What does Pearson's correlation coefficient describe?

• A. The probability of Type I error
• B. The difference between two means
• C. The proportion of variance explained by a model
• D. The strength and direction of a linear relationship between two continuous variables

Answer: (D)

Pearson's correlation coefficient describes the strength and direction of a linear relationship between two continuous variables. It ranges from -1 to 1, with values near 1 indicating a strong positive linear association, near -1 a strong negative linear association, and around 0 little or no linear relationship. It’s calculated by standardizing both variables and looking at how they covary. This measure specifically captures linear ties and may miss nonlinear patterns. It does not convey anything about Type I error probability, nor does it measure differences between means. While r^2 (the square of the correlation) relates to the proportion of variance explained in simple regression, the correlation coefficient itself is about the presence and strength of the linear relationship, not the exact variance explained. Also, remember that correlation does not imply causation, and results can be distorted by outliers or restricted data ranges.