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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Statistics
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If the slopes of the line of regression of $y$ on $x$ and of $x$ on $y$ are $30^{\circ}$ and $60^{\circ}$ respectively. Then $ r(x,y)$ is

$\begin {array} {1 1} (A)\;-1 & \quad (B)\;1 \\ (C)\;\large\frac{1}{\sqrt 3} & \quad (D)\;\sqrt 3 \end {array}$

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1 Answer

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We have
$b_{yx}= \tan 30^{\circ}$
$ \large\frac{1}{\sqrt 3}$
$ \large\frac{1}{b_{xy}}$ $ = \tan 60^{\circ} = \sqrt 3$
$ \therefore b_{yx}.b_{xy} = \large\frac{1}{3}$
$ \Rightarrow r^2=\large\frac{1}{3} \: or \: r=+\large\frac{1}{\sqrt 3}$
$ b_{yx} \: and \: b_{xy}$ are positive
Hence Ans (C)
answered Jan 27, 2014 by thanvigandhi_1
 

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