If for two variable x and y, the covariance, variance of x and variance of y are40, 16 and 256 respectively, what is the value of the correlation coefficient?(a) 0.01(b) 0.625(c) 0.4(d) 0.5
Question
If for two variable x and y, the covariance, variance of x and variance of y are40, 16 and 256 respectively, what is the value of the correlation coefficient?(a) 0.01(b) 0.625(c) 0.4(d) 0.5
Solution
The correlation coefficient, often denoted by r, is calculated using the formula:
r = Cov(X,Y) / sqrt(Var(X) * Var(Y))
Given in the problem, we have:
Cov(X,Y) = 40 Var(X) = 16 Var(Y) = 256
Substituting these values into the formula, we get:
r = 40 / sqrt(16 * 256)
Solving inside the square root first:
sqrt(16 * 256) = sqrt(4096) = 64
So, r = 40 / 64 = 0.625
Therefore, the correlation coefficient is 0.625, which corresponds to option (b).
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