inst/scripts/Linear/ls.R

In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

## "INFOF422 Statistical foundations of machine learning" course
## R package gbcode 
## Author: G. Bontempi


par(ask=TRUE)
X<-seq(-1,1,by=.1)

beta0<-1
beta1<--1
N<-length(X)
R<-10000
sd.w<-0.1


Y<-beta0+beta1*X+rnorm(N,sd=sd.w)
x.hat<-mean(X)
y.hat<-mean(Y)
S.xy<-sum((X-x.hat)*Y)
S.xx<-sum((X-x.hat)^2)

beta.hat.1<-S.xy/S.xx
beta.hat.0<-y.hat-beta.hat.1*x.hat


b0 <- seq(-5, 5, length= 50)
b1<-b0
rss <- function(b0,b1) {
  RSS<-sum((Y-b0-b1*X)^2)
  RSS
}


RSS<-array(NA,c(length(b0),length(b1)))

for (i in 1:length(b0)){
  for (j in 1:length(b1)) {
    RSS[i,j]<-rss(b0[i],b1[j])
  }
}

persp(b0, b1, sqrt(RSS),
      theta = 30,
      phi = 30,
      expand = 0.5,
      col = "lightblue",
      ticktype="detailed",
      main=paste("Beta.hat.0=", round(beta.hat.0,2), ", Beta.hat.1=", round(beta.hat.1,2)))

contour(b0,b1,sqrt(RSS),
        nlevels=100)

title(main=paste("Beta.hat.0=", round(beta.hat.0,2), ", Beta.hat.1=", round(beta.hat.1,2)),
      xlab="b0",
      ylab="b1")


summary(lm(Y~X))