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If the two lines of regression are at right angles, then ρ(X,Y) is equal to
- a)- 1
- b)0
- c)1
- d)1 or - 1
Correct answer is option 'B'. Can you explain this answer?
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If the two lines of regression are at right angles, thenρ(X,Y) is ...
Understanding Regression Lines and Correlation
When two lines of regression are at right angles, it provides critical information about the relationship between the variables X and Y.
Correlation Coefficient (ρ)
- The correlation coefficient (ρ) quantifies the degree of linear relationship between two variables.
- Its value ranges from -1 to +1:
- ρ = 1 indicates a perfect positive correlation.
- ρ = -1 indicates a perfect negative correlation.
- ρ = 0 indicates no correlation.
Right Angles and Independence
- Lines of regression are perpendicular (at right angles) when the product of their slopes equals -1.
- This condition signifies that changes in one variable do not predict changes in the other, indicating independence.
Conclusion: The Value of ρ
- When the lines of regression are at right angles, it implies that:
- There is no linear relationship between X and Y.
- Thus, ρ must equal 0.
This leads us to conclude that the correct answer to the question is option 'B', which states that ρ(X,Y) is equal to 0.
When two lines of regression are at right angles, it provides critical information about the relationship between the variables X and Y.
Correlation Coefficient (ρ)
- The correlation coefficient (ρ) quantifies the degree of linear relationship between two variables.
- Its value ranges from -1 to +1:
- ρ = 1 indicates a perfect positive correlation.
- ρ = -1 indicates a perfect negative correlation.
- ρ = 0 indicates no correlation.
Right Angles and Independence
- Lines of regression are perpendicular (at right angles) when the product of their slopes equals -1.
- This condition signifies that changes in one variable do not predict changes in the other, indicating independence.
Conclusion: The Value of ρ
- When the lines of regression are at right angles, it implies that:
- There is no linear relationship between X and Y.
- Thus, ρ must equal 0.
This leads us to conclude that the correct answer to the question is option 'B', which states that ρ(X,Y) is equal to 0.
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If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer?
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If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer?.
If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the two lines of regression are at right angles, thenρ(X,Y) is equal toa)- 1b)0c)1d)1 or - 1Correct answer is option 'B'. Can you explain this answer?.
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