Correlation coefficients can measure which of the following?

Correlation coefficients are statistical measures that describe the strength and direction of a relationship between two variables. The coefficient values range from -1 to +1. A positive correlation coefficient indicates a positive relationship, meaning that as one variable increases, the other variable also tends to increase. Conversely, a negative correlation coefficient signifies an inverse relationship; as one variable increases, the other variable tends to decrease.

The choice that encompasses both positive and inverse relationships highlights the fundamental ability of correlation coefficients to capture the strength and direction of linear associations between two variables.

While correlation coefficients effectively measure these linear relationships, they do not adequately represent curvilinear relationships, where the connection between the variables does not follow a straight line but rather involves more complex dynamics. As a result, the inclusion of curvilinear relationships in the options would not align with the capabilities of correlation coefficients.

Thus, the correct choice signifies that correlation coefficients can indeed quantify both positive and inverse relationships, capturing their linear nature, while distinguishing them from non-linear relationships that cannot be effectively measured by this statistical tool.