The two regression lines intersect at unique point, then it should be

Options

A. `( vec x, vec y ) `
B. ` (0,0) `
C. ` (-overset(-) x, -overset( -)y)`
D. None of these

Answer

To solve the question regarding the intersection of two regression lines, we need to understand the properties of regression lines and how they relate to the means of the variables involved.

### Step-by-Step Solution:

1. **Understanding Regression Lines**:
- The two regression lines are typically represented as:
- Regression of Y on X: \( Y = a + bX \)
- Regression of X on Y: \( X = c + dY \)
- Here, \( a, b, c, \) and \( d \) are constants derived from the data.

2. **Intersection of Regression Lines**:
- The two regression lines intersect at a unique point, which is the point where both equations yield the same values for \( X \) and \( Y \).

3. **Mean Values**:
- It is a known statistical property that the two regression lines intersect at the point \( ( \bar{x}, \bar{y} ) \), where \( \bar{x} \) is the mean of the X values and \( \bar{y} \) is the mean of the Y values.

4. **Conclusion**:
- Therefore, if the two regression lines intersect at a unique point, that point must be \( (\bar{x}, \bar{y}) \).

### Final Answer:
The correct answer is \( \bar{x}, \bar{y} \).