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Generally, Covariance is computed assuming that two random variables are independent. But in a situation that warrants some association between these two variables, how can we compute covariance.

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    $\begingroup$ The relate only insofar as they are a function of two variables. If two variables $X, Y$ are independent $X \perp Y$, then $\mbox{Cov}(X, Y) = 0$ and your covariate (or regression model parameter) will be set to some null value (e.g. 0 for parameters in linear models). $\endgroup$
    – AdamO
    Jan 8 '14 at 19:02
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    $\begingroup$ I downvoted this question because anyone can easily and quickly resolve the distinction between covariate and covariance by consulting a dictionary. We request that you do some research into the answer before you post any question, because "sharing your research helps everyone. ... This demonstrates that you’ve taken the time to try to help yourself [and] it saves us from reiterating obvious answers." $\endgroup$
    – whuber
    Jan 8 '14 at 20:17
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    $\begingroup$ This question appears to be off-topic because it makes no contribution to the goals of the forum. If anybody could cite any source appearing to conflate or confuse the two ideas, there would be some sense in it, but not otherwise. $\endgroup$
    – Nick Cox
    Jan 7 '15 at 16:45
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    $\begingroup$ @subhashc.davar: Sorry, but I haven't the slightest idea what you want to ask now, & doubt anyone else will have. Makes no sense to talk about correlated but independent variables, or about computing a covariate. $\endgroup$ Jan 11 '15 at 19:57
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    $\begingroup$ Here is a metacomment on this thread, which has been revised many times since first posting. The question has been edited a long way from the original question. There is one good upvoted answer here explaining the difference between covariance and covariate, should they ever be confused. But that is no longer the question. Commentary on everything else indicates a lot of puzzlement shared by a lot of people on what is being asked and why. $\endgroup$
    – Nick Cox
    Oct 27 '15 at 14:24
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A covariate is a variable that potentially varies along with the variable of primary interest.

Covariance is a measure of the relationship between two variables (if divided by the standard deviations it becomes the correlation).

Covariance is generally a single number (though you can have a covariance matrix where each value is a covariance between two variables). A covariate is generally a vector with one observation per subject/unit.

You can calculate the covariance between two covariates.

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    $\begingroup$ In short, covariance and covariate are completely distinct ideas. The resemblance is mostly linguistic in that there is a common underlying picture of variables varying together, but a covariate is a variable and a covariance is a scalar for each pair of variables and a matrix more generally. $\endgroup$
    – Nick Cox
    Jan 8 '14 at 18:48
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    $\begingroup$ Also, watch out: in older literature, the term covariate has a specific meaning still used in "analysis of covariance", while in more recent literature the term (increasingly) is more or less yet another synonym for predictor, explanatory, or independent variables. $\endgroup$
    – Nick Cox
    Jan 8 '14 at 18:51
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    $\begingroup$ I don't agree that this is especially confusing. For example, the first sentence of en.wikipedia.org/wiki/Covariate makes it clear. $\endgroup$
    – Nick Cox
    Jan 13 '14 at 14:45

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