Question

If the lines of regression are $3x+12y=19$ and $3y+9x=46$, then $r$ will be:

• A. $0.289$
• B. $-0.289$
• C. $0.209$
• D. None of these

Answer 1

The correct option is A

$0.289$

Explanation for the correct option:

Coefficient of co-relation

The coefficient of co-relation for two lines of regression is given by: $\mathbf{r}\mathbf{=}\sqrt{\frac{{\mathbf{a}}_{\mathbf{1}}}{{\mathbf{b}}_{\mathbf{1}}}\mathbf{\times }\frac{{\mathit{b}}_{\mathbf{2}}}{{\mathit{a}}_{\mathbf{2}}}}$

Given lines, $3x+12y=19$ and $3y+9x=46$.

Comparing these lines with the general equation, $ax+by+c=0$, we get,

$a_1=3,b_1=12,a_2=9,b_2=3$

So, $r=\sqrt{\frac{3}{12}\times \frac{3}{9}}$

$$\begin{gathered} \Rightarrow r=\sqrt{\frac{3}{12}\times \frac{3}{9}} \\ \Rightarrow r=\sqrt{\frac{1}{12}} \\ \Rightarrow r=0.289 \end{gathered}$$

Hence, option (A) $0.289$ is the correct answer.