Final answer:
The correct statement about the correlation coefficient is (d) all of the above; it ranges from -1 to +1, the sign indicates the direction of the relationship, and the magnitude denotes the strength of the relationship.
Step-by-step explanation:
The correct answer to which of the following is true of the correlation coefficient is (d) all of the above. The correlation coefficient can range from -1 through 0 to +1, its sign tells you about the direction of the relationship between variables, and its magnitude tells you about the strength of the relationship between variables.
To further explain, the correlation coefficient, often represented by the letter r, is a numerical value that ranges from -1 to 1. This range expresses both direction and strength of the linear relationship between two variables. A correlation coefficient close to 1 or -1 signifies a strong relationship, while a coefficient close to 0 signifies a weak relationship. For instance, a correlation coefficient of 0.9 denotes a stronger relationship than a coefficient of 0.3 does.
If the correlation coefficient is positive, there is a positive relationship, meaning both variables move in the same direction. Conversely, if the correlation coefficient is negative, there is a negative relationship, meaning the variables move in opposite directions. Thus, the magnitude indicates the strength of the relationship while the sign indicates its direction.