
Answer-first summary for fast verification
Answer: None of the above
## Explanation All three statements A, B, and C are actually **CORRECT** statements about the correlation coefficient: 1. **Statement A is correct**: The correlation coefficient (typically Pearson's correlation coefficient) measures the strength and direction of the **linear** relationship between two random variables. 2. **Statement B is correct**: The correlation coefficient is a dimensionless quantity - it has no units. This is because it's calculated by dividing the covariance of two variables by the product of their standard deviations, which cancels out the units. 3. **Statement C is correct**: The correlation coefficient always ranges from -1 to +1, where: - +1 indicates a perfect positive linear relationship - -1 indicates a perfect negative linear relationship - 0 indicates no linear relationship Since all three statements are correct, the **INCORRECT** statement is **D. None of the above**, because there IS an incorrect statement among the options - option D itself is incorrect. **Note**: The text states "The correct answer is: D)" but this appears to be a contradiction in the source material. If D says "None of the above" and all A, B, C are correct, then D should be the correct answer for the question asking which is INCORRECT. However, the explanation in the text suggests that all statements about correlation coefficient properties are correct, making D the incorrect statement.
Author: Nikitesh Somanthe
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Which of the following statements is INCORRECT regarding the correlation coefficient?
A
The correlation coefficient measures the strength of the linear relationship between two random variables
B
The correlation coefficient has no units
C
The correlation coefficient ranges from -1 to +1
D
None of the above
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