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If two regression lines between height $(\mathrm{x})$ and weight $(\mathrm{y})$ are $4 y-15 x+410=0$ and $30 x-2 y-825=0$, then what
will be the correlation coefficient between height ang weight?
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will be the correlation coefficient between height ang weight?
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Verified Answer
The correct answer is:
$\frac{2}{3}$
$4 y-15 x+410=0$
$\Rightarrow y-\frac{15}{4} x+\frac{410}{4}=0 \Rightarrow y=\frac{15}{4} x-\frac{410}{4}$
$\mathrm{b}_{\mathrm{yx}}=\frac{15}{4}$
$30 x-2 y-825=0 \Rightarrow x=\frac{2}{30} y+\frac{825}{30}$
$b_{x y}=\frac{2}{30}$
Correlation coefficient $=\sqrt{\left(\mathrm{b}_{\mathrm{yx}}\right)\left(\mathrm{b}_{\mathrm{xy}}\right)}$
$=\sqrt{\frac{15}{4} \times \frac{2}{30}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
$\Rightarrow y-\frac{15}{4} x+\frac{410}{4}=0 \Rightarrow y=\frac{15}{4} x-\frac{410}{4}$
$\mathrm{b}_{\mathrm{yx}}=\frac{15}{4}$
$30 x-2 y-825=0 \Rightarrow x=\frac{2}{30} y+\frac{825}{30}$
$b_{x y}=\frac{2}{30}$
Correlation coefficient $=\sqrt{\left(\mathrm{b}_{\mathrm{yx}}\right)\left(\mathrm{b}_{\mathrm{xy}}\right)}$
$=\sqrt{\frac{15}{4} \times \frac{2}{30}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
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