chapter  17
38 Pages

Modelling Nonlinear Effects

The most popular approach is to consider also the square of the covariate X as an additional covariate. So a quadratic model reads

μ(x) = β0 +β1x+β2x2

and we can fit such a model simply by creating an additional covariate X2 = X2 in our data set and including it in the model. The fitted values

μˆ(x) = βˆ0 + βˆ1x+ βˆ2x2

no longer describe a linear but a quadratic function, and we can see in Figure 17.2 how this quadratic function fits the data well.