`b_(xy)` and `b_(yx)` are __________

Options

A. Independent of change of origin and scale
B. Independent of change of origin but not of scale
C. Independent of change of scale but not of origin
D. Affected by change of origin and scale

Answer

To solve the question regarding the relationship between \( b_{xy} \) and \( b_{yx} \), we need to analyze the definitions and properties of these terms in the context of correlation and standard deviation.

### Step-by-Step Solution:

1. **Understanding \( b_{xy} \) and \( b_{yx} \)**:
- \( b_{xy} \) is defined as \( r \cdot \frac{\sigma_x}{\sigma_y} \), where \( r \) is the coefficient of correlation between variables \( x \) and \( y \), and \( \sigma_x \) and \( \sigma_y \) are the standard deviations of \( x \) and \( y \) respectively.
- \( b_{yx} \) is defined as \( r \cdot \frac{\sigma_y}{\sigma_x} \).

2. **Expressing the relationship**:
- We can express \( b_{yx} \) in terms of \( b_{xy} \):
\[ b_{yx} = r \cdot \frac{\sigma_y}{\sigma_x} = \frac{1}{b_{xy}} \]
- This shows that \( b_{yx} \) is the reciprocal of \( b_{xy} \).

3. **Conclusion**:
- Since \( b_{xy} \) and \( b_{yx} \) are reciprocals of each other, we conclude that they are related through the correlation coefficient and the standard deviations of the respective variables.

### Final Answer:
Thus, \( b_{xy} \) and \( b_{yx} \) are **reciprocals** of each other.