Curvature in X and Z
The model can be extended further to explain curvature in both X and Z by adding a further quadratic term in z.
This model is again a general linear model since its parameters appear linearly in the equation.
Flexibility of the model
The diagram below shows the kinds of regression surface that correspond to this class of linear models.
Drag the red arrows to adjust the parameters.
Click the checkboxes Quadratic in X and Quadratic in Z to add quadratic terms in the two explanatory variables to the model, and drag the extra two arrows to investigate the kinds of surface that correspond to this quadratic model.