`b_(xy) xx b_(yx)` is equal to

Options

A. `rho(X,Y)`
B. Cov (X,Y)
C. `[p(X,Y)]^(2)`
D. None of these

Answer

To solve the problem \( b_{xy} \times b_{yx} \), we need to understand the relationship between the regression coefficients and the correlation coefficient.

### Step-by-Step Solution:

1. **Identify the Regression Coefficients**:
- Let \( b_{xy} \) be the regression coefficient of Y on X.
- Let \( b_{yx} \) be the regression coefficient of X on Y.

2. **Recall the Relationship**:
- The geometric mean of the two regression coefficients \( b_{xy} \) and \( b_{yx} \) is given by:
\[ \sqrt{b_{xy} \times b_{yx}} = r \]
where \( r \) is the correlation coefficient between X and Y.

3. **Square Both Sides**:
- If we square both sides of the equation, we get:
\[ b_{xy} \times b_{yx} = r^2 \]

4. **Conclusion**:
- Therefore, the product \( b_{xy} \times b_{yx} \) is equal to the square of the correlation coefficient:
\[ b_{xy} \times b_{yx} = r^2 \]

### Final Answer:
The value of \( b_{xy} \times b_{yx} \) is equal to \( r^2 \).

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