Question

The Angle Between Two Regression Lines is $90°$. Then $\mathrm{R}=0$, Where $\mathrm{R}$, is the Correlation Coefficient. (True / False).

• A. True
• B. False

Answer 1

The correct option is A True

The angle between regression lines.

The two regression lines will have an angle of $${90}^{\circ }$$, when there is zero coefficient of correlation.

The angle formed by the regression line is $\tan \theta =\frac{1-{\mathrm{R}}^2}{\mathrm{R}}\frac{{\sigma }_x{\sigma }_y}{{\left({\sigma }_x\right)}^2+{\left({\sigma }_y\right)}^2}$.

Substitute $\mathrm{R}=0$ in the above expression:

$$\begin{gathered} \tan \theta =\frac{1-{\mathrm{R}}^2}{\mathrm{R}}\frac{{\sigma }_x{\sigma }_y}{{\left({\sigma }_x\right)}^2+{\left({\sigma }_y\right)}^2} \\ \Rightarrow \tan \theta =\frac{1-0^2}{0}\frac{{\sigma }_x{\sigma }_y}{{\left({\sigma }_x\right)}^2+{\left({\sigma }_y\right)}^2} \\ \Rightarrow \tan \theta =\infty \\ \Rightarrow \theta ={\tan }^{-1}(\infty ) \\ \Rightarrow \theta =90° \end{gathered}$$

When $\mathrm{R}=0$ , the angle between two regression lines is $90°$.

Hence, the given statement is true.