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I would like to know if an increase in the covariance between two variables would imply that the standard deviation for one of the variables has increased?

This is assuming that the standard deviation for the other variable is constant.

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Really I'm afraid this isn't the best site to get an answer for your particular question. You'd do better at one of the sites listed in the FAQ: mathoverflow.net/faq#whatnot. –  Tom Smith May 4 '10 at 18:59
    
Also: think about two independent Bernoulli variables X and Y; compare cov(X,X) to cov(X,Y). –  Tom Smith May 4 '10 at 19:04
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1 Answer

Cov1,2 = ρ1,2 * σ1 * σ2

So if your covariance went up, then you have three choices either one of the standard deviations went up or the correlation went up.

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So what you're saying is that if x = x/y * y then if x increases either y went up or x/y went up? –  Tom Smith May 4 '10 at 18:58
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