##### Polynomial regression on the Rabbit Jawbone Data (Table 8.8)


##########
##
# Reading the data into R:

my.datafile <- tempfile()
cat(file=my.datafile, "
0.01 15.5
0.2 26.1
0.2 26.3
0.21 26.7
0.23 27.5
0.24 27
0.24 27
0.25 26
0.26 28.6
0.34 29.8
0.41 29.7
0.83 37.7
1.09 41.5
1.17 41.9
1.39 48.9
1.53 45.4
1.74 48.3
2.01 50.7
2.12 50.6
2.29 49.2
2.52 49
2.61 45.9
2.64 49.8
2.87 49.4
3.39 51.4
3.41 49.7
3.52 49.8
3.65 49.9
", sep=" ")

options(scipen=999) # suppressing scientific notation

rabbit <- read.table(my.datafile, header=FALSE, col.names=c("age","length")) 
  
attach(rabbit)

#########

## Initial scatterplot of data:

plot(age, length)

# Not a linear trend?

# Defining transformed variables for the polynomial terms:

age2 <- age^2
age3 <- age^3
age4 <- age^4

quartic.reg <- lm(length ~ age + age2 + age3 + age4)
summary(quartic.reg)

## Looks like the fourth-degree term is not needed.

cubic.reg <- lm(length ~ age + age2 + age3)
summary(cubic.reg)

# Plotting the fitted curve (this plotting approach only works well with a moderate to large number of observations)

plot(age, length)
lines(age, fitted(cubic.reg))