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 relationship between the variables \( X \) and \( Y \).

The correct interpretation is:

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

A positive correlation coefficient means that as \( X \) increases, \( Y \) tends to increase as well, and the value of 0.91 suggests this relationship is strong.

Would you like further details on interpreting correlation coefficients or have any other questions?

Here are five related questions to expand your understanding:
1. What does a correlation coefficient of \( r = 0 \) represent?
2. How does a correlation of \( r = -0.9 \) differ from \( r = 0.91 \)?
3. What is the effect of outliers on the value of the correlation coefficient?
4. How can we test the significance of the correlation coefficient?
5. What is the difference between correlation and causation?

**Tip:** A correlation coefficient close to 1 or -1 indicates a strong linear relationship, while a value close to 0 suggests little to no linear relationship.

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. This problem covers statistical concepts such as correlation coefficients and linear relationships, helping students understand the strength and direction of associations between variables. Suitable for Grades 10-12.

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