Question

The population correlation coefficient between 2 variables, X and Y, is to 0. What is true about this?

A) There is a perfect positive correlation
B) There is a perfect negative correlation
C) There is no correlation
D) There is a moderate positive correlation

Answer 1

The correct answer is C) There is no correlation, as a population correlation coefficient of 0 indicates that there is no linear relationship between the two variables X and Y.

Step-by-step explanation:

If the population correlation coefficient between two variables, X and Y, is 0, it means there is no correlation between them. This is choice C) There is no correlation. The correlation coefficient, often represented as 'r', ranges from -1 to +1 and measures the strength and direction of the linear relationship between two variables. A coefficient of 0 indicates that the variables do not have a relationship where one variable's increase or decrease is associated with a change in the other variable. A perfect positive correlation would have a coefficient of +1, and a perfect negative correlation would have a coefficient of -1. Therefore, the correct answer to the given question is C) There is no correlation.