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

Question

If the correlation coefficient is zero, then the angle (in radians) between the two lines of regression is: (A)  (π /2)  (B)  0  (C)  (π /3)  (D)  (π /4)

Tardigrade Admin · Accepted Answer

Since, tan θ =( (1-r2/r) )=(σ xσ y/σ x2+σ y2) Now, if r=0, then tan θ =∞ ⇒ θ =(π /2)

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

$\frac{π}{2}$

$0$

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{6}$

Since, $tan θ = (\frac{1 - r ^{2}}{r}) = \frac{σ _{x} σ _{y}}{σ _{x}^{2} + σ _{y}^{2}}$ Now, if $r = 0,$ then $tan θ = \infty$ $\Rightarrow θ = \frac{π}{2}$