What does a correlation coefficient of -1 indicate?

What does a correlation coefficient of -1 indicate?

• A. No correlation at all
• B. Strong positive correlation
• C. Perfect negative correlation
• D. Weak negative correlation

Answer: (C)

A correlation coefficient of -1 indicates a perfect negative correlation between two variables. This means that as one variable increases, the other variable decreases in a perfectly linear manner. In practical terms, if you were to plot the two variables on a scatter plot, all the data points would lie perfectly on a descending straight line. In the context of statistical analysis, a correlation coefficient ranges from -1 to 1. A value of -1 signifies that there is a completely predictable inverse relationship, where 100% of the variation in one variable can be exactly explained by the movement of the other variable in the opposite direction. This level of correlation is distinct from a positive correlation (which would be indicated by a value close to 1), where both variables move in the same direction. Additionally, values closer to 0 signal little to no linear relationship, which is different from a strong or weak correlation. Thus, the association characterized by a -1 correlation coefficient clearly illustrates the most extreme type of negative relationship in statistics.

A correlation coefficient of -1 indicates a perfect negative correlation between two variables. This means that as one variable increases, the other variable decreases in a perfectly linear manner. In practical terms, if you were to plot the two variables on a scatter plot, all the data points would lie perfectly on a descending straight line.

In the context of statistical analysis, a correlation coefficient ranges from -1 to 1. A value of -1 signifies that there is a completely predictable inverse relationship, where 100% of the variation in one variable can be exactly explained by the movement of the other variable in the opposite direction.

This level of correlation is distinct from a positive correlation (which would be indicated by a value close to 1), where both variables move in the same direction. Additionally, values closer to 0 signal little to no linear relationship, which is different from a strong or weak correlation. Thus, the association characterized by a -1 correlation coefficient clearly illustrates the most extreme type of negative relationship in statistics.