Which of the following scatterplots best represents a dataset with a correlation coefficient $r$ closest to $1$?

• A. A scatterplot where all points lie exactly on a straight line with positive slope.
• B. A scatterplot where all points lie exactly on a straight line with negative slope.
• C. A scatterplot where the points are widely scattered with no apparent pattern.
• D. A scatterplot where the points form a perfect U-shaped curve.

Answer: (A)

Verified step by step guidance

1. Recall that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables, with values ranging from \(-1\) to \$1$.
2. Understand that \(r = 1\) indicates a perfect positive linear relationship, meaning all points lie exactly on a straight line with a positive slope.
3. Recognize that \(r = -1\) indicates a perfect negative linear relationship, where all points lie exactly on a straight line with a negative slope.
4. Note that if points are widely scattered with no apparent pattern, the correlation coefficient \(r\) is close to \$0$, indicating little to no linear relationship.
5. Observe that a perfect U-shaped curve is a nonlinear pattern, so the correlation coefficient \(r\) will not be close to \$1\( or \)-1\( because \)r$ only measures linear relationships.