#Simple regression test

> setwd("c:/Rdata")
> regression=read.table("regression.txt")
> attach(regression)
> regression
> X=V3
> Y=V7
> LM=lm(Y~X)
> LM
> Yhat=fitted(LM)
> e=residuals(LM)
> RESULTS=data.frame(X,Y,Yhat,e)
> plot(X,Y)
> abline(LM,col="green")
> segments(X,Yhat,X,Y,col="blue")
> anova(LM)
> summary(LM)
> cor.test(X,Y,method="pearson",alternative="two.sided",conf.level=.95)

#Plotting regression

> plot(X,Y)
> abline(LM,col="blue")
> segments(X,Yhat,X,Y,col="red")

#Multiple Regression

> setwd("c:/Rdata")
> regression=read.table("regression.txt")
> attach(regression)
> regression
> Y=V7
> X1=V3
> X2=V4
> X3=V5
> X4=V6
> LM=lm(Y~X1+X2+X3+X4)
> LM
> summary(LM)
> anova(LM)

#Choosing optimal model

> Y=V7
> X1=V3
> X2=V4
> X3=V5
> X4=V6
> FM=lm(Y~X1+X2+X3+X4)
> n=length(Y)
> I=diag(n)
> J=matrix(nrow=n,ncol=n,1)
> X=model.matrix(FM)
> p=ncol(X)
> H=X%*%solve(t(X)%*%X)%*%t(X)
> SSR=t(Y)%*%(H-((1/n)*J))%*%Y
> SSE=t(Y)%*%(I-H)%*%Y
> SSTO=t(Y)%*%(I-(1/n)*J)%*%Y
> SSTO
> rbind(SSR,SSE,SSTO)
> AIC=n*log(SSE[1])-n*log(n)+2*p
> AIC
> extractAIC(FM)
> drop1(FM)
> require(car)
> Anova(FM)

#Automated “backwards” Stepwise Regression

> step(FM,direction="backward")