## PRELIMINARY CODE FOR HOMEWORK

## You need to write an R function 
## that fits a smoothing spline with k 
## nodes. 
## Arguments x, y , number of nodes or nodes.
## The function needs to return a list with
## two components (1) X matrix (2) Vector of coefficients.
## To make it realy good you also need (3) Predicted values
## (4) Predicted values on a testing set prespecified as an
## extra argument of the function.

x = runif(30)
y = sin(x*9)+rnorm(30)/10
nod = seq(min(x),max(x), length=7)[-c(1,7)]
X = cbind(1,x,x^2)
for(i in 1:5) { 
		u = x*0
		u[ x > nod[i]] = (x[x>nod[i]]-nod[i])^3
		X = cbind(X,u) 
	}
z = lsfit(X,y,int=F)

plot(x,y)
points(x,y- z$resid,pch=16,col=2)
i = sort.list(x)
lines(x,y- z$resid,col=2)
plot(x,y)
lines(x[i],(y- z$resid)[i],col=2)