ABSTRACT
To provide a framework for a regression modeling methodology, let y represent a single univariate response variable tha t depends on a vector of p predictor variables x where x = ( x i , . . . ,x Vi. . . ,x p). Assume we are given N samples of y and x, namely { y i ,x i}^Ll1 and that we can describe y with the regression model,
y = f (x i , . . . , x p) + € (1 )
over some domain D C IRP, which contains the data. The function / (x ) reflects the true but unknown relationship between y and x. The random additive error variable e, which is assumed to have mean zero and variance reflects the dependence of y on quantities other than x. Quoting Friedman (1991b) “/(x ) is taken to be that component of y tha t varies smoothly with changing values of x, whereas the noise is taken to be the leftover part that does not.”
