rivers<-read.table("Rivers.txt",header=T)
attach(rivers)

?plot.lm

plot(Agr,Nitrogen,col="blue",lwd=3)
agr.lm=lm(Nitrogen~Agr);

plot(agr.lm,which=3)# fitted versus std. res.
plot(agr.lm,which=2) # qqnorm of std res.
plot(agr.lm, which=4) # Cook's distance

plot(ComIndl,Nitrogen,col="blue",lwd=3)
ComIndl.lm=lm(Nitrogen~ComIndl);

plot(hatvalues(ComIndl.lm))

plot(ComIndl.lm,which=3) 
plot(ComIndl.lm,which=2) 
plot(agr.lm, which=4) 
plot(ComIndl.lm,which=5) # leverage versus residuals

# Try these measures of influence

influence.measures(ComIndl.lm)
hatvalues(ComIndl.lm) # hatvalues in R is same thing as leverage.
dffits(ComIndl.lm) 
dfbetas(ComIndl.lm)
cooks.distance(ComIndl.lm)

# You can plot them, for example:
plot(hatvalues(ComIndl.lm),type="h")

# Use the help documentation to learn more about what each does.
?dffits
?dfbetas

# Take out a data point and do a fit without it.
# Here, I took out datapoint number 4 in the slides.
ComIndl.lm.no4=lm(Nitrogen[-4]~ComIndl[-4])
plot(ComIndl,Nitrogen,col="blue",lwd=3)
abline(ComIndl.lm,col="red",lwd=2)
abline(ComIndl.lm.no4,col="green",lwd=2)