Which statement about the correlation coefficient is true?

Which statement about the correlation coefficient is true?

• A. It is bounded between -1 and +1 and reflects a linear relationship
• B. It can exceed 1 in magnitude
• C. It can be greater than 1 in magnitude
• D. It measures nonlinear relationships only

Answer: (A)

The correlation coefficient measures the strength and direction of a linear relationship between two variables. Its value is always between -1 and +1. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and values in between show the strength of that linear association. If the data lie exactly on a straight line, you get ±1; if they follow a curved pattern, the magnitude is less than 1 even if there’s a clear relationship. It cannot exceed 1 in magnitude, and it does not specifically capture nonlinear relationships—strong nonlinear patterns can yield a small correlation even though there’s a strong association.

The correlation coefficient measures the strength and direction of a linear relationship between two variables. Its value is always between -1 and +1. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and values in between show the strength of that linear association. If the data lie exactly on a straight line, you get ±1; if they follow a curved pattern, the magnitude is less than 1 even if there’s a clear relationship. It cannot exceed 1 in magnitude, and it does not specifically capture nonlinear relationships—strong nonlinear patterns can yield a small correlation even though there’s a strong association.