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?A.There is a weak positive linear association between the two variables.B.There is a weak negative linear association between the two variables.C.There is a strong negative linear association between the two variables.D.There is a strong positive linear association between the two variables.

The correct answer is **D. There is a strong positive linear association between the two variables.**

This is because the correlation coefficient, \( r = 0.91 \), is close to 1, indicating a strong linear relationship. Since the value is positive, it represents a **positive** linear association.

### Explanation:
- The correlation coefficient \( r \) ranges from -1 to 1.
  - \( r = 1 \) indicates a perfect positive linear relationship.
  - \( r = -1 \) indicates a perfect negative linear relationship.
  - Values close to 0 indicate a weak or no linear relationship.
  - Values closer to 1 or -1 indicate stronger linear associations.

In this case, since \( r = 0.91 \), it's both strong (close to 1) and positive.

Would you like more details or have any other questions?

### Related questions:
1. What does a correlation coefficient of \( r = -0.8 \) indicate about two variables?
2. Can two variables with a correlation of \( r = 0 \) still be related in a non-linear way?
3. How does adding outliers affect the value of the correlation coefficient?
4. What are the limitations of using the correlation coefficient to interpret data relationships?
5. How does correlation differ from causation in data analysis?

### Tip:
The closer \( r \) is to 1 or -1, the stronger the linear relationship between two variables. Positive values mean as one variable increases, the other tends to increase too.

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? A. There is a weak positive linear association between the two variables. B. There is a weak negative linear association between the two variables. C. There is a strong negative linear association between the two variables. D. There is a strong positive linear association between the two variables.

Learn how to interpret a correlation coefficient of r = 0.91, which indicates a strong positive linear association between two variables. This problem is suitable for students in Grades 10-12 and covers key statistical concepts, including the interpretation of correlation and linear relationships.

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