What is the Pearson correlation coefficient for a perfect positive linear relationship?

What is the Pearson correlation coefficient for a perfect positive linear relationship?

• A. -1
• B. 0.5
• C. 1
• D. 0

Answer: (C)

The Pearson correlation coefficient gauges how straight and in-sync two variables move with each other. For a perfect positive linear relationship, every data point lies exactly on a line that slopes upward, so the degree of association is as strong as it can be. In this situation, the correlation takes its maximum positive value, indicating a perfect alignment where increases in one variable perfectly correspond to proportional increases in the other. The other scenarios—an exact opposite line, no linear pattern, or a positive pattern with some scatter—all yield weaker or opposite signs of correlation. So the statement describing a perfect positive linear relationship is the correct one.

The Pearson correlation coefficient gauges how straight and in-sync two variables move with each other. For a perfect positive linear relationship, every data point lies exactly on a line that slopes upward, so the degree of association is as strong as it can be. In this situation, the correlation takes its maximum positive value, indicating a perfect alignment where increases in one variable perfectly correspond to proportional increases in the other. The other scenarios—an exact opposite line, no linear pattern, or a positive pattern with some scatter—all yield weaker or opposite signs of correlation. So the statement describing a perfect positive linear relationship is the correct one.