Question

If the two regression coefficients between $x$ and $y$ are $0.8$ and $0.2$, then the coefficient of correlation between them is

• A. $0.4$
• B. $0.6$
• C. $0.3$
• D. $0.5$

Answer 1

The correct option is A

$0.4$

Explanation for the correct option

Find the correlation coefficient

The two regression coefficients between $x$ and $y$ are $0.8$ and $0.2$ .

The correlation coefficient will be positive because both the coefficients are positive.

And the correlation coefficient is the geometric mean of both the coefficients. So the correlation coefficient is:

$$\begin{gathered} r=\sqrt{0.8\times 0.2} \\ \Rightarrow r=\sqrt{0.16} \\ \Rightarrow r=\sqrt{{\left(0.4\right)}^2} \\ \Rightarrow r=0.4 \end{gathered}$$

Hence, the correct option is A.