Textbook Question
Put the following correlation coefficients in order from weakest to strongest in terms of strength of linear association.
−1, 0.377, 0.084, −0.436, 0.444, −0.733
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11. Correlation
Correlation Coefficient
Multiple Choice
Which of the following -values represents the weakest correlation between two variables?
A
B
C
D
Verified step by step guidance1
Recall that the correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables. Its value ranges from \(-1\) to \$1$.
Understand that the strength of the correlation is determined by the absolute value of \(r\), regardless of its sign. That means \(r = 0.54\) and \(r = -0.54\) have the same strength but opposite directions.
Compare the absolute values of the given \(r\)-values: \(|0.54| = 0.54\), \(|0.11| = 0.11\), \(|-0.75| = 0.75\), and \(|-0.27| = 0.27\).
Identify the smallest absolute value among these, since the smallest absolute value corresponds to the weakest correlation.
Conclude that the \(r\)-value with the smallest absolute value represents the weakest correlation between the two variables.
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