Question
Download Solution PDFThe standard deviation of Y is double of standard deviation of x. The correlation coefficient between X and Y is 0.5.
The acute angle between lines of regression is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is arctan (3/5)
Key Points
- The acute angle between lines of regression is given by arctan(b), where b is the slope of the regression line.
- The slope of the regression line can be calculated using the correlation coefficient (r) and the standard deviations of X and Y.
- In this case, the correlation coefficient is 0.5 and the standard deviation of Y is double that of X, so the slope of the regression line can be calculated as b = 2 * r * (SDy/SDx) = 2 * 0.5 * (2/1) = 2.
- Hence, the acute angle between lines of regression can be calculated as arctan(b) = arctan(2) = 3/5.
Additional Information
- The relationship between X and Y can be visualized by a scatter plot and a regression line.
- The correlation coefficient represents the strength of the linear relationship between X and Y
- with a value of +1 indicating a perfect positive correlation
- a value of -1 indicating a perfect
- a value of 0 indicating no correlation.
- The angle between the regression line and the x-axis is called the acute angle, which is an indicator of the slope of the regression line.
- In this case, with a correlation coefficient of 0.5, the relationship between X and Y is moderately positive
- the acute angle can be found using the tan inverse function, with the result being arctan (3/5).
- The fact that the standard deviation of Y is double of the standard deviation of X means that Y values have more spread than X values
- the slope of the regression line (represented by the acute angle) helps to describe this relationship.
Last updated on Jun 13, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> Candidates should also use the SSC CGL previous year papers for a good revision.