Math 50

Ploynomial regression

set.seed(1)
x <- seq(from=0, to=20, by=1)
y <- 500 - 4 * (x-10)^3
noise <- rnorm(length(x), mean=10, sd=80)
noisyY <- y + 5*noise
fitted <- lm(noisyY ~ poly(x,3))
plot(x,noisyY,col='blue',xlab='q',main='Observed data')
lines(sort(x), fitted(fitted)[order(x)], col='red') 

Cubic Spline fitting

library(splines) 
set.seed(1)
x <- seq(from=0, to=20, by=0.15)
y <- 500 - 0.25 * (x-4)^2 * (x-16)^2
noise <- rnorm(length(x), mean=10, sd=80)
noisyY <- y + 1*noise
# fitted <- lm(noisyY ~ poly(x,3))
fitted <-lm(noisyY ~ bs(x, knots = c(10)) )
plot(x,noisyY,col='blue',xlab='q',main='Observed data')
lines(sort(x), fitted(fitted)[order(x)], col='red')