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.