What is the correlation coefficient when there is a perfect correlation between two variables?

• A. -1
• B. 1
• C. 0
• D. 0.5

Answer: (B)

The idea being tested is how the correlation coefficient represents a perfect linear relationship between two variables. The correlation coefficient r ranges from -1 to 1. A value of 1 means a perfect positive linear relationship: as one variable increases, the other increases in exact proportion, with all data points lying on a straight line of positive slope. A perfect negative relationship would give -1, where one variable increases as the other decreases. Zero indicates no linear relationship, and values in between show a strong but not perfect linear association. So, for a perfect correlation in the positive direction, the value is 1.