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Question

Given two lines of regression $$x+3y=11$$ and $$2x+y=7$$. Find the coefficient of correlation between x and y.


A
r=0.408
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B
r=0.408
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C
r=0.108
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D
r=0.108
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Solution

The correct option is A $$r=-0.408$$
$$x+3y=11$$
$$y=\cfrac{11}{3}-\cfrac{x}{3}$$
So, $$b_{yx}=\cfrac{-1}{3}$$
$$2x+y=7$$
$$x=\cfrac{7}{2}-\cfrac{1}{2}y$$
So, $$b_{yx}=\cfrac{-1}{2}$$
 $$r=\sqrt{b_{xy}.b_{yx}}=\sqrt{\cfrac{-1}{2}\times \cfrac{-1}{3}}=\sqrt{\cfrac{1}{6}}=0.408$$
Since $$b_{xy}$$ and $$b_{yx}$$ are negative.
$$r=-0.408$$

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