t=seq(0,10,0.01)
y=sin(t)+rnorm(length(t))
plot(t,y,cex=0.1)

# puts a loess smoother through the points
lines(loess.smooth(t,y),col=2)

library(mgcv)
# puts a spline through the points - read Simon Woods work to learn more about this
g<-gam(y~s(t),data=data.frame(t=t,y=y))
lines(t,g$fitted.values,col=3)