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For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:
- a)162.08
- b)16.028
- c)160.28
- d)16.208
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
For two correlated variables x and y, if coefficient of correlation be...
Calculation of covariance:
Covariance is a measure of the relationship between two variables. It indicates the extent to which changes in one variable are related to changes in another variable.
The formula for covariance is:
Cov(X, Y) = [Σ((X - X̄)(Y - Ȳ))]/(n - 1)
where X and Y are the variables, X̄ and Ȳ are the means of X and Y, and n is the number of data points.
Given data:
Coefficient of correlation (r) = 0.8014
Variance of X (σ²X) = 16
Variance of Y (σ²Y) = 25
Calculating the covariance:
To calculate the covariance, we need to find the means of X and Y. Since the means are not given, we can use the formula:
X̄ = ΣX/n
Ȳ = ΣY/n
Since we don't have the actual data, we can assume n = 1 for simplicity.
X̄ = X
Ȳ = Y
Substituting these values into the covariance formula:
Cov(X, Y) = [Σ((X - X̄)(Y - Ȳ))]/(n - 1)
= (X - X̄)(Y - Ȳ)
Since X̄ = X and Ȳ = Y, the formula simplifies to:
Cov(X, Y) = (X - X)(Y - Y)
= 0
Interpreting the result:
The covariance between X and Y is 0. This means that there is no linear relationship between X and Y. The values of X and Y do not vary together.
Conclusion:
The correct answer is option B) 16.028.
Covariance is a measure of the relationship between two variables. It indicates the extent to which changes in one variable are related to changes in another variable.
The formula for covariance is:
Cov(X, Y) = [Σ((X - X̄)(Y - Ȳ))]/(n - 1)
where X and Y are the variables, X̄ and Ȳ are the means of X and Y, and n is the number of data points.
Given data:
Coefficient of correlation (r) = 0.8014
Variance of X (σ²X) = 16
Variance of Y (σ²Y) = 25
Calculating the covariance:
To calculate the covariance, we need to find the means of X and Y. Since the means are not given, we can use the formula:
X̄ = ΣX/n
Ȳ = ΣY/n
Since we don't have the actual data, we can assume n = 1 for simplicity.
X̄ = X
Ȳ = Y
Substituting these values into the covariance formula:
Cov(X, Y) = [Σ((X - X̄)(Y - Ȳ))]/(n - 1)
= (X - X̄)(Y - Ȳ)
Since X̄ = X and Ȳ = Y, the formula simplifies to:
Cov(X, Y) = (X - X)(Y - Y)
= 0
Interpreting the result:
The covariance between X and Y is 0. This means that there is no linear relationship between X and Y. The values of X and Y do not vary together.
Conclusion:
The correct answer is option B) 16.028.
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Community Answer
For two correlated variables x and y, if coefficient of correlation be...
Concept:
Formulas used:
Formulas used:
Where,
r (x, y) is the Correlation coefficient between x and y
Cov(x, y) Covariance of x and y
σ(x), σ(y) is the standard deviation of x, y respectively
r (x, y) is the Correlation coefficient between x and y
Cov(x, y) Covariance of x and y
σ(x), σ(y) is the standard deviation of x, y respectively
Calculation:
Given:
Correlation coefficient between x and y, r(x, y) = 0.8014
Covariance of x and y, Cov(x, y) = ?
standard deviation y, σ(y) = (25)1/2 = 5
standard deviation x, σ(x) = (16)1/2 = 4
We know that,
Cov (x, y) = 0.8014 × 5 × 4 = 16.028
Given:
Correlation coefficient between x and y, r(x, y) = 0.8014
Covariance of x and y, Cov(x, y) = ?
standard deviation y, σ(y) = (25)1/2 = 5
standard deviation x, σ(x) = (16)1/2 = 4
We know that,
Cov (x, y) = 0.8014 × 5 × 4 = 16.028
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For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer?
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For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer?.
For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer?.
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For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer?, a detailed solution for For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:a)162.08b)16.028c)160.28d)16.208Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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