Monotonic relationships

What is a monotonic relationship?
A monotonic relationship between two variables is a relationship where:
  • as one variable goes up, the other variable also goes up, or
  • as one variable goes up, the other variable goes down
Figures A and B below show examples of monotonic relationships. In both figures, as the variable $x$ increases, the variable $y$ also increases. Figure C shows an example of a non-monotonic relationship. In this figure, as the variable $x$ increases, the variable $y$ first increases but then decreases, which makes the relationship non-monotonic.

Monotonic and linear relationship
Monotonic relationship
Non-monotonic relationship