# week 4 exercises
# perform AIC on data from previous week

# class data
h <- c( 5*12+11  , 69 , 5*12+8 , 62,5*12+11,72,5*12+8,69,75,71,61,61,62,5*12+11 , 68,70,74,5*12+2,67,65.75 , 76 , 69 , 65 , 67 , 5*12+4 , 5*12+8 , 68 , 75 )

w <- c( 135,165,165,120,220,170,150,165,245,160,110,136,112,195,150,155,200,137,160,150,225,140,128,150,130,140,145,210 )

d <- data.frame( height=h , weight=w )

library(bbmle)

m0 <- lm( d$height ~ 1 )
m1 <- lm( d$height ~ d$weight )

plot( d$height ~ d$weight )
abline(m1)
abline(m0,col="red")

fakew <- sample( min(d$weight):max(d$weight) , 100 , replace=TRUE )

k0 <- coef(m0)
sd0 <- sd(residuals(m0))
hm0 <- rnorm( 100 , mean=k0["(Intercept)"] , sd=sd0 )

k1 <- coef(m1)
sd1 <- sd(residuals(m1))
hm1 <- rnorm( 100 , mean=k1["(Intercept)"] + k1["d$weight"] * fakew , sd=sd1 )
plot( hm1 ~ fakew , xlab="weight" , ylab="height" , pch=16 )
points( fakew , hm0 )

AICtab( m0 , m1 , base=TRUE , weights=TRUE )
AICctab( m0 , m1 , base=TRUE , weights=TRUE , nobs=28 )