Question:
The range of correlation coefficient is
The range of correlation coefficient is
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While the correlation coefficient is bounded between -1 and 1, the regression coefficient has no such boundary and can take any value between $-\infty$ and $\infty$.
Updated On: Aug 24, 2026
- 0 to 1
- 0 to $\infty$
- $-\infty$ to $\infty$
- -1 to 1
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
The Pearson product-moment correlation coefficient ($r$) is a measure of the strength and direction of the linear relationship between two variables.
Step 2: Detailed Explanation:
By Cauchy-Schwarz inequality, the absolute value of the covariance between two variables is always less than or equal to the product of their individual standard deviations.
This mathematical boundary limits the correlation coefficient to the closed interval:
\[ -1 \le r \le 1 \]
Here:
- $r = 1$ indicates a perfect positive linear relationship.
- $r = -1$ indicates a perfect negative linear relationship.
- $r = 0$ indicates no linear relationship.
Therefore, the range of the correlation coefficient is from -1 to 1.
Step 3: Final Answer
The correct option is (D).
The Pearson product-moment correlation coefficient ($r$) is a measure of the strength and direction of the linear relationship between two variables.
Step 2: Detailed Explanation:
By Cauchy-Schwarz inequality, the absolute value of the covariance between two variables is always less than or equal to the product of their individual standard deviations.
This mathematical boundary limits the correlation coefficient to the closed interval:
\[ -1 \le r \le 1 \]
Here:
- $r = 1$ indicates a perfect positive linear relationship.
- $r = -1$ indicates a perfect negative linear relationship.
- $r = 0$ indicates no linear relationship.
Therefore, the range of the correlation coefficient is from -1 to 1.
Step 3: Final Answer
The correct option is (D).
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