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Sign of Correlationcorrelation of Logged Variableslogged variables

If we know that random variables $X$ and $Y$ are positively correlated, do we know that the random variables $Z = log(X)$$Z = \log(X)$ and $W = log(Y)$$W = \log(Y)$ are positively correlated?

Sign of Correlation of Logged Variables

If we know that random variables $X$ and $Y$ are positively correlated, do we know that the random variables $Z = log(X)$ and $W = log(Y)$ are positively correlated?

Sign of correlation of logged variables

If we know that random variables $X$ and $Y$ are positively correlated, do we know that the random variables $Z = \log(X)$ and $W = \log(Y)$ are positively correlated?

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Sign of Correlation of Logged Variables

If we know that random variables $X$ and $Y$ are positively correlated, do we know that the random variables $Z = log(X)$ and $W = log(Y)$ are positively correlated?