Q.If X and Y are two variables then there can be atmost :

The regression line of $y$ on $x$, $y-\bar y=b_{yx}(x-\bar x)$, and the regression line of $x$ on $y$, $x-\bar x=b_{xy}(y-\bar y)$, are both satisfied by $x=\bar x, y=\bar y$, so the two lines always intersect at exactly the point of means $(\bar x,\bar y)$. This fact works in both directions: given the means and coefficie …