# Diagnostics
# Reproduces code for Fox Chapter 11 and Faraway Ch 7


##########################
# get data and fit model #
##########################

library(faraway)
data(savings)

# fit the model
m <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data=savings)
summary(m)


###################
# leverage points #
###################

# make plot
par(mfrow=c(1,1))
plot(hatvalues(m),ylab="Leverages",main="Index plot of leverages")
abline(h=2*(4+1)/50)

# identify points interactively
countries <- row.names(savings)
identify(c(1:50), hatvalues(m), countries)
# stop process by clicking 'stop' in the menu, or use middle 
# (and if not available, right) mousebutton


#################
# residual plot #
#################

par(mfrow=c(2,2))

plot(fitted(m),resid(m), ylab="Residuals", main="Residuals vs. fitted values")
abline(h=0)
identify(fitted(m), resid(m), countries)

plot(fitted(m),rstandard(m), ylab="Standardized residuals", 
  main="Standardized residuals vs fitted values")
abline(h=0)
abline(h=-2)
abline(h=2)
identify(fitted(m), rstandard(m), countries)

plot(fitted(m),rstudent(m), ylab="Studentized residuals", 
  main="Studentized residuals vs fitted values")
abline(h=0)
abline(h=-2)
abline(h=2)
identify(fitted(m), rstudent(m) , countries)


#############
# Influence #
#############

par(mfrow=c(1,1))
plot(cooks.distance(m), ylab="Cook's distance", 
  main="Index plot of Cook's distance")
n <- nrow(savings)
abline(h = 4/(n-4-1))
identify(c(1:50), cooks.distance(m) , countries)


####################################
# easy built-in plotting functions #
####################################

par(mfrow=c(2,3))
plot(m, which=c(1:5))