Question

The regression lines will be perpendicular to each other if the coefficient of correlation $r$ is equal to.
A. 1 only
B. 1 or $ - 1$
C. $ - 1$ only
D. 0

Answer 1

Hint: If the two regression lines are completely correlated then the correlation coefficient is either -1 or 1. If the regression lines are not related then the correlation coefficient is given as 0.

Complete step-by-step answer:
The correlation coefficient is a measure of degree of association. It is denoted by $r$ and is also called Pearson's correlation coefficient.
Linear association is measured through the correlation coefficient.
The correlation coefficient is measured on a scale that is varied between -1 and 1, where -1 and 1 represents complete correlation.
If the two regression lines coincide, the correlation coefficient will be -1 or 1.
The coefficient will be -1 if one variable increases and the other decreases.
If the two variables are completely out of correlation then the correlation coefficient is 0.
If the two regression lines are perpendicular to each other, there is no correlation between the two regression lines.
Thus the correlation coefficient will be 0
Hence, option D is correct.

Note: The regression line is a straight line that defines the change of a response variable $y$ as the independent variable $x$ changes. It is often used to predict the outcome $y$ on a new observation point $x$.