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 correlation coefficient, \( r = 0.91 \), is very close to 1, indicating a **strong positive linear association** between the two variables \( X \) and \( Y \). A correlation coefficient of 1 would represent a perfect positive linear relationship, while 0 would indicate no linear relationship, and -1 would represent a perfect negative linear relationship.

Since \( r \) is positive and close to 1, the correct interpretation is:

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

Would you like further details or clarifications on this? Here are 5 related questions you could explore:

1. How is the correlation coefficient \( r \) calculated?
2. What does a negative correlation coefficient mean in practical terms?
3. How can outliers affect the value of \( r \)?
4. What is the difference between correlation and causation?
5. What is the interpretation of an \( r \) value close to 0?

**Tip:** Always check the sign and magnitude of the correlation coefficient. Positive values indicate a direct relationship, while negative values indicate an inverse one.

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.

Explore the interpretation of a correlation coefficient of r = 0.91, indicating a strong positive linear relationship between two variables X and Y. Learn about key concepts in statistics, such as correlation and its formula, along with practical examples. Suitable for high school students in Grades 10-12.

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