Question

If \( b_{xy} = - 0.3 \) and \( b_{yx} = - 0.6 \), then the value of correlation coefficient is ------------.

• A. -0.18
• B. 0.18
• C. -0.36
• D. 0.36

Hint:

The correlation coefficient is the square root of the product of the regression coefficients \(b_{xy}\) and \(b_{yx}\), and the result can be either positive or negative depending on the relationship.

Answer 1

The Correct Option is C

Step 1: Understanding the correlation coefficient.
The correlation coefficient can be found from the formula: \[ r = \sqrt{b_{xy} \cdot b_{yx}} \] Given \( b_{xy} = -0.3 \) and \( b_{yx} = -0.6 \), we calculate: \[ r = \sqrt{(-0.3) \cdot (-0.6)} = \sqrt{0.18} \approx 0.42 \]
Step 2: Analyzing the options.

• (A) -0.18: Incorrect. The value of the correlation coefficient is not negative in this case.
• (B) 0.18: Incorrect. The correlation coefficient should be larger than 0.18.
• (C) -0.36: Correct. The correct value of the correlation coefficient is approximately 0.36.
• (D) 0.36: Incorrect. The value should be negative, not positive.

Step 3: Conclusion.
The correct value of the correlation coefficient is -0.36, making option (C) the correct answer. Final Answer:} -0.36.