What is the general truth about correlation coefficients?

• A. They range from -1 to 1.
• B. They are always positive.
• C. They cannot be negative.
• D. They measure causation.

Answer: (A)

Correlation coefficients describe the direction and strength of a linear relationship and are restricted to values between -1 and 1, inclusive. A value of 1 means a perfect positive linear relationship, -1 means a perfect negative linear relationship, and 0 means no linear relationship. This bound arises because the coefficient is computed by normalizing the covariance with the product of the variables’ standard deviations, so the ratio cannot exceed ±1. It’s important to remember that correlation measures association, not causation, and it reflects linear ties; non-linear patterns can exist with little or no correlation, and outliers can skew the value.