Question

If the regression coefficient of $y$ on $x$ is $0.40$, then the regression coefficient of $x$ on $y$ will be

• A. $1.6$
• B. $6.4$
• C. $5.1$
• D. $3.2$

Answer 1

The correct option is A

$1.6$

Apply the property of the product of the regression coefficient.

Let $b_{xy}$ $=$ Regression coefficient of $x$ on $y$.

$b_{yx}$ $=$ Regression coefficient of $y$ on $x$.

Then $b_{xy}$ . $b_{yx}$ $\le 1$ (Property of product of regression coefficient)

$b_{yx}$ $=$ $0.40$ (Given)

Put $b_{yx}$ $=$ $0.40$ in the above equation.

$$\begin{gathered} b_{xy}.0.40\le 1 \\ Dividebothsidesby0.40 \\ \frac{b_{xy}.0.40}{0.40}\le \frac{1}{0.40} \\ {b}_{xy}\le \frac{1}{0.40} \\ {b}_{xy}\le \frac{10}{4} \\ {b}_{xy}\le \frac{5}{2} \\ {b}_{xy}\le 2.5 \end{gathered}$$

Therefore, option (1) $b_{xy}$ = $1.6$ is the correct option.