Question

For two variables $x$ and $y$ regression equations are given as $7x-3y-18=0$ and $4x-y-11=0$ then the correlation coefficient between $x$ and $y$ is

• A. $0.7048$
• B. $0.7500$
• C. $0.7638$
• D. None of the above

Answer 1

The correct option is C $0.7638$

Let $7x-3y-18=0$ represents the regression line of $y$ on $x$
$\Rightarrow y=-6+\frac{7}{3}x\Rightarrow b_{yx}=\frac{7}{3}$
Then $4x-y-11=0$ is the regression line of $x$ on $y$.
$\Rightarrow x=\frac{11}{4}+\frac{y}{4}\Rightarrow b_{xy}=\frac{1}{4}$
Both $b_{yx}$ and $b_{yx}$ are positive.
$\Rightarrow r=\sqrt{b_{yx}\times b_{xy}}\Rightarrow r=\sqrt{\frac{7}{3}\times \frac{1}{4}}=0.7638$
So, option C is correct.