The truth is almost never linear but often the linearity assumption is good enough. (Linearity is an approximation)
When its not (increasing in complexity):
- local regression, and
- generalized additive models
offer a lot of flexibility, without losing the ease and interpretability of linear models.
In a linear model with two predictors, we will add another predictor: the interaction predictor which is:
- the product of the (two) predictors
- then a non-additive facts
We could then test for non-additive effects (ie to see if one predictor moderates the relationship between the other predictor and the outcome).
There might be an interaction or moderation effect between this predictors. If that is the case, then the interaction predictor would be a significant predictor of the outcome measure.