Monotonic relationships

Definition of a monotonic relationship and some examples

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-D show examples of monotonic relationships. In Figures A and B, the relationships are also linear. In Figures C and D, the relationships are monotonic but not linear. In Figures A and C, the relationships are positive: as the variable $x$ increases, the variable $y$ also increases. In Figures B and D, the relationships are negative: as the variable $x$ increases, the variable $y$ decreases. Figure E shows an example of a non-monotonic relationship. Note how in this figure the direction of the relationship differs across different values for $x$.

Negative monotonic and linear relationship