## R code for 7440 Midterm 1, 2011
##   (binary version of Katie bowling data)

bowl <- list(week=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14), W = 14, G = 3,
  game1=c( 85,78,64,94,87,110,122,100,110,123,105,112,103,140),
  game2=c(136,142,87,129,113,65,110,103,92,133,118,94,132,125),
  game3=c(92,127,136,149,119,148,120,159,127,121,117,153,118,108))  

Y<- cbind(bowl$game1,bowl$game2,bowl$game3)
D21 <- Y[,2]-Y[,1];  Z1 <- as.integer(D21>0)
D32 <- Y[,3]-Y[,2];  Z2 <- as.integer(D32>0)
 
par(mfrow=c(2,1),lwd=1.2,cex=1.2)

LR1 <- glm(Z1~bowl$week, family=binomial("logit"))
summary(LR1)
plot(bowl$week,Z1)
lines(bowl$week,LR1$fitted.values)
#  Now add Bayes fitted values to compare:
beta0 <- 0.843;  beta1 <- -0.283
p_logit <- exp(beta0 + beta1*(bowl$week-mean(bowl$week)))/(1 + exp(beta0 + beta1*(bowl$week-mean(bowl$week)))) 
points(bowl$week,p_logit,pch="*")
legend("bottomleft",c("data","Bayes est"),pch=c("o","*"))
title("Katie's bowling improvement, Game1->Game2")

LR2 <- glm(Z2~bowl$week, family=binomial("logit"))
summary(LR2)
plot(bowl$week,Z2)
lines(bowl$week,LR2$fitted.values)
#  Now add Bayes fitted values to compare:
beta0 <- 0.350;  beta1 <- -0.136
p_logit <- exp(beta0 + beta1*(bowl$week-mean(bowl$week)))/(1 + exp(beta0 + beta1*(bowl$week-mean(bowl$week))))
points(bowl$week,p_logit,pch="*")
legend("bottomleft",c("data","Bayes est"),pch=c("o","*"))
title("Katie's bowling improvement, Game2->Game3")

#  end of program