Let two lines of regression be x+y+11=0 and 2x+3y+4=0 for some...

Let the regression line of $y$ on $x$ be $2x+3y+4=0$.

$3y = -2x - 4 \Rightarrow y = -\dfrac{2}{3}x - \dfrac{4}{3}$

The regression coefficient of $y$ on $x$ is $b_{yx} = -\dfrac{2}{3}$.

Let the regression line of $x$ on $y$ be $x+y+11=0$.

$x = -y - 11$

The regression coefficient of $x$ on $y$ is $b_{xy} = -1$.

The square of the correlation coefficient is given by $r^2 = b_{yx} \times b_{xy}$.

$r^2 = \left(-\dfrac{2}{3}\right) \times (-1) = \dfrac{2}{3}$

Since $r^2 \le 1$, our assumption for the regression lines is correct. Furthermore, since both regression coefficients $b_{yx}$ and $b_{xy}$ are negative, the correlation coefficient $r$ must also be negative.

$r = -\sqrt{\dfrac{2}{3}}$

Answer: $-\sqrt{\dfrac{2}{3}}$