Which value of correlation coefficient r indicates a stronger correlation? Group of answer choices
-0.30 0.0
-0.55
0.38
The correct answer and explanation is:
The correct answer is -0.55.
The correlation coefficient, denoted by rr, measures the strength and direction of the linear relationship between two variables. The value of rr ranges from -1 to 1. The sign of rr indicates the direction of the relationship: a positive value indicates a positive correlation, while a negative value indicates a negative correlation. The magnitude (absolute value) of rr indicates the strength of the correlation, with values closer to 1 or -1 indicating stronger correlations and values closer to 0 indicating weaker correlations.
In this case, r=−0.55r = -0.55 represents a moderate negative correlation. The negative sign indicates that as one variable increases, the other tends to decrease, but the relationship is not perfectly linear. The magnitude, 0.55, is higher than the other options provided, which means it represents a stronger correlation.
Let’s compare all the values:
- r=−0.30r = -0.30: This is a weak negative correlation.
- r=0.0r = 0.0: This represents no correlation at all, meaning there is no linear relationship between the two variables.
- r=−0.55r = -0.55: This is a moderate negative correlation, stronger than -0.30.
- r=0.38r = 0.38: This is a weak positive correlation, weaker than -0.55.
Therefore, the strongest correlation among these choices is -0.55, as it has the highest magnitude, indicating a moderately strong negative linear relationship between the two variables.