Locally weighted regression. Like kernel smoothing, locally weighted re- gression is a linear approach to nonparametric regression. Let W be a continuous, nonnegative, symmetric (W(x) = W(x)) function, decreas- ing on (0,) with support [1,1]. The estimate for f at a point xis based on weighted least squares, fitting a polynomial to the data with weights emphasizing data with xi near x. This problem considers quadratic models in which is chosen to minimize