source('../../Data/get_arsenic_data.R')
DF = get_arsenic_data()
leng = dim(DF)[1]

## Use all of the data:
##
m1 = lm(Arsenic_in_nail_ppm ~ 0 + Arsenic_in_water_ppm + Sex, data=DF)
print(summary(m1))

m2 = lm(Arsenic_in_nail_ppm ~ 0 + ., data=DF)
print(summary(m2))

m3 = lm(Arsenic_in_nail_ppm ~ 0 + Drinking_Use + Cooking_Use + Arsenic_in_water_ppm, data=DF)
print(summary(m3))

## Remove index==14:
##
m1 = lm(Arsenic_in_nail_ppm ~ 0 + Arsenic_in_water_ppm + Sex, data=DF[c(-14), ])
print(summary(m1))

m2 = lm(Arsenic_in_nail_ppm ~ 0 + ., data=DF[c(-14), ])
print(summary(m2))

m3 = lm(Arsenic_in_nail_ppm ~ 0 + Drinking_Use + Cooking_Use + Arsenic_in_water_ppm, data=DF[c(-14), ])
print(summary(m3))

## Lets plot some diagnostics for some of the linear regressions:
##
m1 = lm(Arsenic_in_nail_ppm ~ 0 + Arsenic_in_water_ppm + Sex, data=DF)

inf = influence(m1)
plot(m1$fitted.values, inf$hat, type='p', pch=19, xlab='Fitted values', ylab='Hat diagonals')
ext = match(sort(inf$hat)[leng - (0:1)], inf$hat)
text(m1$fitted.values[ext], inf$hat[ext], labels=row.names(DF)[ext], pos=c(2, 4, 4, 2))
grid()

## Jackknife diagnostics:
##
im = influence.measures(m1)
print(im)