The two lines of regression meet at

Options

A. `(overset(-)x,overset(-)y)`
B. `(sigmax, sigmay)`
C. `(sigma x^2, sigma y^2)`
D. None of these

Answer

To find the point where the two lines of regression meet, we can follow these steps:

### Step 1: Understand the Concept of Regression Lines
The two lines of regression are derived from the relationship between two variables, say \(X\) and \(Y\). The regression line of \(Y\) on \(X\) predicts \(Y\) based on \(X\), and the regression line of \(X\) on \(Y\) predicts \(X\) based on \(Y\).

### Step 2: Identify the Means
The two lines of regression intersect at the point where the means of \(X\) and \(Y\) are located. This point is represented as \((\bar{x}, \bar{y})\), where \(\bar{x}\) is the mean of \(X\) and \(\bar{y}\) is the mean of \(Y\).

### Step 3: Use the Property of Intersection
According to the properties of regression lines, the intersection point of the regression lines of \(Y\) on \(X\) and \(X\) on \(Y\) is given by the coordinates \((\bar{x}, \bar{y})\).

### Step 4: Conclusion
Thus, the two lines of regression meet at the point \((\bar{x}, \bar{y})\).

### Final Answer
The two lines of regression meet at the point \((\bar{x}, \bar{y})\).

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