The coefficient of correlation $r_{x y}$ and the two regression coefficients $b_{x y}; b_{y x}$ are related as

b_{x y} / b_{y x}

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r_{x y} = b_{x y} . b_{y x}

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r_{x y} = b_{x y} + b_{y x}

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r_{x y} = (S g n b_{y x}) \sqrt{∣ ∣ b_{x y} ∣ ∣ ∣ ∣ b_{y x} ∣ ∣}

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Solution

The correct option is D $r_{x y} = (S g n b_{y x}) \sqrt{∣ ∣ b_{x y} ∣ ∣ ∣ ∣ b_{y x} ∣ ∣}$
We know that
$r^{2} =$ coefficient of regression $y$ on $x$ $\times$ coefficient of regression ( $x$ on $y$ )
$r^{2} = b_{y x} \times b_{x y}$
$r = \pm \sqrt{b_{y x} . b_{x y}}$
$r = (s g n o f b_{x y}) \sqrt{∣ ∣ b_{y x} ∣ ∣ . ∣ ∣ b_{x y} ∣ ∣}$
as $b_{y x}, b_{x y}, r (x, y)$ have same sign.

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