# 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 3.18 on P149 in NKNW to illustrate
# tranformations on the response variable

# Created by C. Andy Tsao, 031027.

t<-matrix(scan("CH03PR18.DAT"),ncol=2,byrow=T)
reserror <-data.frame(y=t[,1],x=t[,2])
attach(reserror)
# Numerical Summary
summary(reserror)
# Graphical Displays

plot(x,y,main="Response Errors (Y) vs Month (X)")
windows()

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

# Transformation on X
x1<-sqrt(x);
x2<-x^2

m1<-lm(y~x1);
m2<-lm(y~x2);

summary(m1);summary(m2);

windows(); par(mfrow=c(2,2));
plot(x1,y);abline(coef(m1));
plot(x2,y);abline(coef(m2));

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

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