Which of the following scatterplots best represents a situation where the correlation coefficient $r$ is approximately zero?

• A. A scatterplot where the points are randomly dispersed with no apparent pattern.
• B. A scatterplot where the points form a clear downward trend from left to right.
• C. A scatterplot where the points form a clear upward trend from left to right.
• D. A scatterplot where the points form a perfect straight line.

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables.
2. Recall that when \(r\) is close to zero, it indicates there is little to no linear relationship between the variables.
3. Recognize that a scatterplot with points randomly dispersed without any clear pattern or trend suggests no linear correlation.
4. Contrast this with scatterplots showing clear upward or downward trends, which correspond to positive or negative values of \(r\) respectively.
5. Note that a perfect straight line in a scatterplot corresponds to \(r\) being exactly 1 or -1, indicating a perfect linear relationship.