Math Problem Statement
Solution
The correct answer to this question is:
- "-1 and 1"
The correlation coefficient, denoted by , measures the strength and direction of the linear relationship between two variables and always falls within the range .
- If , it indicates a perfect positive linear correlation.
- If , it indicates a perfect negative linear correlation.
- If , it suggests no linear correlation.
Would you like further details on how the correlation coefficient is interpreted?
Here are some related questions to expand your understanding:
- What does it mean if the correlation coefficient is close to 0?
- How is the correlation coefficient calculated between two variables?
- What are some limitations of using the correlation coefficient?
- Can a correlation coefficient alone determine causation between two variables?
- How does the correlation coefficient relate to covariance?
Tip: Remember that correlation only indicates the strength and direction of a linear relationship; it does not imply causation.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Coefficient
Linear Relationship
Formulas
-1 ≤ r ≤ 1
Theorems
Properties of Correlation Coefficient
Suitable Grade Level
Grades 10-12
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