Which statistical measure indicates the strength and direction of a linear relationship between variables?

The strength and direction of a linear relationship between variables is best indicated by correlation. Correlation quantifies how closely two variables move together; it provides a numerical value, known as the correlation coefficient, which ranges from -1 to 1. A coefficient close to 1 suggests a strong positive linear relationship, meaning that as one variable increases, the other tends to increase as well. Conversely, a coefficient close to -1 indicates a strong negative linear relationship, where one variable increases as the other decreases. A correlation coefficient of zero suggests no linear relationship.

While regression analysis also deals with the relationship between variables and can indicate the nature of this relationship, it primarily focuses on predicting the value of one variable based on the other. In contrast, correlation directly measures the linear association without implying any cause-and-effect relationship.

Variance and standard deviation are measures of variability or spread within a set of data, but they do not provide information about the relationship between two different variables. Thus, correlation is the appropriate measure in this context.