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If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x?
Most Upvoted Answer
If the regression coefficient of y on x the coefficient of correlation...
Solution:
Given,
Regression coefficient of y on x = -3/4
Coefficient of correlation between x and y = √3/2
Variance of y = 4
We need to find the variance of x.
Relation between Regression coefficient of y on x and Coefficient of correlation between x and y:
Regression coefficient of y on x (βyx) = rxy * (Sy/Sx)
Where,
rxy = Coefficient of correlation between x and y
Sy = Standard deviation of y
Sx = Standard deviation of x
Let's substitute the given values in the above equation to find Sy/Sx.
-3/4 = (√3/2) * (4/Sx)
Simplifying the above equation we get,
Sx = (√3/2) * (4/(-3/4)) = (√3/2) * (-16/3)
Sx = -2√3
Variance of x:
Variance of x (σ^2x) = Sx^2
σ^2x = (-2√3)^2 = 12
∴ The variance of x is 12.
Therefore, the variance of x is 12.
Given,
Regression coefficient of y on x = -3/4
Coefficient of correlation between x and y = √3/2
Variance of y = 4
We need to find the variance of x.
Relation between Regression coefficient of y on x and Coefficient of correlation between x and y:
Regression coefficient of y on x (βyx) = rxy * (Sy/Sx)
Where,
rxy = Coefficient of correlation between x and y
Sy = Standard deviation of y
Sx = Standard deviation of x
Let's substitute the given values in the above equation to find Sy/Sx.
-3/4 = (√3/2) * (4/Sx)
Simplifying the above equation we get,
Sx = (√3/2) * (4/(-3/4)) = (√3/2) * (-16/3)
Sx = -2√3
Variance of x:
Variance of x (σ^2x) = Sx^2
σ^2x = (-2√3)^2 = 12
∴ The variance of x is 12.
Therefore, the variance of x is 12.
Community Answer
If the regression coefficient of y on x the coefficient of correlation...
Byx= r×SDof Y÷ SD of x
-3/4 = √3/2 × 2 / x
-3/4 = √3/x
x= - 4√3/3
we need variance of x
therefore
x^2 = (-4√3/3)^2
= 16×3/9
=16/3
-3/4 = √3/2 × 2 / x
-3/4 = √3/x
x= - 4√3/3
we need variance of x
therefore
x^2 = (-4√3/3)^2
= 16×3/9
=16/3
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If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x?
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If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x?.
If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the regression coefficient of y on x the coefficient of correlation between x and y and variance of y are -3/4,√3/2,and 4 respectively, what is variance of x?.
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