Question

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

• A. $r=-0.408$
• B. $r=0.408$
• C. $r=-0.108$
• D. $r=0.108$

Answer 1

The correct option is A $r=-0.408$

$x+3y=11$

$y=\frac{11}{3}-\frac{x}{3}$

So, $b_{yx}=\frac{-1}{3}$

$2x+y=7$

$x=\frac{7}{2}-\frac{1}{2}y$

So, $b_{yx}=\frac{-1}{2}$

$r=\sqrt{b_{xy}.b_{yx}}=\sqrt{\frac{-1}{2}\times \frac{-1}{3}}=\sqrt{\frac{1}{6}}=0.408$

Since $b_{xy}$ and $b_{yx}$ are negative.

$r=-0.408$