Pearson's correlation coefficient, r, is a measure of the linear relationship between two variables X and Y, with r ranging from:

Pearson's correlation coefficient, r, is a measure of the linear relationship between two variables X and Y, with r ranging from:

• A. -1 to 1
• B. 0 to 1
• C. -2 to 2
• D. 0 to 0

Answer: (C)

Pearson's r measures the strength and direction of a linear relationship between two variables. It can take values only between -1 and 1: -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. This bound comes from the way r is computed as a standardized covariance, so its magnitude cannot exceed 1. Therefore, the correct range is -1 to 1, not -2 to 2. The other ranges fail because they either omit the possibility of a negative relationship or propose impossible bounds for this measure.

Pearson's r measures the strength and direction of a linear relationship between two variables. It can take values only between -1 and 1: -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. This bound comes from the way r is computed as a standardized covariance, so its magnitude cannot exceed 1. Therefore, the correct range is -1 to 1, not -2 to 2. The other ranges fail because they either omit the possibility of a negative relationship or propose impossible bounds for this measure.