Indicator variable for male

Indicator variable for respondents at least 35 years old

:
(men make about 14% more than women, on average)

:
(people at least 35 years old make about 81% more than those under 35, on average)

Interaction between both indicators

Z is a causal factor on both X and Y.

Must be “controlled for” to establish non-spurious relationship between X and Y.

E.g.:
Race confounds the relationship between education and income.

Z is influenced by X and influences Y.

Including as covariate elaborates on relationship between X and Y.

E.g.:
Occupation mediates the relationship between gender and income.

Z alters the relationship between X and Y.

Can be included as interaction variable to better describe the relationship between X and Y.

E.g.:
Marital status moderates the relationship between gender and income.

Z causally influenced by both X and Y.

Must not be “controlled for” when establishing relationship between X and Y.

E.g.:
Income is a collider for the relationship between gender and occupation.