###########Read the data "Senility and WAIS"############

wais <- read.table("Senility and WAIS.txt", header=T)

wais

summary(wais)

attach(wais)

x1=unique(x)
y= rep(NA, length(x1))
n=rep(NA, length(x1))
for (i in 1:length(x1))
{
n[i]=length(s[x==x1[i]])
y[i]=sum(s[x==x1[i]])
}

plot(x1, y/n, xlab="WAIS score", ylab="Proportion of Symptoms")

response=cbind(y, n-y)

fit1 <- glm(response~x1, family=binomial)

summary(fit1)

resid1.pearson <- residuals(fit1, type="pearson")

resid1.deviance <- residuals(fit1, type="deviance")

sum(resid1.pearson^{2})

sum(resid1.deviance^{2})

par(mfrow=c(2,2))

plot(x1, y/n, xlab="WAIS score", ylab="Proportion of Symptoms", pch="O")
points(predict(fit1, type="r"),  pch="E")

qqnorm(resid1.pearson)
qqline(resid1.pearson)

plot(x1, resid1.pearson, xlab="WAIS score", ylab="Pearson Residuals")

plot(x1, resid1.deviance, xlab="WAIS score", ylab="Deviance Residuals")

predict1 <- predict(fit1, type="r")

final <- data.frame(x1,y,n, resid1.pearson, resid1.deviance, predict1)

final