State True or False: `y = 5 + 2.8x` and `x = 3 + 0.5y` be the regression lines of `y` on `x` and `x` on `y` respectively ,then `b_(yx) = - 0.5`

Answer

To determine whether the statement `b_(yx) = -0.5` is true or false, we need to analyze the provided regression lines.

1. **Identify the regression lines**:
- The first regression line given is \( y = 5 + 2.8x \). This represents the regression of \( y \) on \( x \).
- The second regression line given is \( x = 3 + 0.5y \). This represents the regression of \( x \) on \( y \).

2. **Extract the regression coefficient \( b_{yx} \)**:
- The regression line of \( y \) on \( x \) can be expressed in the form \( y = b_{yx} \cdot x + a \).
- From the equation \( y = 5 + 2.8x \), we can see that \( b_{yx} = 2.8 \).

3. **Compare with the statement**:
- The statement claims that \( b_{yx} = -0.5 \).
- However, we have found that \( b_{yx} = 2.8 \), which does not equal -0.5.

4. **Conclusion**:
- Since \( b_{yx} \) is not equal to -0.5, the statement is **False**.

### Summary of Steps:
1. Identify the regression lines.
2. Extract the regression coefficient \( b_{yx} \) from the first regression line.
3. Compare the extracted value with the statement.
4. Conclude whether the statement is true or false.