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If the coefficient of correlation between x and y is 0.28, covariance between x and y is 7.6, and the variance of x is 9, then the standard deviation of the y series is
- a)9.8
- b)10.1
- c)9.05
- d)10.05
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the coefficient of correlation between x and y is 0.28, covariance ...
N the given problem it is SD of x is 3: (or Variance of x is 9). As Variance = (Sx)^2. We know the relation : correlation coefficient (r) = Cov (x,y) / (Sx * Sy) so, 0.28 = 7.6 / (3 * Sy) From here we get the value of SD of Y : Sy = 9.05.
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If the coefficient of correlation between x and y is 0.28, covariance ...
Given:
- Coefficient of correlation between x and y = 0.28
- Covariance between x and y = 7.6
- Variance of x = 9
We are asked to find the standard deviation of the y series.
Formula:
The formula for calculating the standard deviation of the y series is:
σy = √(Var(y))
To find Var(y), we need to first find the covariance between x and y.
Calculations:
1. Covariance between x and y:
cov(x, y) = ρ(x, y) * σx * σy
where ρ(x, y) is the coefficient of correlation between x and y, and σx and σy are the standard deviations of x and y, respectively.
Plugging in the given values, we get:
7.6 = 0.28 * √9 * σy
Solving for σy, we get:
σy = 7.6 / (0.28 * 3)
σy = 9.05
2. Standard deviation of y:
Using the formula mentioned above, we get:
σy = √(Var(y))
Plugging in the value of Var(y), we get:
σy = √(cov(x, y))
σy = √(7.6)
σy = 2.76
Therefore, the standard deviation of the y series is 9.05 (Option C).
- Coefficient of correlation between x and y = 0.28
- Covariance between x and y = 7.6
- Variance of x = 9
We are asked to find the standard deviation of the y series.
Formula:
The formula for calculating the standard deviation of the y series is:
σy = √(Var(y))
To find Var(y), we need to first find the covariance between x and y.
Calculations:
1. Covariance between x and y:
cov(x, y) = ρ(x, y) * σx * σy
where ρ(x, y) is the coefficient of correlation between x and y, and σx and σy are the standard deviations of x and y, respectively.
Plugging in the given values, we get:
7.6 = 0.28 * √9 * σy
Solving for σy, we get:
σy = 7.6 / (0.28 * 3)
σy = 9.05
2. Standard deviation of y:
Using the formula mentioned above, we get:
σy = √(Var(y))
Plugging in the value of Var(y), we get:
σy = √(cov(x, y))
σy = √(7.6)
σy = 2.76
Therefore, the standard deviation of the y series is 9.05 (Option C).
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If the coefficient of correlation between x and y is 0.28, covariance ...
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If the coefficient of correlation between x and y is 0.28, covariance between x and y is 7.6, and the variance of x is 9, then the standard deviation of the y series isa)9.8b)10.1c)9.05d)10.05Correct answer is option 'C'. Can you explain this answer?
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