$\begin {array} {1 1} (A)\;4 & \quad (B)\;5 \\ (C)\;2 & \quad (D)\;None\: of \: these \end {array}$

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Slopes of regression lines are $ -\large\frac{1}{2}$ and $ \large\frac{-2}{3}$

$ \therefore b_{yx} = -\large\frac{ 1}{2}$ and $ b_{xy}= -\large\frac{3}{2}$

$ \therefore r^2 = \bigg( -\large\frac{1}{2} \bigg) \bigg( -\large\frac{3}{2} \bigg) = \large\frac{3}{4} $ $( < 1)$

$ \Rightarrow r = -\large\frac{\sqrt 3}{2}$

Also $b_{yx}=r\large\frac{\sigma_y}{\sigma_x}$

$ \sigma_x=2\sqrt 3$

$ \therefore \sigma_x^2 = 12$

$ -\large\frac{1}{2} $ $= -\large\frac{\sqrt 3}{2}.\large\frac{\sigma_y}{2\sqrt 3}$

$ \sigma_y = 2$

Hence Ans (C)

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