Question

In her dissertation research, a graduate student finds a correlation of +0.95 between two of the variables being studied. How should she interpret this correlation coefficient?​

a. ​The variables have a moderate, positive relationship.
b. ​The variables have a moderate, negative relationship.
c. ​The variables have a strong, positive relationship.
d. ​The variables have a strong, negative relationship.

Answer 1

A correlation coefficient of +0.95 indicates a strong, positive relationship between two variables, meaning they tend to move in the same direction; as one increases, so does the other. Option c: The variables have a strong, positive relationship is the correct interpretation of this coefficient.

Step-by-step explanation:

The correlation coefficient, often denoted by r, is a statistical measure that calculates the strength of the relationship between the paired values in two datasets. When discussing the interpretation of a correlation coefficient, the value of +0.95 indicates a very strong, positive linear relationship between two variables. This is because the number 0.95 is very close to +1, which is the maximum positive value r can take, signifying that as one variable increases, the other variable tends to also increase, and vice versa.

The correct interpretation of the correlation coefficient of +0.95 is that the variables have a strong, positive relationship. Therefore, the answer to the student's question would be option c: The variables have a strong, positive relationship. It's important to note that correlation does not imply causation; the high correlation merely indicates that the variables move together, not that one variable causes the change in the other.