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The problem involves interpreting the correlation coefficient, \( r \), which measures the strength and direction of the linear relationship between two variables, \( X \) and \( Y \). In the provided question, \( r = 0.91 \).

The possible values of the correlation coefficient, \( r \), range from -1 to 1:
- A value of 1 indicates a perfect positive linear relationship.
- A value of -1 indicates a perfect negative linear relationship.
- A value of 0 indicates no linear relationship.
- Values closer to 1 or -1 indicate a stronger linear relationship, while values closer to 0 indicate a weaker relationship.

Since \( r = 0.91 \) is close to 1, this suggests a **strong positive linear association** between the two variables.

Thus, the correct answer is:
- **D. There is a strong positive linear association between the two variables.**

Let me know if you want more details or have any further questions!

Here are 5 related questions to explore further:
1. What does a correlation coefficient of \( r = -0.91 \) imply about two variables?
2. How would you interpret a correlation coefficient of \( r = 0 \)?
3. What are some limitations of using correlation to describe relationships between variables?
4. How is the correlation coefficient calculated from raw data?
5. Can a correlation coefficient suggest causation between two variables?

**Tip:** Always remember that correlation does not imply causation. Even a strong correlation doesn't mean that one variable causes changes in another.

Values of X and Y were recorded for an additional three weeks, and the correlation coefficient, r, for the augmented data set was found to be r = 0.91. Which of the following statements best interprets this result?

Understand how to interpret a correlation coefficient of r = 0.91, indicating a strong positive linear association between two variables X and Y. Learn about key concepts in statistics, including correlation and linear relationships. Suitable for students in Grades 10-12.

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