Question

If tangent of the angle made by the line of regression of $y$ on $x$ is $0.6$ and ${\sigma }_y=2{\sigma }_x$. Find the correlation coefficient between $x$ and $y$.

• A. $0.1$
• B. $0.2$
• C. $0.3$
• D. $0.4$

Answer 1

The correct option is C $0.3$

Let $L_{yx}$ be the line of regression of $y$ on $x$.

Let the angle made by $L_{yx}$ with $X$-axis be $\theta$.

Thus tangent of the angle made by $L_{yx}$ with $X$- axis is $\tan \theta =0.6$

But , slope of any line with $X$-axis is $\tan \theta$

θHowever, slope of $L_{yx}=b_{yx}$

$\therefore b_{yx}=tan\theta =0.6$

But $b_{yx}=r\frac{{\sigma }_y}{{\sigma }_x}$

Therefore, $0.6=r\frac{2{\sigma }_x}{{\sigma }_x}(\because {\sigma }_y=2{\sigma }_x)$

$\Rightarrow 2r=0.6$

$\Rightarrow r=0.3$

Therefore, correlation coefficient between $x$ and $y$ is $r=0.3$.