Correlated variables can have zero correlation coeffficient. True or False?

TRUE
nan
nan
nan

The correct answer is: False.

A correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is a number between -1 and 1, inclusive. A correlation coefficient of 0 indicates that there is no linear relationship between the two variables.

For example, let’s say we have two variables: height and weight. We would expect to see a positive correlation between these two variables, meaning that taller people tend to weigh more. However, there is no guarantee that this will always be the case. There are many tall people who weigh very little, and there are many short people who weigh a lot. This is because there are many other factors that affect weight, such as diet and exercise.

In this case, the correlation coefficient between height and weight would be close to 0. This would indicate that there is no linear relationship between the two variables.

In conclusion, correlated variables can have a correlation coefficient of 0. However, this does not mean that there is no relationship between the two variables. It simply means that there is no linear relationship between them.