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Chapter 5: Problem 2

Is the following statement correct? Explain why or why not. A correlation coefficient of 0 implies that no relationship exists between the two variables under study.

Short Answer

Expert verified
The statement is incorrect. A correlation coefficient of 0 means that there is no linear relationship between the variables. However, a non-linear relationship could still exist.

Step by step solution

01

Understanding the Correlation Coefficient

Recall that the correlation coefficient, usually denoted as r, measures the strength and direction of a linear relationship between two variables. It can range from -1 (perfect negative correlation) to 1 (perfect positive correlation). A correlation coefficient of 0 suggests no linear relationship.
02

Clarifying the Misconception

While a correlation of 0 does mean there is no linear relationship, it's critical to understand that this doesn't necessarily mean there's no relationship at all. It could be, for example, that there's a non-linear relationship between the two variables. A correlation of 0 simply means that you can't use a line of best fit to predict one variable's behavior based on the other.
03

Applying Knowledge

Thus, the statement given in the problem is not entirely accurate. It correctly states that a correlation coefficient of 0 suggests no linear relationship, but it incorrectly assumes this necessarily implies no relationship exists at all.

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