How is the Pearson correlation coefficient interpreted?

How is the Pearson correlation coefficient interpreted?

• A. r measures the variance of residuals.
• B. r measures the slope of the regression line.
• C. r measures the probability of independence.
• D. r measures the strength and direction of linear association between two continuous variables.

Answer: (D)

Pearson correlation coefficient shows how strong and in what direction two continuous variables relate in a straight-line way. It’s found by dividing the covariance of the variables by the product of their standard deviations, so its value ranges from -1 to 1. A positive value means as one variable goes up, the other tends to go up; a negative value means as one goes up, the other tends to go down. The larger the magnitude (closer to ±1), the tighter the points lie along a straight line, indicating a strong linear relationship; values near 0 suggest little linear association. It’s key to remember that this measures linear association only and does not imply causation, nor does it describe residual spread or the slope by itself (though in simple regression the slope relates to r via b = r × (sy/sx)).

Pearson correlation coefficient shows how strong and in what direction two continuous variables relate in a straight-line way. It’s found by dividing the covariance of the variables by the product of their standard deviations, so its value ranges from -1 to 1. A positive value means as one variable goes up, the other tends to go up; a negative value means as one goes up, the other tends to go down. The larger the magnitude (closer to ±1), the tighter the points lie along a straight line, indicating a strong linear relationship; values near 0 suggest little linear association. It’s key to remember that this measures linear association only and does not imply causation, nor does it describe residual spread or the slope by itself (though in simple regression the slope relates to r via b = r × (sy/sx)).