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If $r_1$ and $r_2$ are regression coefficients of $y$ on $x$ and $x$ on $y$ respectively

$\begin {array} {1 1} (A)\;r_1+r_2=2r & \quad (B)\;r_1+r_2<2r \\ (C)\;r_1+r_2 \geq 2r & \quad (D)\;None \: of \: these \end {array}$



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Given $r_1=\large\frac{r \sigma_y}{\sigma_x}$
$r_2=\large\frac{r \sigma_x}{\sigma_y}$
$ \therefore r_1 r_2 = r^2 \Rightarrow r$ is GM of $r_1\: and \; r_2$
AM $= \large\frac{r_1+r_2}{2}$
But $ AM \geq GM$
$ \Rightarrow \large\frac{r_1+r_2}{2} \geq r$
$ \therefore r_1+r_2 \geq 2r$
Ans : (C)
answered Jan 28, 2014 by thanvigandhi_1

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