B Com Exam > B Com Questions > Coefficient of correlation between two variab...
Start Learning for Free
Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.?
Most Upvoted Answer
Coefficient of correlation between two variables X and Y is 0.8 and th...
Calculation of Standard Deviation of Y
Coefficient of Correlation
The coefficient of correlation, denoted as r, is a measure of the strength and direction of the linear relationship between two variables.
Given, coefficient of correlation between X and Y is 0.8.
Covariance
Covariance is a measure of how much two variables change together, and it is denoted as Cov(X,Y).
Given, covariance between X and Y is 20.
Variance
Variance is a measure of how spread out a set of data is, and it is denoted as Var(X).
Given, variance of X is 25.
Formula
The formula for the standard deviation of Y, denoted as SD(Y), is:
SD(Y) = sqrt(Var(Y))
where
Var(Y) = Var(X) * (1 - r^2) * (SD(Y))^2
Substituting the given values in the formula,
Var(Y) = 25 * (1 - 0.8^2) * (SD(Y))^2
Var(Y) = 25 * 0.36 * (SD(Y))^2
Var(Y) = 9 * (SD(Y))^2
SD(Y) = sqrt(Var(Y))
SD(Y) = sqrt(9 * (SD(Y))^2)
SD(Y) = 3 * SD(Y)
Hence, the standard deviation of Y is 3.
Coefficient of Correlation
The coefficient of correlation, denoted as r, is a measure of the strength and direction of the linear relationship between two variables.
Given, coefficient of correlation between X and Y is 0.8.
Covariance
Covariance is a measure of how much two variables change together, and it is denoted as Cov(X,Y).
Given, covariance between X and Y is 20.
Variance
Variance is a measure of how spread out a set of data is, and it is denoted as Var(X).
Given, variance of X is 25.
Formula
The formula for the standard deviation of Y, denoted as SD(Y), is:
SD(Y) = sqrt(Var(Y))
where
Var(Y) = Var(X) * (1 - r^2) * (SD(Y))^2
Substituting the given values in the formula,
Var(Y) = 25 * (1 - 0.8^2) * (SD(Y))^2
Var(Y) = 25 * 0.36 * (SD(Y))^2
Var(Y) = 9 * (SD(Y))^2
SD(Y) = sqrt(Var(Y))
SD(Y) = sqrt(9 * (SD(Y))^2)
SD(Y) = 3 * SD(Y)
Hence, the standard deviation of Y is 3.
Community Answer
Coefficient of correlation between two variables X and Y is 0.8 and th...
20
|
Explore Courses for B Com exam
|
|
Similar B Com Doubts
Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.?
Question Description
Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.?.
Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.?.
Solutions for Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? in English & in Hindi are available as part of our courses for B Com.
Download more important topics, notes, lectures and mock test series for B Com Exam by signing up for free.
Here you can find the meaning of Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? defined & explained in the simplest way possible. Besides giving the explanation of
Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.?, a detailed solution for Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? has been provided alongside types of Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? theory, EduRev gives you an
ample number of questions to practice Coefficient of correlation between two variables X and Y is 0.8 and their covariance is 20. If the variance of X is 25, the standard deviation of Y is.? tests, examples and also practice B Com tests.
|
|
Explore Courses for B Com exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup