library(MASS)

summary(menarche)
plot(menarche)
plot(menarche$Age, menarche$Menarche/menarche$Total)

menarche$SF<- cbind(menarche$Menarche,menarche$Total-menarche$Menarche)
mn<- glm(SF~Age, data=menarche, family=binomial(link="logit"))
summary(mn)
anova(mn)
lines(menarche$Age, fitted(mn), lty=2, col=4)

mnp<- glm(SF~Age, data=menarche, family=binomial(link="probit"))
summary(mnp)
anova(mnp)

mnq<- glm(SF~Age, data=menarche, family=quasibinomial(link="logit"))
summary(mnq)
mnpq<- glm(SF~Age, data=menarche, family=quasibinomial(link=probit))
summary(mnpq)

mnfull<- glm(SF~as.factor(Age), data=menarche, family=binomial(link="logit"))
summary(mnfull)
anova(mn,mnfull)
# the test against the full model is not significant

mn2<- update(mn, .~.+I(Age^2))
summary(mn2)
mn3<- update(mn2, .~.+I(Age^3))
summary(mn3)
lines(menarche$Age, fitted(mn3), lty=5, col=4)
# some indication of non-linearity