CA Foundation Exam  >  CA Foundation Questions  >  If u = 2x 5 and v = –3y – 6 and regression ... Start Learning for Free
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?
Most Upvoted Answer
If u = 2x 5 and v = –3y – 6 and regression coefficient of y on x is ...
Regression Coefficient of v on u


To find the regression coefficient of v on u, we need to use the formula:

βv,u = (cov(v,u))/(var(u))

where βv,u is the regression coefficient of v on u, cov(v,u) is the covariance between v and u, and var(u) is the variance of u.

Covariance between v and u


To find the covariance between v and u, we need to use the formula:

cov(v,u) = cov(-3y-6, 2x+5)
= -3 cov(y,x)

Since the regression coefficient of y on x is given to be 2.4, we know that:

cov(y,x) = 2.4 σx σy

where σx and σy are the standard deviations of x and y, respectively.

Standard deviation of x and y


We don't have the standard deviations of x and y, but we can use the following substitutions:

u = 2x+5, so x = (u-5)/2
v = -3y-6, so y = -(v+6)/3

Substituting these expressions into the formula for cov(y,x), we get:

cov(y,x) = 2.4 σx σy
= 2.4 cov(u-5, -(v+6))/6
= -0.4 cov(u-5, v+6)

Covariance between v and u (continued)


Substituting this expression for cov(y,x) into the formula for cov(v,u), we get:

cov(v,u) = -3 cov(y,x)
= 1.2 cov(u-5, v+6)

Variance of u


To find the variance of u, we need to use the formula:

var(u) = var(2x+5)
= 4 var(x)

Regression coefficient of v on u (final calculation)


Substituting the expressions for cov(v,u) and var(u) into the formula for βv,u, we get:

βv,u = (cov(v,u))/(var(u))
= (1.2 cov(u-5, v+6))/(4 var(x))
= (0.3 cov(u-5, v+6))/(var(x))

Since we don't have the values for cov(u-5, v+6) and var(x), we cannot calculate the exact value of βv,u. However, we can see that it is proportional to cov(u-5, v+6)/var(x), which means that it will be positive if cov(u-5, v+6) is positive (i.e. u and v have the same direction of change) and if var(x) is positive (which it should be, since u = 2x+5). Therefore, we can conclude that the regression coefficient of v on u is positive and greater than zero.
Explore Courses for CA Foundation exam
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?
Question Description
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? 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? 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?.
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? in English & in Hindi are available as part of our courses for CA Foundation. Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice CA Foundation tests.
Explore Courses for CA Foundation exam
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev