The Pearson correlation coefficient can take values in which range?

The Pearson correlation coefficient can take values in which range?

• A. -1 to +1
• B. 0 to +1
• C. -∞ to +∞
• D. -1 to 0

Answer: (A)

It measures the strength and direction of a linear relationship between two continuous variables, and its value always falls between -1 and 1. A value near +1 indicates a strong positive linear relationship—both variables tend to move upward together. A value near -1 indicates a strong negative linear relationship—one variable tends to increase while the other decreases. A value near 0 suggests little to no linear association. The bounds come from how the statistic is calculated: it standardizes the covariance by the product of the variables’ standard deviations, and the Cauchy–Schwarz inequality shows this ratio cannot exceed 1 in absolute value. So the theoretical range is -1 to 1, inclusive, which is why that option is correct.

It measures the strength and direction of a linear relationship between two continuous variables, and its value always falls between -1 and 1. A value near +1 indicates a strong positive linear relationship—both variables tend to move upward together. A value near -1 indicates a strong negative linear relationship—one variable tends to increase while the other decreases. A value near 0 suggests little to no linear association. The bounds come from how the statistic is calculated: it standardizes the covariance by the product of the variables’ standard deviations, and the Cauchy–Schwarz inequality shows this ratio cannot exceed 1 in absolute value. So the theoretical range is -1 to 1, inclusive, which is why that option is correct.