# reading the dat for HW1
Y=read.csv('C:/Users/rsmith/jan16/UNC/STOR556/Data/ProportionNotReturned.csv',header=T)

hist(Y$PNR,main='Proportion Absentee Ballots Not Returned - NC Nov 2018')
plot(density(Y$PNR),main='Proportion Absentee Ballots Not Returned - NC Nov 2018')
rug(Y$PNR)

# illustration of the slick method to omit Robeson and Bladen counties from the analysis
# these are the only two counties with PNR>0.1

wts=Y$PNR<0.1
# example of a plausible linear model (not the solution to HW1)
lm1=lm(Y$PNR~Y$Hsgrad+Y$Collgrad,weights=as.numeric(wts))
# note use of "as.numeric" to turn wts into a numerical variable

# now create predictions
predict(lm1,se.fit=T)

# the predictions for founties 9 and 78 are what you want


#####################################
# continuation of faraway's example
#####################################

# rerun basic set up 
 
library(faraway)
data(gavote)
gavote$undercount=(gavote$ballots-gavote$votes)/gavote$ballots
summary(gavote$undercount)
names(gavote)[4]='usage'
gavote$pergore = gavote$gore/gavote$votes

# fit linear model

lmod=lm(undercount~pergore+perAA,gavote)

summary(lmod)

# the next command is specific to the faraway package
sumary(lmod)


predict(lmod)

predict(lmod,se.fit=T)

# how to omit some data
wts=c(0,0,rep(1,157))

lmodw=lm(undercount~pergore+perAA,gavote,weights=wts)
predict(lmodw,se.fit=T)

# several of the diagnostics associated with lmod
deviance(lmod)

df.residual(lmod)

nrow(gavote)-length(coef(lmod))

sqrt(deviance(lmod)/df.residual(lmod))


summary(lmod)$r.squared

cor(predict(lmod),gavote$undercount)^2


lmodsum$adj.r.squared

# now fit a more complicated linear model, includes an interaction term

gavote$cpergore=gavote$pergore-mean(gavote$pergore)
gavote$cperAA=gavote$perAA-mean(gavote$perAA)
lmodi=lm(undercount~cperAA+cpergore*usage+equip,gavote)


summary(lmodi)

# illustrates hypothesis testing through F test
anova(lmod,lmodi)

# p-value is 0.003 - reject null hypothesis that the simpler model (lmod) is correct

drop1(lmodi,test='F')
# drops variables one at a time using F tests to determine which are significant


confint(lmodi)

plot(lmodi)
# this defines the sequence of four diagnostic plots. The first three should be self-explanatory -
I'll discuss the fourth next time