Define Pearson correlation coefficient r and its range.

Define Pearson correlation coefficient r and its range.

• A. Measure of the linear association between two continuous variables; r ranges from -1 to 1.
• B. Measures the strength of a nonlinear relationship.
• C. Measures the central tendency for two variables.
• D. The slope of the regression line.

Answer: (A)

Pearson's r measures how strongly and in what direction two continuous variables are related in a linear fashion. It standardizes their covariance, so the value falls between -1 and 1. A value near 1 indicates a strong positive linear relationship, near -1 indicates a strong negative linear relationship, and around 0 suggests little to no linear association. It captures linear association but not nonlinear patterns, and it isn’t a measure of central tendency nor simply the slope of the regression line (although the slope relates to r in the regression equation). This is why the option describing a measure of linear association with a range from -1 to 1 is the best match.

Pearson's r measures how strongly and in what direction two continuous variables are related in a linear fashion. It standardizes their covariance, so the value falls between -1 and 1. A value near 1 indicates a strong positive linear relationship, near -1 indicates a strong negative linear relationship, and around 0 suggests little to no linear association. It captures linear association but not nonlinear patterns, and it isn’t a measure of central tendency nor simply the slope of the regression line (although the slope relates to r in the regression equation). This is why the option describing a measure of linear association with a range from -1 to 1 is the best match.