Auta=read.table("samochody.txt",skip=9,header=TRUE)
X=as.matrix(Auta[,-1]); y=as.vector(Auta[,1])
x7=X[,2]/sd(X[,2]) + 2*X[,4]/sd(X[,4]) - 7*X[,5]/sd(X[,5])
x8=X[,1]/sd(X[,1]) + 3*X[,2]/sd(X[,2]) - 2*X[,3]/sd(X[,3])
x9=X[,4]/sd(X[,4]) + 2*X[,5]/sd(X[,5]) - 5*X[,6]/sd(X[,6])
X=cbind(X,x7,x8,x9)

### lm
mm=lm(y~X)
beta1=mm$coeff
cat("\nbeta1 = ",sum((y-cbind(1,X[,1:6])%*%beta1[1:7])^2))

### Uogolniona odrotnosc
library(MASS)
Xp=ginv(cbind(1,X)); beta2=as.vector(Xp%*%y)
cat("\nbeta2 = ",sum((y-cbind(1,X[,1:6])%*%beta2[1:7])^2),"\n")

### Outliers
X=Auta; n=ncol(X)
par(mfrow=c(1,n))
for(i in 1:n){
  out=which(is.element(X[,i],boxplot.stats(X[,i])$out))
  boxplot(X[,i],main=colnames(Auta)[i])
  print("***********"); print(colnames(Auta)[i]); print(cbind(out,X[out,i]))
}
par(mfrow=c(1,1))