Question
Download Solution PDFIf r and R denote correlation and multiple correlation coefficient for the data set for X1, X2 and X3. Which option is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is r12=0.69, r13=0.22, r23=0.23, R1.23=.69
Key Points
- Correlation coefficient (r) measures the linear association between two variables.
- Multiple correlation coefficient (R) measures the strength of the association between multiple predictor variables and a single criterion variable.
- The values of r and R range between -1 and 1.
- Values close to 1 indicate a strong positive association (or relationship), values close to -1 indicate a strong negative association (or relationship), and values close to 0 indicate no or weak association (or relationship).
- Correlation coefficients (r) and multiple correlation coefficients (R) are useful for understanding the relationships between variables in a data set.
Additional Information
- If r12 represents the correlation between X1 and X2, r13 represents the correlation between X1 and X3, and r23 represents the correlation between X2 and X3, then the values of r12, r13, and r23 should range between -1 and 1, with values close to 1 indicating a strong positive association, values close to -1 indicating a strong negative association, and values close to 0 indicating no or weak association.
- The multiple correlation coefficient (R) measures the strength of the association between multiple predictor variables (X1, X2, X3) and a single criterion variable.
- In this case, R1.23 represents the multiple correlation between X1, X2, and X3 with respect to the criterion variable.
- Like r, R values range between -1 and 1, with values close to 1 indicating a strong relationship and values close to 0 indicating a weak relationship.
- So, based on the given values, r12=0.69, r13=0.22, r23=0.23, R1.23=.69
Important Points
- It is important to note that correlation does not imply causation, meaning that just because two variables are correlated does not mean that one causes the other.
- Correlation and multiple correlation coefficients are based on linear relationships and may not capture non-linear relationships between variables.
- Interpreting the strength and direction of relationships between variables is an important aspect of data analysis and interpretation.
Last updated on Jun 11, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The UPSC Prelims Result 2025 and UPSC IFS Result 2025 has been released @upsc.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.