Question:
Which of the following statements are correct about the correlation co-efficient ?
A. Its value falls between $-1$ and $+1$.
B. Its value changes when the unit of measurement gets changed.
C. It measures only the strength of linear association between variables.
D. It is a dimensionless quantity.
Choose the correct answer from the options given below :
Which of the following statements are correct about the correlation co-efficient ?
A. Its value falls between $-1$ and $+1$.
B. Its value changes when the unit of measurement gets changed.
C. It measures only the strength of linear association between variables.
D. It is a dimensionless quantity.
Choose the correct answer from the options given below :
A. Its value falls between $-1$ and $+1$.
B. Its value changes when the unit of measurement gets changed.
C. It measures only the strength of linear association between variables.
D. It is a dimensionless quantity.
Choose the correct answer from the options given below :
Show Hint
Correlation is unit-free. Whether you measure your data in grams or tons, the correlation coefficient will stay exactly the same.
Updated On: May 20, 2026
- A, B, C, D
- A, B, C only
- A, C, D only
- A, B, D only
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
Pearson's correlation coefficient ($r$) is a statistical measure of the strength and direction of a linear relationship between two variables.
Step 1: Evaluate Statement A and D.
Statement A is correct; $r$ is always restricted to the range $[-1, 1]$. Statement D is also correct because the units in the numerator and denominator cancel out, making the coefficient a "pure number" or dimensionless.
Step 2: Evaluate Statement B.
This is incorrect. One of the most important properties of the correlation coefficient is that it is independent of scale and origin. Changing the units (e.g., measuring height in cm vs. inches) will not change the value of $r$.
Step 3: Evaluate Statement C.
This is correct. Correlation only detects linear relationships. If two variables have a perfect non-linear relationship (like a parabola), the correlation coefficient might still be zero.
Step 1: Evaluate Statement A and D.
Statement A is correct; $r$ is always restricted to the range $[-1, 1]$. Statement D is also correct because the units in the numerator and denominator cancel out, making the coefficient a "pure number" or dimensionless.
Step 2: Evaluate Statement B.
This is incorrect. One of the most important properties of the correlation coefficient is that it is independent of scale and origin. Changing the units (e.g., measuring height in cm vs. inches) will not change the value of $r$.
Step 3: Evaluate Statement C.
This is correct. Correlation only detects linear relationships. If two variables have a perfect non-linear relationship (like a parabola), the correlation coefficient might still be zero.
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