# body fat interaction effect example
w <- c(89,88,66,59,93,73,82,77,100,67,57,68,69,59,62,59,56,66,72) 
f <- c(28,27,24,23,29,25,29,25,30,23,29,32,35,31,29,26,28,33,33) 
m <- c(rep(0,10),rep(1,9)) 
dat <- data.frame( weight=w , fat=f , male=m ) 

# model that ignores sex 
m <- lm( weight ~ fat , data = dat ) 
plot( dat$weight ~ dat$fat , cex=2 , pch=ifelse(dat$male==1,16,1) ) 
abline(m,col="red") 

# model that includes sex as main effect 
m2 <- lm( weight ~ fat + male , data = dat ) 
plot( dat$weight ~ dat$fat , cex=2 , pch=ifelse(dat$male==1,16,1) ) 
abline( a=coefficients(m2)[1] , b=coefficients(m2)[2] ,col="red") # female line 
abline( a=coefficients(m2)[1] + coefficients(m2)[3] , b=coefficients(m2)[2] ,col="red")

# model that includes interaction 
m3 <- lm( weight ~ fat*male , data = dat ) 
plot( dat$weight ~ dat$fat , cex=2 , pch=ifelse(dat$male==1,16,1) ) 
abline( a=coefficients(m3)[1] , b=coefficients(m3)[2] ,col="red") # female line 
abline( a=coefficients(m3)[1] + coefficients(m3)[3] , b=coefficients(m3)[2] + 
coefficients(m3)[4] ,col="red") # male line 


# age at death example transformation
age <- rexp( 600 , rate=0.1 )
hist(age , xlab="age at death")
lines( c(mean(age),mean(age)) , c(0,250) , col="red" )
hist( log(age) , xlab="log(age at death)")
lines( c(mean(log(age)),mean(log(age))) , c(0,250) , col="red" )

male <- c( rep(0,300) , rep(1,300) )
age <- c( rexp(300,rate=0.08) , rexp(300,rate=0.11) )
boxplot(age~male,xlab="male",ylab="age at death")
boxplot(log(age)~male,xlab="male",ylab="log(age at death)")

# fit model
m <- lm( log(age) ~ male )
summary(m)

# convert coef back to probability scale
exp( coef(m)['male'] )

# works for confidence intervals too
exp( confint(m)['male',] )