Question

The coefficient of correlation between two variables $x$ and $y$ are $0.8$ while the regression coefficient of $y$ on $x$ is $0.2$. Then the regression coefficient of $x$ on $y$ is

• A. $-3.2$
• B. $3.2$
• C. $4$
• D. $0.16$

Answer 1

The correct option is B

$3.2$

Explanation for the correct option:

Finding regression coefficient of $x\text{on}y$:

The coefficient of correlation $\rho$ is $0.8$.

The regression coefficient of $y$ on $x$ is $b_{xy}=0.2$.

The regression coefficient of $x$ on $y$ is $b_{yx}$.

Relation between the correlation coefficient and regression coefficient is given by the formula $\rho =\sqrt{b_{xy}\times b_{yx}}$.

Substitute values in the above formula, we get:

$$\begin{gathered} \Rightarrow 0.8=\sqrt{0.2\times b_{yx}} \\ \Rightarrow 0.64=0.2\times b_{yx} \\ \Rightarrow b_{yx}=3.2 \end{gathered}$$

Hence, the regression coefficient of $x$ on $y$ is $3.2$.

Therefore, the correct answer is Option (B).