The image shows a question regarding the interpretation of a correlation coefficient $r = 0.91$ between two variables X and Y. The possible answer choices are:

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.

Explanation:

• The value of the correlation coefficient $r$ ranges from -1 to 1.
  • If $r = 1$, it indicates a perfect positive linear relationship.
  • If $r = -1$, it indicates a perfect negative linear relationship.
  • If $r = 0$, it suggests no linear relationship.
  • Values closer to 1 or -1 indicate a stronger linear relationship, while values near 0 indicate a weaker one.

In this case, $r = 0.91$, which is close to 1, indicating 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.

Do you want more details on correlation interpretation or have any other questions?

Here are five related questions to deepen your understanding:

1. What does a correlation coefficient of 0.5 imply about the relationship between two variables?
2. How does the correlation coefficient differ from the coefficient of determination $R^2$?
3. What are some common methods to calculate the correlation coefficient?
4. How does the correlation coefficient change if the scale of the variables is altered (e.g., converting units)?
5. What are the assumptions required for interpreting the correlation coefficient correctly?

Tip: Remember, correlation only measures linear relationships. A high $r$ value doesn't imply causality, and nonlinear relationships can exist even with low $r$ values.