Arizona State University (ASU) ECN221 Business Statistics Exam 2 Practice

A correlation coefficient of -1 indicates a perfect negative linear relationship between two variables. This means that as one variable increases, the other variable decreases in a perfectly linear manner. In practical terms, every change in one variable corresponds to a precise and consistent change in the opposite direction of the other variable. For example, if we were to graph these two variables on a scatterplot, the points would fall exactly along a straight line with a negative slope.

This characteristic distinguishes it from a perfect positive linear relationship, which is indicated by a correlation of +1, where both variables increase together consistently. The concept of no relationship suggests a correlation of 0, where variables do not influence each other, and a weak negative relationship would typically be represented by a value closer to 0 but still negative, indicating some degree of inverse association without being strong or perfect. Thus, the choice of a perfect negative linear relationship accurately reflects the nature of a correlation coefficient of -1.