# This sample program demonstrates how transformations
# can be employed to make simple linear model applicable
# for complicated relation between "y" and "x"
# Here we use 3.16 on P148 in NKNW to illustrate
# tranformations on the response variable

# Created by C. Andy Tsao

t<-matrix(scan("CH03PR15.DAT"),ncol=2,byrow=T)
solution <-data.frame(conc=t[,1],time=t[,2])
attach(solution)
# Numerical Summary
summary(solution)
# Graphical Displays

plot(time,conc,main="Concentration (Y) vs Time (X)")
windows()

par(mfrow=c(2,2));
m0<-lm(conc~time)
summary(m0)
plot.lm(m0)
# Exam the prelim analysis: numerical and graphical summaries

# Box-Cox Transformation (Use (3.33))
y1<-conc^(-.2);
y2<-conc^(-.1);
y3<-log(conc);
y4<-conc^(.1);
y5<-conc^(.2);
x<-time;

m1<-lm(y1~x);
m2<-lm(y2~x);
m3<-lm(y3~x);
m4<-lm(y4~x);
m5<-lm(y5~x);

summary(m1);summary(m2);summary(m3);summary(m4);summary(m5);

windows(); par(mfrow=c(2,2));
plot(x,y1);abline(coef(m1));
plot(x,y2);abline(coef(m2));
plot(x,y3);abline(coef(m3));
plot(x,y4);abline(coef(m4));
plot(x,y5);abline(coef(m5)); 

windows(); par(mfrow=c(2,2)); plot.lm(m1);
windows(); par(mfrow=c(2,2)); plot.lm(m2);
windows(); par(mfrow=c(2,2)); plot.lm(m3);
windows(); par(mfrow=c(2,2)); plot.lm(m4);
windows(); par(mfrow=c(2,2)); plot.lm(m5);

# Question:
# Use scatterplots and residual analyses to
# Find out some appropriate models and explain
# why you choose them.