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If for two variable x and y, the covariance, variance of x and variance of y are 40, 16 and 256 respectively, what is the value of the correlation coefficient?
  • a)
    0.01
  • b)
    0.625
  • c)
    0.4
  • d)
    0.5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If for two variable x and y, the covariance, variance of x and varianc...
Solution:

Given, Covariance (x,y) = 40, Variance (x) = 16, Variance (y) = 256

We know that,

Correlation coefficient (r) = Covariance (x,y) / (Standard deviation of x * Standard deviation of y)

Calculation of Standard deviation of x and y:

Standard deviation of x = √Variance (x) = √16 = 4

Standard deviation of y = √Variance (y) = √256 = 16

Calculation of Correlation coefficient:

r = Covariance (x,y) / (Standard deviation of x * Standard deviation of y)

r = 40 / (4 * 16) = 0.625

Therefore, the value of the correlation coefficient is 0.625.

Hence, option B is the correct answer.
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If for two variable x and y, the covariance, variance of x and varianc...
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If for two variable x and y, the covariance, variance of x and variance of y are 40, 16 and 256 respectively, what is the value of the correlation coefficient?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer?
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