Question

Correlation coefficient is the

• A. Sum of byx and bxy
• B. Difference of byx and bxy
• C. Product of byx and bxy
• D. Square root of the product byx and bxy

Hint:

The sign of the correlation coefficient (\(r\)) is always identical to the sign of the regression coefficients. If both \(b_{yx}\) and \(b_{xy}\) are negative, \(r\) will also be negative.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In statistics, the correlation coefficient (\(r\)) and regression coefficients (\(b_{yx}\) and \(b_{xy}\)) are mathematically interrelated.

Step 2: Key Formula or Approach:
The mathematical relationship is given by:
\[ r^2 = b_{yx} \times b_{xy} \]
Therefore:
\[ r = \pm \sqrt{b_{yx} \times b_{xy}} \]

Step 3: Detailed Explanation:
The correlation coefficient (\(r\)) is defined as the geometric mean of the two regression coefficients: the regression coefficient of Y on X (\(b_{yx}\)) and the regression coefficient of X on Y (\(b_{xy}\)).
Hence, \(r\) is the square root of the product of the regression coefficients.

Step 4: Final Answer:
The correlation coefficient is the square root of the product of \(b_{yx}\) and \(b_{xy}\), which corresponds to option (D).