Math Problem Statement
you are a scientist who wishes to obtain as high a correlation as possible. Which one of the following would you consider to be the best result?
- A. -0.70
- B. +0.11
- C. +1.46
- D. -1.19
Solution
The correlation coefficient, often denoted as , measures the strength and direction of the linear relationship between two variables. The value of ranges from -1 to +1:
- A correlation of +1 indicates a perfect positive linear relationship.
- A correlation of -1 indicates a perfect negative linear relationship.
- A correlation of 0 indicates no linear relationship.
In this context:
- A. -0.70: Indicates a strong negative linear relationship.
- B. +0.11: Indicates a very weak positive linear relationship.
- C. +1.46: This is not a valid value for correlation as must be between -1 and +1.
- D. -1.19: This is also not a valid value for correlation as must be between -1 and +1.
Given the valid options, A. -0.70 is the best result, as it has the highest magnitude of correlation (closest to -1 or +1), indicating a stronger linear relationship compared to the other valid option, B (+0.11).
Would you like more details or have any questions?
Here are 5 related questions:
- What are the limitations of correlation coefficients?
- How does correlation differ from causation?
- What is the meaning of a correlation of 0?
- What statistical tests are used to determine the significance of a correlation?
- How does sample size affect the reliability of a correlation?
Tip: Always check the range of the correlation coefficient to ensure it falls between -1 and +1.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Coefficient
Formulas
Pearson Correlation Coefficient (r)
Theorems
Range of Correlation (-1 to +1)
Suitable Grade Level
Grades 10-12
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