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If u = 2x + 5 and v = –3y – 6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u?
- a)3.6
- b)–3.6
- c)2.4
- d)–2.4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If u = 2x + 5 and v = –3y – 6 and regression coefficient o...
Regression coefficient of y on x
- The regression coefficient of y on x is given by the formula:
bxy = (covariance of x and y) / (variance of x)
- We are given that the regression coefficient of y on x is 2.4.
bxy = 2.4
Expressing u and v in terms of x and y
- We are given that:
u = 2x + 5
v = 3y - 6
- We can express x and y in terms of u and v:
x = (u - 5) / 2
y = (v + 6) / 3
Regression coefficient of v on u
- We want to find the regression coefficient of v on u.
- We can use the formula for the regression coefficient of y on x, but with u and v switched:
bvu = (covariance of u and v) / (variance of u)
- We can express the covariance of u and v in terms of the covariance of x and y:
covariance of u and v = covariance of (2x + 5) and (3y - 6)
= 6 * covariance of x and y
- We can express the variance of u in terms of the variance of x:
variance of u = variance of (2x + 5)
= 4 * variance of x
- Substituting these expressions into the formula for bvu:
bvu = (6 * covariance of x and y) / (4 * variance of x)
= (3/2) * (covariance of x and y) / (variance of x)
= (3/2) * bxy
= 3.6
Answer: (B) 3.6
- The regression coefficient of y on x is given by the formula:
bxy = (covariance of x and y) / (variance of x)
- We are given that the regression coefficient of y on x is 2.4.
bxy = 2.4
Expressing u and v in terms of x and y
- We are given that:
u = 2x + 5
v = 3y - 6
- We can express x and y in terms of u and v:
x = (u - 5) / 2
y = (v + 6) / 3
Regression coefficient of v on u
- We want to find the regression coefficient of v on u.
- We can use the formula for the regression coefficient of y on x, but with u and v switched:
bvu = (covariance of u and v) / (variance of u)
- We can express the covariance of u and v in terms of the covariance of x and y:
covariance of u and v = covariance of (2x + 5) and (3y - 6)
= 6 * covariance of x and y
- We can express the variance of u in terms of the variance of x:
variance of u = variance of (2x + 5)
= 4 * variance of x
- Substituting these expressions into the formula for bvu:
bvu = (6 * covariance of x and y) / (4 * variance of x)
= (3/2) * (covariance of x and y) / (variance of x)
= (3/2) * bxy
= 3.6
Answer: (B) 3.6
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If u = 2x + 5 and v = –3y – 6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u?a)3.6b)–3.6c)2.4d)–2.4Correct answer is option 'B'. Can you explain this answer?
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Solutions for If u = 2x + 5 and v = –3y – 6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u?a)3.6b)–3.6c)2.4d)–2.4Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
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