Question
If the Correlation Coefficient (r) between two variables
X and Y is -0.8, and their standard deviations are 4 and 5 respectively, the covariance between X and Y is:Solution
- The formula connecting Correlation Coefficient (r), Covariance (Cov), and Standard Deviations ( Ο ) is:
r = Cov(X, Y) / ( Ο β * Ο α΅§ )
We need to find Cov(X, Y). Rearranging the formula:
Cov(X, Y) = r * Ο β * Ο α΅§
Given: r = -0.8, Ο β = 4, Ο α΅§ = 5.
Cov(X, Y) = (-0.8) * (4) * (5)
Cov(X, Y) = (-0.8) * 20 =Β -16 .
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