locpoly是非参数方法中的局部线性估计。可以再R软件中用？locpoly查看函数解释。

Usage
locpoly(x, y, drv = 0L, degree, kernel = "normal",
        bandwidth, gridsize = 401L, bwdisc = 25,
        range.x, binned = FALSE, truncate = TRUE)

Arguments
x vector of x data. Missing values are not accepted.  
bandwidth the kernel bandwidth smoothing parameter. It may be a single number or an array having length gridsize, representing a bandwidth that varies according to the location of estimation.  
y vector of y data. This must be same length as x, and missing values are not accepted.  
drv order of derivative to be estimated.  
degree degree of local polynomial used. Its value must be greater than or equal to the value of drv. The default value is of degree is drv + 1.  
kernel "normal" - the Gaussian density function. Currently ignored.  
gridsize number of equally-spaced grid points over which the function is to be estimated.  
bwdisc number of logarithmically-equally-spaced bandwidths on which bandwidth is discretised, to speed up computation.  
range.x vector containing the minimum and maximum values of x at which to compute the estimate.  
binned logical flag: if TRUE, then x and y are taken to be grid counts rather than raw data.  
truncate logical flag: if TRUE, data with x values outside the range specified by range.x are ignored.  

请问解决了吗，要输出在每一观测点的多项式展开式的系数预测值吗？该用什么命令？

建议使用Piecewise Polynomials方法，即把自变量分成不同的连续区域，针对不同区域拟合不同的多项式回归。
library(spline)
fit<-lm(y~bs(x,df=))
其中df默认为3，即有立方项。

可以展开的，不过要用到一个函数，我找了好久才找到，一般书上都不写这个