Which statistic measures the strength and direction of a relationship between two variables?

Which statistic measures the strength and direction of a relationship between two variables?

• A. Correlation
• B. Regression
• C. Causation
• D. Covariance

Answer: (A)

The key idea here is how to quantify both the direction and the strength of how two quantitative variables relate to each other. The correlation is the statistic that does this with a single number. Its sign shows the direction: a positive correlation means the variables tend to rise together, while a negative correlation means one tends to rise when the other falls. The magnitude, ranging from -1 to 1, tells how strong that linear relationship is—the closer to ±1, the stronger the relationship, and the closer to 0, the weaker. Correlation is unitless because it standardizes the covariance by the variables’ standard deviations, so it’s comparable across different measures. Covariance also indicates direction but its size depends on the units and scales of the variables, making it harder to interpret universally. Regression describes how one variable changes with the other and yields a slope, but that depends on which variable you designate as the predictor and is not a symmetric measure of association. Causation relates to cause-and-effect, not to the strength or direction of an association. So the statistic that best captures both how strong the relationship is and which way it tends to go is correlation.

The key idea here is how to quantify both the direction and the strength of how two quantitative variables relate to each other. The correlation is the statistic that does this with a single number. Its sign shows the direction: a positive correlation means the variables tend to rise together, while a negative correlation means one tends to rise when the other falls. The magnitude, ranging from -1 to 1, tells how strong that linear relationship is—the closer to ±1, the stronger the relationship, and the closer to 0, the weaker.

Correlation is unitless because it standardizes the covariance by the variables’ standard deviations, so it’s comparable across different measures. Covariance also indicates direction but its size depends on the units and scales of the variables, making it harder to interpret universally. Regression describes how one variable changes with the other and yields a slope, but that depends on which variable you designate as the predictor and is not a symmetric measure of association. Causation relates to cause-and-effect, not to the strength or direction of an association.

So the statistic that best captures both how strong the relationship is and which way it tends to go is correlation.