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Covariance and Correlation-ECO6416

Covariance and Correlation-ECO6416 - Covariance and...

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Covariance and Correlation Suppose that X and Y are two random variables for the outcome of a random experiment. The covariance of X and Y is defined by Cov (X, Y) = E{[X - E(X)][Y - E(Y)]} and, given that the variances are strictly positive, the correlation of X and Y is defined by ρ (X, Y) = Cov(X, Y) / [sd(X) . sd(Y)] Correlation is a scaled version of covariance; note that the two parameters always have the same sign (positive, negative, or 0). When the sign is positive, the variables are said to be positively correlated; when the sign is negative, the variables are said to be negatively correlated; and when it is 0, the variables are said to be uncorrelated. Notice that the correlation between two random variables is often due only to the fact that both variables are correlated with the same third variable. As these terms suggest, covariance and correlation measure a certain kind behavior in both variables. Correlation is very similar to the derivative of a function that you may have studies in high school.
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