source('../../Data/get_university_endowment_data.R')
DF = get_university_endowment_data()

##DF$Endowment = DF$Endowment - mean(DF$Endowment) ## subtract the mean
##DF$Endowment = log(DF$Endowment)

## Plot the data:
##
pairs(DF[, c(-1)])

m = lm(Endowment ~ Percent_Change + Number_Students, data=DF)
print(summary(m))

## Plot the hat matrix diagonal against the fitted values:
##
inf = influence(m)
plot(m$fitted.values, inf$hat, type='p', pch=19, xlab='Fitted values', ylab='Hat diagonals')
ext = match(sort(inf$hat)[dim(DF)[1] - (0:3)], inf$hat)
text(m$fitted.values[ext], inf$hat[ext], labels=row.names(DF)[ext], pos=c(4, 4, 4, 4))
grid()

## Based on index=5 having the largest hat value we will drop this sample and refit assuming it is "incorrect":
##
m1 = lm(Endowment ~ Percent_Change + Number_Students, data=DF[c(-5), ])
print(summary(m1))