Which of the following correlation coefficients ($r$) represents the weakest linear correlation?

• A. $r=-0.80$
• B. $r=0.62$
• C. $r=0.05$
• D. $r=-0.45$

Answer: (C)

Verified step by step guidance

1. Recall that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables, ranging from \(-1\) to \$1$.
2. Understand that the strength of the correlation is determined by the absolute value of \(r\), where values close to \$1\( or \)-1\( indicate a strong linear relationship, and values close to \)0$ indicate a weak linear relationship.
3. Calculate the absolute values of the given correlation coefficients: \(| -0.80 | = 0.80\), \(| 0.62 | = 0.62\), \(| 0.05 | = 0.05\), and \(| -0.45 | = 0.45\).
4. Compare these absolute values to identify 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.