Which value of r indicates a stronger correlation: r = 0.834 or r = -0.925? Explain your reasoning.
The correct answer and explanation is:
The value of r=−0.925r = -0.925 indicates a stronger correlation than r=0.834r = 0.834.
The correlation coefficient, rr, measures the strength and direction of the linear relationship between two variables. The value of rr ranges from -1 to 1. A correlation of r=1r = 1 means a perfect positive linear relationship, while r=−1r = -1 indicates a perfect negative linear relationship. A correlation of r=0r = 0 means no linear relationship.
In this case, both r=0.834r = 0.834 and r=−0.925r = -0.925 represent strong correlations, but the strength of a correlation depends on how close the absolute value of rr is to 1. The further away the value of rr is from 0, the stronger the correlation.
The value r=−0.925r = -0.925 is closer to -1 than r=0.834r = 0.834 is to 1. Therefore, r=−0.925r = -0.925 represents a stronger correlation, even though it is negative. The negative sign simply indicates that the relationship is inversely proportional, meaning as one variable increases, the other decreases. On the other hand, r=0.834r = 0.834 indicates a positive relationship, where both variables increase or decrease together.
In terms of the magnitude, −0.925-0.925 is closer to the extreme value of -1 than 0.8340.834 is to 1. Thus, the correlation represented by r=−0.925r = -0.925 is stronger because it indicates a more consistent, near-perfect relationship between the variables, even though the direction is negative.