Multiple Choice
In a correlation analysis, the correlation coefficient indicates the weakest linear relationship between two variables when its value is closest to which number?
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11. Correlation
Correlation Coefficient
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In a bivariate data set, if the correlation coefficient is negative, what does this indicate about the relationship between the two variables?
A
As one variable increases, the other variable tends to decrease (a negative linear association).
B
One variable causes the other variable to decrease.
C
As one variable increases, the other variable tends to increase (a positive linear association).
D
There is no linear relationship between the variables, so .
Verified step by step guidance1
Understand that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables.
Recall that the value of \(r\) ranges from \(-1\) to \$1$, where positive values indicate a positive linear association and negative values indicate a negative linear association.
Recognize that a negative correlation coefficient means that as one variable increases, the other variable tends to decrease, showing an inverse relationship.
Note that correlation does not imply causation, so a negative \(r\) does not mean one variable causes the other to decrease.
Conclude that a negative \(r\) indicates a negative linear association between the two variables, meaning they move in opposite directions on average.
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