When the value of the correlation coefficient (r) is equal to 0.5, what does this mean for the relationship between two variables?
A. Weak negative relationship
B. Perfect positive relationship
C. No relationship
D. Fairly strong positive relationship
Answer (1)
When the value of the correlation coefficient r is equal to 0.5, it indicates a fairly weak to moderate positive relationship between two variables. The correlation coefficient r is a statistical measure that describes the strength and direction of a linear relationship between two variables.
Here are some important points to understand:
The correlation coefficient r ranges from -1 to 1.
r = 1 : This represents a perfect positive linear relationship, where all data points lie exactly on a line with positive slope.
r = − 1 : This represents a perfect negative linear relationship, where all data points lie exactly on a line with negative slope.
r = 0 : This indicates no linear relationship between the variables.
Since r = 0.5 is a positive value, it implies that as one variable increases, the other variable tends to increase as well, but the relationship is not strong.
Correct Answer: (D) Fairly strong positive relationship - In this context, it's indicating a moderate positive relationship, as a correlation of 0.5 is considered to reveal a fair level of association, albeit not a strong one.
In summary, a correlation coefficient of 0.5 suggests that there is some degree of positive linear relationship between the two variables, but it is not very strong.
