###Q1(b)

summary(lm(Chick_survival ~ Disturbance + Nest_failure, data=BO))

summary(ivreg(Chick_survival ~ Disturbance + Nest_failure | South_shore + Nest_failure, data=BO))


###Q2(a)

summary(lm(Followup_infection_rate ~ Baseline_infection_rate + Treatment, data=infection))

summary(ivreg(Followup_infection_rate ~ Baseline_infection_rate + Treatment | Baseline_infection_rate + Dropout, data=infection))


###Q2(b)

###Make a table for categorical variables:
table(infection$Sex,infection$Treatment)

###Make a histogram for continuous variables:
par(mfrow=c(1,2))
hist(infection$BMI[infection$Treatment==0])
hist(infection$BMI[infection$Treatment==1])



###Q2(c)

psmod <- glm(formula= Treatment ~ Sex + Age + Ethnicity + BMI, family=binomial, data=infection)
infection$ps <- exp(fitted(psmod))/(1+exp(fitted(psmod)))

summary(ivreg(Followup_infection_rate ~ Baseline_infection_rate + ps + Treatment | Baseline_infection_rate + ps + Dropout, data=infection))