In a scatterplot, which of the following Pearson correlation coefficients represents the weakest linear correlation?

• A. $r=0.10$
• B. $r=-0.60$
• C. $r=0.95$
• D. $r=-0.80$

Answer: (A)

Verified step by step guidance

1. Recall that the Pearson correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables. Its values range from \(-1\) to \$1$.
2. Understand that the strength of the linear correlation is determined by the absolute value of \(r\), not the sign. Values closer to \$1\( or \)-1\( indicate a stronger linear relationship, while values closer to \)0$ indicate a weaker linear relationship.
3. Look at the given correlation coefficients: \(r = 0.10\), \(r = -0.60\), \(r = 0.95\), and \(r = -0.80\). Calculate the absolute values: \(|0.10| = 0.10\), \(|-0.60| = 0.60\), \(|0.95| = 0.95\), and \(|-0.80| = 0.80\).
4. Compare these absolute values to determine which is the smallest, as the smallest absolute value corresponds to the weakest linear correlation.
5. Conclude that the correlation coefficient with the smallest absolute value represents the weakest linear correlation in the scatterplot.