CA Foundation Exam > CA Foundation Questions > The coefficient of correlation between x and ...
Start Learning for Free
The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?
Most Upvoted Answer
The coefficient of correlation between x and y is 0.6. If x and y valu...
Explanation:
When x and y values are multiplied by -1, the direction of the relationship between x and y changes, but the strength of the relationship remains the same. This is because the correlation coefficient measures the strength of the linear relationship between two variables, and multiplying both variables by a constant does not affect the linearity of the relationship.
To prove that the coefficient of correlation between x and y remains 0.6 after multiplication by -1, we can use the formula for the correlation coefficient:
r = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
where n is the sample size, Σ is the sum of the variable, and Σxy is the sum of the product of x and y.
If we multiply both x and y by -1, the formula becomes:
r' = (nΣ(-x)(-y) - Σ(-x)Σ(-y)) / [√(nΣ(-x)^2 - (Σ(-x))^2) √(nΣ(-y)^2 - (Σ(-y))^2)]
which simplifies to:
r' = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
This is the same as the original formula for r, which means that r' = r = 0.6.
Therefore, the correct answer is A) 0.6.
When x and y values are multiplied by -1, the direction of the relationship between x and y changes, but the strength of the relationship remains the same. This is because the correlation coefficient measures the strength of the linear relationship between two variables, and multiplying both variables by a constant does not affect the linearity of the relationship.
To prove that the coefficient of correlation between x and y remains 0.6 after multiplication by -1, we can use the formula for the correlation coefficient:
r = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
where n is the sample size, Σ is the sum of the variable, and Σxy is the sum of the product of x and y.
If we multiply both x and y by -1, the formula becomes:
r' = (nΣ(-x)(-y) - Σ(-x)Σ(-y)) / [√(nΣ(-x)^2 - (Σ(-x))^2) √(nΣ(-y)^2 - (Σ(-y))^2)]
which simplifies to:
r' = (nΣxy - ΣxΣy) / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]
This is the same as the original formula for r, which means that r' = r = 0.6.
Therefore, the correct answer is A) 0.6.
Community Answer
The coefficient of correlation between x and y is 0.6. If x and y valu...
-0.6
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?
Question Description
The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? 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 The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?.
The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? 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 The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?.
Solutions for The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? 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 The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? defined & explained in the simplest way possible. Besides giving the explanation of
The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.?, a detailed solution for The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? has been provided alongside types of The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? theory, EduRev gives you an
ample number of questions to practice The coefficient of correlation between x and y is 0.6. If x and y values are multiplied by -1, then the coefficient of correlation will be: A) 0.6 B) -0.6 C) 1/0.6 D) 1-0.6 Correct ans is A. Please explain this answer.? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation 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