | +1 for fitting it in a single, simple sentence, but isn't that correlation? I mean, I know greater cov=> greater corr, but with that sentence, I'd expect something like "80%" as an answer, which corresponds to corr=0.8. Doesn't cov also describe the variance within the data? ie. "Covariance is proportional to how much one variable goes up when the other goes up, and also proportional to the spread of the data in both variables", or something? | |
| Nov 8, 2011 at 11:37 | comment | added | Peter Flom | @nupul Well, the opposite of "up" is "down" and the opposite of "positive" is "negative". I tried to give a one sentence answer. Yours is much more complete. Even your "how two variables change together" is more complete, but, I think, a little harder to understand. | |
| Nov 8, 2011 at 2:29 | comment | added | PhD | I think that that's what determines the sign of covariance...as per my posted 'answer' | |
| Nov 8, 2011 at 2:07 | comment | added | PhD | Is it always in the 'same' direction? Also, does it apply for inverse relations too (i.e., as one goes up the other goes down)? | |
| Nov 7, 2011 at 23:33 | history | answered | Peter Flom | CC BY-SA 3.0 |