$\begin {array} {1 1} (A)\;-\sqrt{\large\frac{5}{21}} & \quad (B)\;\sqrt{\large\frac{5}{21}} \\ (C)\;\large\frac{5}{21} & \quad (D)\;None \: of \: these \end {array}$

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$5x+3y=55$............(i)

$7x+y=45$............(ii)

If we regard (i) as line of regression of $y$ on $x$ and (ii) that of $x$ on $y$ then

$ b_{yx} =$ Slope of (i)

$ = -\large\frac{5}{3}$

$ b_{xy} = \large\frac{1}{slope \: of \: (ii)}$

$ = -\large\frac{1}{7}$

$ r = -\sqrt{b_{yx}+b_{xy}}$

$ = -\sqrt{\large\frac{5}{3} \times \large\frac{1}{7}}$

$ = -\sqrt{\large\frac{5}{21}}$

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