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The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation is
- a)0.48
- b)0.78
- c)0.87
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
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The value of covariance of two variables x and y is -(148/3) and the v...
Given,
Covariance of x and y, Cov(x,y) = -(148/3)
Variance of x, Var(x) = (272/3)
Variance of y, Var(y) = (131/3)
We need to find the coefficient of correlation between x and y.
Formula to calculate coefficient of correlation:
r = Cov(x,y) / (σx * σy)
where,
Cov(x,y) = covariance of x and y
σx = standard deviation of x
σy = standard deviation of y
Steps to solve the problem:
1. Calculate the standard deviation of x and y.
σx = √Var(x) = √(272/3) = 8.28
σy = √Var(y) = √(131/3) = 6.07
2. Substitute the given values in the formula of r
r = Cov(x,y) / (σx * σy)
r = -(148/3) / (8.28 * 6.07)
r = -0.31
3. Check the options given and choose the correct answer.
The calculated value of r is negative and its absolute value is less than 0.5. None of the options given match with the calculated value. Hence, the correct answer is option 'D' (none of these).
Note: The absolute value of the coefficient of correlation ranges from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation. A negative value of r indicates a negative correlation between x and y, while a positive value indicates a positive correlation.
Covariance of x and y, Cov(x,y) = -(148/3)
Variance of x, Var(x) = (272/3)
Variance of y, Var(y) = (131/3)
We need to find the coefficient of correlation between x and y.
Formula to calculate coefficient of correlation:
r = Cov(x,y) / (σx * σy)
where,
Cov(x,y) = covariance of x and y
σx = standard deviation of x
σy = standard deviation of y
Steps to solve the problem:
1. Calculate the standard deviation of x and y.
σx = √Var(x) = √(272/3) = 8.28
σy = √Var(y) = √(131/3) = 6.07
2. Substitute the given values in the formula of r
r = Cov(x,y) / (σx * σy)
r = -(148/3) / (8.28 * 6.07)
r = -0.31
3. Check the options given and choose the correct answer.
The calculated value of r is negative and its absolute value is less than 0.5. None of the options given match with the calculated value. Hence, the correct answer is option 'D' (none of these).
Note: The absolute value of the coefficient of correlation ranges from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation. A negative value of r indicates a negative correlation between x and y, while a positive value indicates a positive correlation.
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The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer?
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