Question

If $b_{yx}and{b}_{xy}$ are both positive regression coefficients, then,

• A. $\left(\frac{1}{b_{yx}}\right)+\left(\frac{1}{b_{xy}}\right)<\left(\frac{2}{r}\right)$
• B. $\left(\frac{1}{b_{yx}}\right)+\left(\frac{1}{b_{xy}}\right)>\left(\frac{2}{r}\right)$
• C. $\left(\frac{1}{b_{yx}}\right)+\left(\frac{1}{b_{xy}}\right)<\left(\frac{r}{2}\right)$
• D. $noneofthese$

Answer 1

The correct option is B

$\left(\frac{1}{b_{yx}}\right)+\left(\frac{1}{b_{xy}}\right)>\left(\frac{2}{r}\right)$

Explantion for the correct options:

Finding the value of the given regression coefficients:

$$\begin{gathered} \Rightarrow b_{yx}+b_{yx}>2\sqrt{b_{yx}}.b_{xy} \\ \Rightarrow b_{yx}+b_{xy}>2r \\ \Rightarrow \frac{\left[b_{yx}+b_{xy}\right]}{r^2}>\frac{2}{r} \\ \Rightarrow \frac{\left[b_{yx}+b_{xy}\right]}{\left[b_{yx}.b_{xy}\right]}>\frac{2}{r} \\ \Rightarrow \mathbf{\left(}\frac{\mathbf{1}}{{\mathbf{b}}_{\mathbf{y}\mathbf{x}}}\mathbf{\right)}\mathbf{+}\mathbf{\left(}\frac{\mathbf{1}}{{\mathbf{b}}_{\mathbf{x}\mathbf{y}}}\mathbf{\right)}\mathbf{>}\mathbf{\left(}\frac{\mathbf{2}}{\mathbf{r}}\mathbf{\right)} \end{gathered}$$

Hence option(B) is correct.