## Setup Variables
library(alr4)
Highway$sigs1 <- with(Highway, (sigs * len + 1)/len)
f <- ~ log(len) + shld + log(adt) + log(trks) + lane + slim +lwid +
itg + log(sigs1) + acpt + htype

##Forward Selection
m0 <- lm(log(rate) ~ log(len), Highway) # the base model
m.forward <- step(m0, scope=f, direction="forward")


##Backward Elimination
m1 <- update(m0, f)
m.backward <- step(m1, scope = c(lower = ~ log(len)), direction="backward")



##Stepwise Regression
m.stepup <- step(m0, scope=f)


## A Cautionary Example -- A criterion and 99 totally random predictors
library(MASS)
set.seed(12345)
mu <- rep(0,100)
R <- matrix(rep(0,10000),100,100) + diag(100)
data <- mvrnorm(120,mu,R)
colnames(data) <- paste("X",1:100,sep="")
data <- data.frame(round(data,2))
write.table(data,"data.txt",row.names=F,col.names=T,sep=",")
m0 <- lm(X1~X2,data=data)
bogus.model <- step(m0,scope=list(lower=~X2,
upper=~X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14
+X14+X16+X17+X18+X19+X20
+X21+X22+X23+X24+X25+X26+X27+X28+X29+X30
+X31+X32+X33+X34+X35+X36+X37+X38+X39+X40
+X41+X42+X43+X44+X45+X46+X47+X48+X49+X50
+X51+X52+X53+X54+X55+X56+X57+X58+X59+X60
+X61+X62+X63+X64+X65+X66+X67+X68+X69+X70
+X71+X72+X73+X74+X75+X76+X77+X78+X79+X80
+X81+X82+X83+X84+X85+X86+X87+X88+X89+X90
+X91+X92+X93+X94+X95+X96+X97+X98+X99+X100),
direction="forward",data=data)

summary(bogus.model)