#read in just first sixteen rows
cards=read.table("cards.txt",header=T,nrows=16)
#re-code the throwers to be numeric
cards$thr=-1*(cards$thrower=="Valerie")+1*(cards$thrower=="Thy")
attach(cards)
#plot main effects
par(mfrow=c(2,2))
boxplot(dis~angle,ylab="distance",xlab="angle")
boxplot(dis~vel,ylab="distance",xlab="velocity")
boxplot(dis~grip,ylab="distance",xlab="grip")
boxplot(dis~thr,ylab="distance",xlab="thrower")
par(mfrow=c(1,1))
#find effects
2*coef(lm(dis~angle*vel*grip*thr))
#how can we tell which are significant?  
#first try assuming all third and higher order intractions are zero
# (these are elements 12-16 of the coefficient vector)
cards.se=sqrt(mean((2*coef(lm(dis~angle*vel*grip*thr))[12:16])^2))
cards.se
cards.se*qt(.975,5)
#another possible assumption is that most of the effects are zero
qqnorm(2*coef(lm(dis~angle*vel*grip*thr))[2:16])
qqline(2*coef(lm(dis~angle*vel*grip*thr))[2:16])
sort(2*coef(lm(dis~angle*vel*grip*thr))[2:16])


#fitted model is  dis = 84.7 + 27.8*angle + 37.1*thr + 27.7*angle*thr
#fitted value for Thy throwing at a high angle:  84.7+27.8+37.1+27.7=177.3
#fitted value for Valerie throwing at high angle: 84.7+27.8-37.1-27.7=47.7
#all fitted values
fitted(lm(dis~angle*thr))
#basically we can't see a significant difference in how Valerie throws cards,
# but Thy throws them much better at a higher angle