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  4. If the correlation coefficient is zero, then the angle (in radians) between the two lines of regression is:

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Q. If the correlation coefficient is zero, then the angle (in radians) between the two lines of regression is:

KEAMKEAM 2000

Solution:

Since, $ \tan \theta =\left( \frac{1-{{r}^{2}}}{r} \right)=\frac{{{\sigma }_{x}}{{\sigma }_{y}}}{\sigma _{x}^{2}+\sigma _{y}^{2}} $ Now, if $ r=0, $ then $ \tan \theta =\infty $ $ \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\theta =\frac{\pi }{2} $