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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?
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If u = 2x 5 and v-3y - 6 and regression coefficient of y on x is 2.4...
Solution:
Given, u = 2x + 5 and v = 3y - 6
Regression coefficient of y on x is 2.4
We need to find the regression coefficient of v on u.
To find the regression coefficient of v on u, we need to find the value of (covariance of u and v) / (variance of u).
Let us first find the values of covariance of u and v and variance of u.
covariance of u and v = covariance of (2x+5) and (3y-6)
= 6(covariance of x and y)
[since covariance is a linear operator, we can take the constants outside]
variance of u = variance of (2x+5)
= 4(variance of x)
[since variance is a quadratic operator, we can take the constants outside and square it]
Now, we need to find the regression coefficient of v on u, which is given by (covariance of u and v) / (variance of u).
Substituting the values of covariance of u and v and variance of u, we get:
Regression coefficient of v on u = (6(covariance of x and y)) / (4(variance of x))
= (3/2)(covariance of x and y) / (variance of x)
= 3/2(regression coefficient of y on x)
= 3/2(2.4)
= 3.6
Hence, the regression coefficient of v on u is 3.6.
Answer: (a) 3.6
Given, u = 2x + 5 and v = 3y - 6
Regression coefficient of y on x is 2.4
We need to find the regression coefficient of v on u.
To find the regression coefficient of v on u, we need to find the value of (covariance of u and v) / (variance of u).
Let us first find the values of covariance of u and v and variance of u.
covariance of u and v = covariance of (2x+5) and (3y-6)
= 6(covariance of x and y)
[since covariance is a linear operator, we can take the constants outside]
variance of u = variance of (2x+5)
= 4(variance of x)
[since variance is a quadratic operator, we can take the constants outside and square it]
Now, we need to find the regression coefficient of v on u, which is given by (covariance of u and v) / (variance of u).
Substituting the values of covariance of u and v and variance of u, we get:
Regression coefficient of v on u = (6(covariance of x and y)) / (4(variance of x))
= (3/2)(covariance of x and y) / (variance of x)
= 3/2(regression coefficient of y on x)
= 3/2(2.4)
= 3.6
Hence, the regression coefficient of v on u is 3.6.
Answer: (a) 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) 3.6 (b) -3.6 (c) 2.4 (d) -2.4?
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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? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 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? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below 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) 3.6 (b) -3.6 (c) 2.4 (d) -2.4?.
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? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 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? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below 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) 3.6 (b) -3.6 (c) 2.4 (d) -2.4?.
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