What does a correlation coefficient of -1 signify?

A correlation coefficient of -1 signifies a perfect negative correlation between two variables. This means that as one variable increases, the other variable decreases in a perfectly linear relationship. For instance, if one were to plot the data points of these two variables on a graph, they would lie perfectly on a straight line that slopes downwards from left to right.

This type of correlation is important in research as it indicates a strong and consistent relationship in the opposite direction between two measured phenomena. A perfect negative correlation suggests that every increase in one variable corresponds to a specific and equivalent decrease in the other variable, allowing predictions about one variable based on the other to be very precise, provided the relationship continues to hold true.

In contrast, the other options describe different forms of correlation or the lack thereof, such as a perfect positive correlation (where both variables increase together), no correlation (indicating that changes in one variable do not predict changes in the other), and weak positive correlation (where the relationship exists but not strongly or consistently). Each of these scenarios represents different interactions between variables, illustrating the diverse findings that can arise from correlation analysis.