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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Statistics
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Lines of regression of $y$ on $x$ and $x$ on $y$ are respectively $y=ax+b$ and $x=\alpha y+ \beta$. If mean of $x$ and $y$ series is same then its value is

$\begin {array} {1 1} (A)\;\large\frac{b}{1-a} \: or \: \large\frac{\beta}{1- \alpha} & \quad (B)\;\large\frac{1-a}{b} \\ (C)\;\large\frac{\beta}{1-\beta} & \quad (D)\;\large\frac{\alpha}{1-\alpha} \end {array}$

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Let mean of $x$ and $y$ series are $ \overline x $ and $ \overline y $
Lines of regression pass through mean $ ( \overline x , \overline y )$ hence
$ \overline y = a \overline x +b$
$ \overline x = \alpha \overline y + \beta$
Given that $ \overline x = \overline y$
$ \Rightarrow \large\frac{b}{1-a} = \large\frac{ \beta}{1- \alpha}$
Ans : (A)
answered Jan 31, 2014 by thanvigandhi_1

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