Final answer:
The Spearman coefficient of rank correlation is used when two quantitative variables have a monotonic relationship, regardless of whether the relationship is linear or not.
Step-by-step explanation:
The Spearman coefficient of rank correlation is commonly used in regression analysis to assess the relationship between two quantitative variables when the variables have a monotonic relationship. Unlike Pearson's correlation coefficient, which measures the strength of a linear association and requires the data to be normally distributed, the Spearman's rank correlation is used when the relationship between the variables is not necessarily linear but monotonic, which means that the variables tend to move in the same direction at a consistent rate but not necessarily at a constant rate.
The sign of the Spearman correlation coefficient indicates the direction of the association, similar to Pearson's coefficient. A positive value indicates that as one variable increases, the other tends to increase as well, whereas a negative value suggests that as one variable increases, the other tends to decrease.