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Unformatted text preview: he oﬀset, and fj : R → R, with fj (0) = 0. The functions fj are called
the regressor functions. When each fj is linear, i.e., has the form wj xj , the generalized additive
model is the same as the standard (linear) regression model. Roughly speaking, a generalized
additive model takes into account nonlinearities in each regressor xj , but not nonlinear interactions
among the regressors. To visualize a generalized additive model, it is common to plot each regressor
function (when n is not too large).
We will restrict the functions fj to be piecewise-aﬃne, with given knot points p1 < · · · < pK . This
means that fj is aﬃne on the intervals (−∞, p1 ], [p1 , p2 ], . . . , [pK −1 , pK ], [pK , ∞), and continuous at
p1 , . . . , pK . Let C denote the total (absolute value of) change in slope across all regressor functions
and all knot points. The value C is a measure of nonlinearity of the regressor functions; when
C = 0, the generalized additive model reduces to a linear regres...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid