Twenty different statistics students are randomly selected. For each of​ them, their body temperature ​(degrees​C) is measured and their head circumference​ (cm) is measured. If it is found that requals​0, does that indicate that there is no association betwen these two​ variables?
Question content area bottom
Part 1
Choose the correct answer below.
A.
​Yes, because if requals​0, the variables are completely unrelated.
B.
​No, because r does not measure the strength of the​ relationship, only its direction.
C.
​No, because if requals​0, the variables are in a perfect linear relationship.
D.
​No, because while there is no linear​ correlation, there may be a relationship that is not linear.

The correct answer is:

**D. No, because while there is no linear correlation, there may be a relationship that is not linear.**

### Explanation:
The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. If \( r = 0 \), it indicates that there is no linear relationship between the variables. However, this does not mean there is no association at all; it simply means that the association is not linear. There could still be a nonlinear relationship between the two variables.

Would you like more details or have any questions?

Here are 8 related questions to consider:
1. What are some examples of nonlinear relationships between variables?
2. How is the correlation coefficient \( r \) calculated?
3. What does a correlation coefficient \( r \) of +1 or -1 indicate?
4. How can we detect nonlinear relationships between two variables?
5. What is the difference between correlation and causation?
6. How do you interpret a correlation coefficient that is close to 0 but not exactly 0?
7. What statistical tests can be used to determine if a relationship between variables is nonlinear?
8. What are some limitations of using the correlation coefficient \( r \) in data analysis?

**Tip:** When analyzing data, always consider the possibility of nonlinear relationships, especially if the correlation coefficient suggests no linear association.

Explore the concept of correlation coefficient in statistics with a focus on its interpretation when the coefficient equals zero. This problem discusses the presence of linear versus nonlinear relationships between variables, particularly in the context of statistics and data analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation