Question

If the lines of regression are $x-y=0$ and $4x-y-3=0$ and ${{\sigma }_x}^2=1$, then the coefficient of correlation is:

• A. $-0.5$
• B. $0.5$
• C. $1.0$
• D. $-1.0$

Answer 1

The correct option is B

$0.5$

Explanation for the correct option:

Evaluate the coefficient of correlation for the given lines

Given lines, $x-y=0$ and $4x-y-3=0$

Applying the formula for correlation, $\mathbf{r}\mathbf{=}\sqrt{\frac{{\mathbf{a}}_{\mathbf{1}}}{{\mathbf{b}}_{\mathbf{1}}}\mathbf{\times }\frac{{\mathbf{b}}_{\mathbf{2}}}{{\mathbf{a}}_{\mathbf{2}}}}$, we get,

$$\begin{gathered} \Rightarrow r=\sqrt{\frac{1}{\cancel{-1}}\times \frac{\cancel{-1}}{4}}\mathbf{}\mathbf{}\left[\because a_1=1,a_2=-1.b_1=4,b_2=-1\right] \\ \Rightarrow r=\sqrt{\frac{1}{4}} \\ \Rightarrow r=0.5 \end{gathered}$$

Hence, the correct option is (B)