What does the Pearson correlation coefficient indicate?

The Pearson correlation coefficient is a statistical measure that captures the strength and direction of a linear relationship between two variables. When the coefficient is calculated, it yields a value ranging from -1 to 1. A value of 1 indicates a perfect positive linear correlation, meaning that as one variable increases, the other also increases proportionally. Conversely, a value of -1 indicates a perfect negative linear correlation, where an increase in one variable corresponds to a proportional decrease in the other. A value of 0 suggests no linear correlation between the variables.

This understanding is crucial in fields such as business and social sciences, where recognizing and interpreting relationships between different variables helps in making informed decisions and predictions based on the data analysis. The Pearson correlation coefficient does not provide probabilities, address dependencies in systems of equations, or indicate variability in datasets, which differentiates it from those other concepts.