Which correlation shows the weakest linear relationship?
A 0.14
B 0.64
C 0.37
D -0.69
E 0.23
The correct answer and explanation is:
The correct answer is A) 0.14.
Correlation values range from -1 to +1, where values closer to 1 or -1 indicate a stronger linear relationship, either positive or negative, respectively. On the other hand, values closer to 0 suggest a weaker linear relationship. The strength of the correlation increases as the value moves further away from 0, regardless of whether it is positive or negative.
In this case, the correlation coefficients are as follows:
- 0.14 indicates a very weak positive linear relationship.
- 0.64 represents a moderate positive linear relationship.
- 0.37 suggests a weak to moderate positive linear relationship.
- -0.69 indicates a strong negative linear relationship.
- 0.23 shows a weak positive linear relationship.
The value 0.14 is the smallest absolute value among the options, which means it represents the weakest linear relationship. This suggests that the two variables in question are only weakly associated with each other in a positive direction. A correlation of 0.14 does not provide much predictive power about how one variable changes in response to the other.
To summarize, the correlation coefficient tells us about both the direction (positive or negative) and strength of the linear relationship. The smaller the value, the weaker the relationship, which is why 0.14 shows the weakest relationship in this set of options.