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predict.gam problem

I thought the documentation you quoted is rather clear.  The GAM is
something like:

g(Y) = sum f_j(x_j)

so predict.gam() returns sum f_j(x_j) by default, and if type="response",
g^-1(sum f_j(x_j)).  This is similar to predict.glm, I believe.

HTH,
Andy