The question asks which scatterplot represents a data set with a correlation coefficient of $r = -1$.

A correlation coefficient of $r = -1$ signifies a perfect negative linear relationship, meaning the data points lie exactly on a downward-sloping straight line. In such a case, as one variable increases, the other decreases proportionally.

Looking at the options:

• Option A: This scatterplot shows a clear downward-sloping linear pattern, which suggests a perfect negative correlation.
• Option B: The points do not follow a straight line; they fluctuate, showing no consistent negative trend.
• Option C: The points show a positive linear trend, indicating a positive correlation.
• Option D: This scatterplot has no visible pattern, with data points scattered randomly.
• Option E: This scatterplot shows no variation in the vertical direction, indicating no correlation.

Therefore, the correct answer is Option A, as it shows a perfect negative linear relationship consistent with $r = -1$.

Would you like further details or have any questions?

Here are five related questions you might explore:

1. What is the range of values for the correlation coefficient $r$?
2. How does a correlation coefficient of $r = 0$ appear on a scatterplot?
3. Can a scatterplot with a correlation of $r = 1$ contain outliers?
4. What does the slope of a regression line represent in a scatterplot?
5. How does the strength of correlation affect predictions from a scatterplot?

Tip: A correlation coefficient close to -1 or 1 indicates a strong linear relationship, while values near 0 suggest a weak or no linear relationship.