Which statistic measures the strength and direction of the linear relationship between two variables, with values ranging from -1 to +1?

Which statistic measures the strength and direction of the linear relationship between two variables, with values ranging from -1 to +1?

• A. Correlation coefficient
• B. Regression slope
• C. R-squared
• D. P-value

Answer: (A)

The statistic that captures both the strength and direction of a linear relationship between two variables, with values ranging from -1 to +1, is the correlation coefficient. It tells you how tightly the points lie around a straight line and whether they move together in the same direction (positive) or in opposite directions (negative). A value near +1 means a strong positive linear relationship—when one variable increases, the other tends to increase proportionally. A value near -1 means a strong negative linear relationship—when one increases, the other tends to decrease. A value near 0 indicates little or no linear relationship. This measure is unitless and standardized, making it easy to compare across different pairs of variables. It’s important to keep in mind that a high correlation doesn’t imply causation, and the figure can be distorted by outliers or by nonlinear relationships. The regression slope, by contrast, depends on the units of measurement and isn’t bounded by -1 to +1. R-squared reflects how much of the variation in one variable is explained by the other, not the direction of the relationship. P-value addresses whether the observed relationship is statistically significant, not how strong or in what direction it is.

The statistic that captures both the strength and direction of a linear relationship between two variables, with values ranging from -1 to +1, is the correlation coefficient. It tells you how tightly the points lie around a straight line and whether they move together in the same direction (positive) or in opposite directions (negative). A value near +1 means a strong positive linear relationship—when one variable increases, the other tends to increase proportionally. A value near -1 means a strong negative linear relationship—when one increases, the other tends to decrease. A value near 0 indicates little or no linear relationship.

This measure is unitless and standardized, making it easy to compare across different pairs of variables. It’s important to keep in mind that a high correlation doesn’t imply causation, and the figure can be distorted by outliers or by nonlinear relationships. The regression slope, by contrast, depends on the units of measurement and isn’t bounded by -1 to +1. R-squared reflects how much of the variation in one variable is explained by the other, not the direction of the relationship. P-value addresses whether the observed relationship is statistically significant, not how strong or in what direction it is.