# using the same Autos1 data frame from the previous R code

library(leaps)

Auto.SmallFit <-  regsubsets(LMPG ~ VOL +HP +SP +WT +lowvol +hihp, data=Autos1, nbest=5)

library(car)

subsets(Auto.SmallFit,statistic="bic",cex.subsets=.8,min.size=2,max.size=6)



 # Here we have picked the best model according to the SBC criterion
 #  for further investigation 
 


Auto.SmallModel1 <- lm(LMPG ~ SP +WT +lowvol , data=Autos1)
summary(Auto.SmallModel1)


  # this code creates a residual-by-predicted plot and a normal plot of the residuals
par(mfrow=c(2,2))                                 # makes all future plots appear four per page
plot(fitted(Auto.SmallModel1),resid(Auto.SmallModel1),xlab="Predicted Values",
     ylab="Residuals",main="Residual by Predicted plot")
qqnorm(resid(Auto.SmallModel1))
qqline(resid(Auto.SmallModel1))
plot(Auto.SmallModel1$model$SP,resid(Auto.SmallModel1),xlab="SP",ylab="Residuals",main="Residuals vs. Fat")
plot(Auto.SmallModel1$model$WT,resid(Auto.SmallModel1),xlab="WT",ylab="Residuals",main="Residuals vs. Cholesterol")
par(mfrow=c(1,1))                                 # restores one plot per page

windows()

 # this plots Studentized residuals vs. Leverage values, with reference lines 
 # to help identify points that have high leverage and are outliers
plot(hatvalues(Auto.SmallModel1),rstudent(Auto.SmallModel1),xlim=c(0,1),main=c("Studentized Residuals vs. Hat values"))
abline(h=-2)
abline(h=2)
abline(v=2*length(Auto.SmallModel1$coefficients)/length(Auto.SmallModel1$residuals))     # reference line at 2p/n
text(hatvalues(Auto.SmallModel1),rstudent(Auto.SmallModel1),labels=rownames(Auto.SmallModel1$model),pos=4,cex=.8)