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I have some data in which some yield percentages are given for different temperatures and stirring rates. I calculate the correlation coefficient (r) in each case. Say $r_1$ is for temperature and yield, $r_2$ is for stirring rate and yield, and $r_3$ is for temperature and stirring rate.

I get $r_1=0.7323$, $r_2=0.7513$, $r_3=0.9064$.

Now, I'm asked if this data provides good evidence that increasing temperature increases yield, and likewise for stirring rate, or is it due to confounding.

I don't understand how to interpret this result. I know that if the correlation coefficient is $1$, then we have a linear correlation. But how to determine whether this correlation is due to confounding or not?

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  • $\begingroup$ Even if you controlled for stirring rate, you couldn't say much of anything on the information provided in this question. There's no hint of anything here that would give a clue to the size of the standard error of the correlation (whether raw or partial), for example. Better to start with the data, rather than summarize to the extent that you remove what we'd need to know. $\endgroup$
    – Glen_b
    Commented Nov 21, 2015 at 2:55
  • $\begingroup$ By the way, please note what the help says about crossposting (see the third-last paragraph) $\endgroup$
    – Glen_b
    Commented Nov 21, 2015 at 2:59
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    $\begingroup$ Oh.. I didn't know about that crossposting.. I'll keep that in mind.. $\endgroup$
    – Tejas
    Commented Nov 21, 2015 at 4:46
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    $\begingroup$ Thanks. In cases where the answers are likely to be of very different kinds on different SE sites, there'd be some scope for crossposting a similar question, but when you're after a particular kind of answer it's better to migrate a post to the site you think is most likely to provide that sort of answer. $\endgroup$
    – Glen_b
    Commented Nov 21, 2015 at 4:48
  • $\begingroup$ I think I'll delete that question from math.se. It hasn't received any comments or answers anyway. $\endgroup$
    – Tejas
    Commented Nov 21, 2015 at 4:53

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Trying to determine if temperature and/or stirring rate increases yield is not clear because of the high correlation coefficient $r_3$. Because $r_3$ is so close to 1, this shows that stirring rate and temperature are highly correlated: as stirring rate goes up, so does temperature (and visa-versa).

Regarding the question of if increasing temperature increases yield: it's not clear because you cannot separate the effect of temperature and stirring rate. For example, as temperature increases, the yield increases (because $r_1$ is a fairly large positive correlation), but as stated above, we know stirring rate will increase as well (because $r_3$ is a large positive correlation). Therefore, we have no idea whether the temperature or stirring rate caused the yield to go up, since they both went up together.

The same argument holds for if stirring rate increases yield. So this suggests that the given correlation coefficients are confounding.

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