A correlation coefficient is a single value that summarizes the strength and direction of a linear relationship.

• A. False
• B. Not always
• C. True
• D. Unrelated

Answer: (C)

The key idea here is that the correlation coefficient, specifically Pearson’s r, is a single statistic that captures both the direction and the strength of the linear relationship between two quantitative variables. It is defined to range from -1 to 1. A value close to +1 means a strong positive linear relationship—when one variable rises, the other tends to rise in a proportional way. A value close to -1 means a strong negative linear relationship—one variable rises while the other tends to fall. Values near 0 indicate little or no linear association, meaning the points don’t align along any straight line.

Because it’s a single number, it provides a concise summary of the linear pattern you’d observe in a scatterplot. Remember, this measure specifically reflects linear relationships; it may miss non-linear patterns, and it can be influenced by outliers. It also doesn’t imply causation, only association.