Things are not Always Linear; Additive Modelling

Abstract

In the previous chapter, we looked at linear regression, and although the word linear implies modelling only linear relationships, this is not necessarily the case. A model of the form Y _i = α + β ₁ × X _i + β ₂ × X _i ² + ɛ _i is a linear regression model, but the relationship between Y _i and X _i is modelled using a second-order polynomial function. The same holds if an interaction term is used. For example, in Chapter 2, we modelled the biomass of wedge clams as a function of length, month and the interaction between length and month. But a scatterplot between biomass and length may not necessarily show a linear pattern.