What does the Pearson correlation coefficient measure?

What does the Pearson correlation coefficient measure?

• A. Represents the variance of each variable.
• B. Measures the degree and direction of the linear relationship between two variables.
• C. Measures the nonlinear association only.
• D. Indicates causation between variables.

Answer: (B)

The Pearson correlation coefficient measures the degree and direction of the linear relationship between two variables. It standardizes how much the variables vary together and scales that by their individual variability, producing a value between -1 and 1. A positive value means the variables tend to move in the same direction, a negative value means they move in opposite directions, and the magnitude tells how tightly the data fit a straight line. It’s best for detecting linear patterns; a strong nonlinear relationship can have a small or even zero value, so the statistic doesn’t capture curved associations well. It also doesn’t imply causation—two variables can be correlated without one causing the other. Additionally, it’s sensitive to outliers and is invariant to linear transformations, focusing specifically on linear relationship structure rather than variance in each variable on its own.

The Pearson correlation coefficient measures the degree and direction of the linear relationship between two variables. It standardizes how much the variables vary together and scales that by their individual variability, producing a value between -1 and 1. A positive value means the variables tend to move in the same direction, a negative value means they move in opposite directions, and the magnitude tells how tightly the data fit a straight line. It’s best for detecting linear patterns; a strong nonlinear relationship can have a small or even zero value, so the statistic doesn’t capture curved associations well. It also doesn’t imply causation—two variables can be correlated without one causing the other. Additionally, it’s sensitive to outliers and is invariant to linear transformations, focusing specifically on linear relationship structure rather than variance in each variable on its own.