both splines were significant for this data set,

ݕൌ2.02 െ0.072 ൈݏሺݔଵሻ

൏2݁െ16

൅1.75 ൈݏሺݔଶሻ

൏2݁െ16



Fig. 4.17. The GAM model for a 2D data.

ugh GAM can model some nonlinear data, it still belongs to the

linear algorithms because the estimation of the parameters of a

odel follows a similar procedure as that used to construct an OLR

ing LSE. A vector-matrix format of a GAM model is shown

where ܡൌሺݕଵ, ݕଶ, ⋯, ݕேሻ stands for a vector as a dependent

for N data points, ઺ൌሺߚ଴, ߚଵ, ߚଶ, ⋯, ߚ௄ሻ stands for a vector of

rameters for K splines of K independent variables and S stands

line function matrix,

ܡ= ܁ൈ઺൅ઽ

(4.28)

pline matrix S which is composed of an intercept vector is shown

܁ൌ൮

1

ܵሺݔଵଵሻ

⋯

ܵሺݔଵ௄ሻ

1

ܵሺݔଶଵሻ

⋯

ܵሺݔଶ௄ሻ

⋮

1

⋮

ܵሺݔேଵሻ

⋱

⋯

⋮

ܵሺݔே௄ሻ

൲

(4.29)

E estimation is used, the solution of this model is shown below,