Little Green Book


In unrestricted nonparametric multiple regression, we model the conditional average value of y as a general, smooth function of several x 's, In linear regression analysis, in contrast, the average value of the response variable is modeled as a linear function of the predictors, Like the linear model, the additive regression model specifies that the average value of y is the sum of separate terms for each predictor, but these terms are merely assumed to be smooth functions of the x 's: Because it excludes interactions among the x 's, the additive regression model is more restrictive than the general nonparametric regression model, but more flexible than the standard linear regression model. A substantial advantage of the additive regression model is that it reduces to a series of two-dimensional partial regression problems. This is true both in the computational sense and, even more importantly, with respect to interpretation: Because each ...

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