Question

Consider the following statements:
(1) If the correlation coefficient $r_{xy}=0$, then the two lines of regression are parallel to each other.
(2) If the correlation coefficient $r_{xy}=+1$, then the two lines of regression are perpendicular to each other?
Which of the above statements is/are correct?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is D Neither 1 nor 2

If $r=0⟹$ lines do not have anything common and hence, lines of regression are perpendicular.

when $r=1⟹$ then the lines superimpose one another and hence, lines of regression are parallel/co-incident. So, both statements are wrong.