data("engine")
engine
attach(engine)
plot(size,wear,xlab='Engine capacity',ylab='Wear index')
tf<-function(x,xj,j){
dj<-xj*0;
dj[j]<-1
approx(xj,dj,x)$y # approx return two subject, only return y here
}
tf.X<-function(x,xj){
##tent function basis matrix given data x
## and knot sequnce xj
nk<-length(xj);
n<-length(x)
X<-matrix(NA,n,nk)
for(j in 1:nk){
X[,j]<-tf(x,xj,j)
}
X
}
sj<-seq(min(size),max(size),length=6)
sj
X<-tf.X(size,sj)
X
b<-lm(wear~X-1)
b
s<-seq(min(size),max(size),length=200)
Xp<-tf.X(s,sj)
plot(size,wear)
lines(s,Xp%*%coef(b))
Xp
library(splines)
B=bs(size,knots=sj,Boundary.knots=c(1.420,2.980),degree=1)
B
b2<-lm(wear~B-1)
b2
s2<-seq(min(size),max(size),length=200)
s2
Xp2<-bs(s2,knots=sj,Boundary.knots=c(1.420,2.980),degre=1)
Xp2[,1:6]
plot(size,wear)
lines(s2,Xp2[,1:6]%*%coef(b))
B=bs(s,knots=sj,Boundary.knots=c(1.420,2.980),degree =1)
matplot(s,B,type="l")
