Multiple Choice
Which of the following values of the correlation coefficient indicates the strongest correlation?
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11. Correlation
Correlation Coefficient
Multiple Choice
Which of the following is true of the correlation coefficient ?
A
A value of close to indicates a strong linear relationship.
B
A negative value of means there is no relationship between the variables.
C
The correlation coefficient can be greater than for some data sets.
D
The value of is always between and , inclusive.
Verified step by step guidance1
Recall that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables.
Understand that the value of \(r\) ranges from \(-1\) to \$1\(, where \)r = 1\( indicates a perfect positive linear relationship, \)r = -1\( indicates a perfect negative linear relationship, and \)r = 0$ indicates no linear relationship.
Recognize that a value of \(r\) close to \$0$ does not indicate a strong linear relationship; rather, it suggests a weak or no linear relationship.
Note that a negative value of \(r\) indicates a negative linear relationship, meaning as one variable increases, the other tends to decrease, not that there is no relationship.
Remember that \(r\) cannot be greater than \$1\( or less than \)-1$ for any data set, as these are the theoretical bounds of the correlation coefficient.
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