Bears = read.table("c:/413/beardata.txt", header=T)
attach(Bears)

### Problem 1 ###
# Fit a quadratic regression:
bear1=lm(WEIGHT~AGE+I(AGE^2))
summary(bear1)
# R^2 = 0.6235 and Adj R^2=0.6087.  R^2 is low but both terms are significant.
# This might imply that we are missing terms in our model.
# Try plotting the data with the curve:
plot(AGE, WEIGHT)
abline(bear1) ## doesn't work because have quadratic function now.
# Try again...
plot(AGE, WEIGHT, xlab="Age of Bear", ylab="Weight of Bear", main="Regression with Data")
PREDICTIONS = predict(bear1, newdata=data.frame(AGE=sort(AGE)))
lines(sort(AGE), PREDICTIONS) # Why does this look weird near AGE=150?

### Problem 2 ###
# Test whether or not there is a regression relation:
# Pull everything from summary table!
# F-stat = 42.22 with df1=2, df2=51, p-value=1.525e-11
# YES! reject H_0

### Problem 3 ###
# Test whether we can drop quadratic term:
# Pull everything we need from the summary.
# t-stat=-2.908, p-value=.00537.
# Yes! reject H_0

### Problem 4 ###
# Can also test higher order regressions (lack of fit):
bear2=lm(WEIGHT~AGE + I(AGE^2) + I(AGE^3) + I(AGE^4))
summary(bear2)
# Can test dropping one term at a time (here, drop X4, run reg. again, repeat)
# OR test 3rd and 4th terms together, etc

## Problem 5 ###
summary(AGE) # gives us info on AGE so can choose how many subsets to consider
coplot(WEIGHT~CHEST|AGE, number=4, overlap=0)
# number is how many subsets of AGE we want to consider.
# overlap is if we want any of these subsets to overlap.
coplot(WEIGHT~CHEST|SEX, number=2, overlap=0)
# if overlap = 0 gives overlapping subsets, then try making overlap = negative #
coplot(WEIGHT~CHEST|SEX, number = 2, overlap=-1)

### Problem 6 ###
names(Bears)
# scatterplot matrix
pairs(~AGE + SEX + HEADLEN + HEADWTH + NECK + LENGTH + CHEST)
#correlation matrix
cor(data.frame(AGE, CHEST, NECK))

### Problem 7 ###
bear3=lm(WEIGHT~AGE + CHEST + NECK)
summary(bear3)
# NECK is not that important if include CHEST and AGE
bear4 = lm(WEIGHT~AGE + NECK)
summary(bear4)
# CHEST not included; now NECK is really important
cor(CHEST, NECK)
# highly correlated.  So, if CHEST is included, NECK doesn't "add" much to the regression.

detach(Bears)

#### adding a column to datset (for problem 8.20) ####
GradePoint = read.table("c:/413/CH01PR19.txt", header=F)
NewCol = read.table("c:/413/CH08PR16.txt", header=F)
GradePoint<-edit(GradePoint) # col1=GPA, col2=ACT
NewCol<-edit(NewCol) # col=Major
GradePoint=c(GradePoint, NewCol) #attach the new column to the original dataset
GradePoint # you can see that it worked
GradePoint<-edit(GradePoint) # this is why I suggest changing 
				     #column names before using c() command
attach(GradePoint) # can still attach column names and proceed as normal.
detach(GradePoint)