# This sample program shows the calculuation and limitation of R^2
# Refer to Sect 2.9 in NKNW, particularly Fig 2.8-2.9

x<-seq(0.5,20,.5)    # X=0.5, 1, ..., 20
ne<-rnorm(40,0,1)  # Generate 41 iid N(0,1) random errors
y1<-1+ .5*x + ne
y2<-2+4*sin(x)+ ne

# Numerical Summary
summary(y1);summary(y2);summary(x);summary(ne);
# Graphical Displays
par(mfrow=c(2,2));    # Setup the graphical device
plot(x,y1);plot(x,y2)

par(mfrow=c(2,2));
m1<-lm(y1~x)
m2<-lm(y2~x)
summary(m1);summary(m2);
plot.lm(m1)
plot.lm(m2)

windows()
par(mfrow=c(2,2));
plot(x,y1); abline(coef(m1))
plot(x,y2); abline(coef(m2))

x2<-sin(x)
m3<-lm(y2~x2)
summary(m3)
plot(x2,y2); abline(coef(m3))

# Question:
# a. How these figures will be if there are no errors terms
#    added? And how does it affect the R^2?
# b. Construct Figure 2.9
# c. Refer to "Limitation of r^2 and r" on p 82--83, do you
#    think the larger r^2 indicates better fit? Explain.