Smoothing Kernels

set.seed(1)
x <- seq(from=0, to=20, by=0.4)
y <- 500 + 0.25 * (x-4)^2 * (x-16)^2
noise <- rnorm(length(x), mean=10, sd=80)
noisyY <- y + 1*noise
y <- noisyY 
ySmooth <- y ; 
cc <- 5:(length(y)-4) 
# Manual smoothing
for (i in cc)
{
  ySmooth[i] = (   1.0 * y[i-4] + 2.0 * y[i-3] + 3.0 * y[i-2] + 4.0 * y[i-1] + 4.0 * y[i] 
                 + 1.0 * y[i+4] + 2.0 * y[i+3] + 3.0 * y[i+2] + 4.0 * y[i+1] 
               ) / 24
}
plot(x[cc],noisyY[cc],col='blue',xlab='q',main='Observed data')
lines(ksmooth(x,y,  "normal", bandwidth = 3.72 ))

lines( x[cc],ySmooth[cc], col="red")