# Ch 7: Basic concepts of regression
# R code


##  Figure 7.1.  Examples of interaction patterns

par(mfrow=c(2,2))
x11 <- 10
x21 <- 20
y11 <- .05
y12 <- .10
y21 <- .10
y22 <- .15
plot(c(x11,x21),c(y11,y12),xlab=expression(x[1]),ylab="Mean", main="No Interaction", type="l", ylim=c(0,.20), lwd=2, cex=2)
lines(c(x11,x21),c(y21,y22),type="l",lty=2, lwd=2, cex=2)
#legend(16,.05, c("x2=0", "x2=1"), lty=c(1,2),bty="n")

x11 <- 10
x21 <- 20
y11 <- .10
y12 <- .15
y21 <- .05
y22 <- .20
plot(c(x11,x21),c(y11,y12),xlab=expression(x[1]),ylab="Mean", main="Interaction", type="l", ylim=c(0,.20), lwd=2)
lines(c(x11,x21),c(y21,y22),type="l",lty=2, lwd=2)
#legend(16,.05, c("x2=0", "x2=1"), lty=c(1,3),bty="n")

x11 <- 10
x21 <- 20
y11 <- .10
y12 <- .20
y21 <- .05
y22 <- .10
plot(c(x11,x21),c(y11,y12),xlab=expression(x[1]),ylab="Mean", main="Interaction", type="l", ylim=c(0,.20), lwd=2)
lines(c(x11,x21),c(y21,y22),type="l",lty=2, lwd=2)
#legend(16,.05, c("x2=0", "x2=1"), lty=c(1,3),bty="n")

x11 <- 10
x21 <- 20
y11 <- .05
y12 <- .10
y21 <- .20
y22 <- .15
plot(c(x11,x21),c(y11,y12),xlab=expression(x[1]),ylab="Mean", main="Interaction", type="l", ylim=c(0,.20), lwd=2)
lines(c(x11,x21),c(y21,y22),type="l",lty=2, lwd=2)
#legend(16,.05, c("x2=0", "x2=1"), lty=c(1,3),bty="n")






## FEV data

FEVdata <- read.table(file="F:\\MyDocuments\\BAYES\\LinearRegression\\CodeandData\\FEVdataAge10to19.txt",header=T, sep="\t")
attach(FEVdata)
options(contrasts=c("contr.treatment","contr.poly"))


## Interaction plot
plot(Age,FEV,xlab="Age", ylab="FEV")
lines(lowess(Age[Smoke==1],FEV[Smoke==1],f=.95),lwd=2,cex=1.2)
lines(lowess(Age[Smoke==0],FEV[Smoke==0],f=.95),lty=3,lwd=2,cex=1.2)
legend("bottomright", c("Smoker", "Nonsmoker"), lty=c(1,3))

## Interaction plot.  LOWESS plot for the FEV data  
plot(Age,FEV,xlab="Age", ylab="FEV")
lines(lowess(Age[Smoke==1],FEV[Smoke==1],f=.95),lwd=2,cex=1.2)
lines(lowess(Age[Smoke==0],FEV[Smoke==0],f=.95),lty=2,lwd=2,cex=1.2)
legend("bottomright", c("Smoker", "Nonsmoker"), lty=c(1,2))



## Figure 7.2.  Plot of Bayesian posterior means from a linear regression with interaction term and diffuse prior for the FEV data
BayesSmoker <- c(3.058,3.124,3.191,3.258,3.324,3.391,3.458,3.525,3.591,3.658)
BayesNonsmoker <- c(2.772,2.982,3.192,3.402,3.612,3.821,4.031,4.241,4.451,4.661)
Age1 <- seq(10,19,1)
plot(Age,FEV,xlab="Age", ylab="FEV", lwd=1.5)
lines(Age1,BayesSmoker,type='l', lty=1, lwd=2,cex=1.2)
lines(Age1,BayesNonsmoker,type='l', lty=2, lwd=2,cex=1.2)
legend("bottomright", c("Smoker", "Nonsmoker"), lty=c(1,2), lwd=2)