If the correlation coefficient is zero, then the angle between the two lines of regression is:

Question

Question

This question was previously asked in

SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)

Answer 1

The correct answer is π/2

Key Points

If the correlation coefficient between two variables is zero, then the angle between the two lines of regression is π/2 (90 degrees).
The lines of regression represent the best-fit lines that minimize the vertical distances between the data points and the line. In simple linear regression, there are two lines of regression: one representing the regression of Y on X and the other representing the regression of X on Y.
When the correlation coefficient is zero, it indicates that there is no linear relationship between the variables. In other words, the variables are not linearly associated.
Consequently, the lines of regression will be perpendicular to each other, resulting in an angle of π/2 (90 degrees) between them.
This relationship holds because a zero correlation implies that the variables have no linear dependence, leading to lines of regression that are perpendicular to each other.

Hence, if the correlation coefficient between two variables is zero, then the angle between the two lines of regression is π/2 (90 degrees).