The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to

Options

A. 1 only
B. 1 or `-1`
C. `-1` only
D. 0

Answer

D

Explanation

When regression lines perpendicular to each other then angle will be :
`tantheta={((1-r^(2))/(r))((sigma_(x).sigma_(y))/(sigma_(x)^(2)+sigma_(y)^(2)))}`
`rArr tan.(pi)/(2)=((1-r^(2))/(r))((sigma_(x).sigma(9y))/(sigma_(x)^(2)+sigma_(y)^(2)))`
`rArr r.(sigma_(x)^(2)+sigma_(y)^(2))=0`
`therefore r=0`