# Homework 6, problem 2
# edps 589
# fall 2019
# c.j.anderson
#
# Problem 4.30 from Agresti(2007)
#
numbers <- c(796, 1625, 143, 660,  498, 878,  54, 197, 1,1,0,0,   1,0,1,0)
(ncaa <- matrix(numbers,nrow=4,ncol=4))
ncaa <- as.data.frame(ncaa)
names(ncaa) <- c("ncases","graduate","race","gender")
ncaa$race <- as.factor(ncaa$race)
ncaa$gender <- as.factor(ncaa$gender)

# saturated
summary(saturated <- glm(graduate/ncases ~ race + gender + race*gender, weights=ncases, data=ncaa, family=binomial))

# additive
summary(additive <- glm(graduate/ncases ~ race + gender, weights=ncases, data=ncaa, family=binomial))

# race
summary(race <- glm(graduate/ncases ~ race , weights=ncases, data=ncaa,  family=binomial))

# gender
summary(gender <- glm(graduate/ncases ~ gender, weights=ncases, data=ncaa, family=binomial))