Question

The correlation coefficient of two variables $x$and $y$are $0.8$. 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 A

$3.2$

Explanation for correct option:

Calculating the regression coefficient of $x$ on$y$ :

The correlation coefficient ($r$)=$0.8$

The regression coefficient of $y$ on $x$($b_{yx}$)=$0.2$

Finding the regression coefficient of $x$ on$y$, using the coefficient of correlation formula,

$\mathit{r}\mathbf{=}\sqrt{{\mathbf{b}}_{\mathbf{y}\mathbf{x}}\mathbf{.}{\mathbf{b}}_{\mathbf{x}\mathbf{y}}}$

$\Rightarrow$ $r^2=b_{xy}.b_{yx}$

$\begin{array}{rcl}& \Rightarrow & b_{xy}=\frac{r^2}{b_{yx}}\\ & =& \frac{0.8\times 0.8}{0.2}\\ & =& \frac{0.64}{0.2}\\ & =& 3.2\end{array}$

$b_{xy}=3.2$

Hence, option (A) is the correct answer.