Which of the following scatterplots best represents a correlation coefficient of $0.7$?

• A. A scatterplot where the points form a moderately tight upward-sloping linear pattern.
• B. A scatterplot where the points are widely scattered with no apparent pattern.
• C. A scatterplot where the points form a perfect straight upward-sloping line.
• D. A scatterplot where the points form a moderately tight downward-sloping linear pattern.

Answer: (A)

Verified step by step guidance

1. Recall that the correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables. It ranges from \(-1\) to \$1$.
2. Understand that a correlation coefficient of \$0.7$ indicates a moderately strong positive linear relationship between the variables.
3. Interpret the value \$0.7$ as meaning the points in the scatterplot should generally trend upward, but not perfectly; there should be some scatter around a line with positive slope.
4. Eliminate options that show no pattern (which would correspond to \(r\) near \$0\(), a perfect line (which corresponds to \)r = 1\( or \)r = -1\(), or a downward trend (which would correspond to a negative \)r$).
5. Conclude that the scatterplot best representing \(r = 0.7\) is the one where points form a moderately tight upward-sloping linear pattern.