### Bootstrap Regression Coefficients

### Example:  The hormone data.  Amount in milligrams of anti-inflammatory hormone 
### remaining in 27 devices, after a certain number of hours of wear.  The devices 
### were sampled from 3 different manufacturing lots, called 1, 2, 3.  Lot 3 looks 
### like it had greater amounts of remaining hormone, but it also was worn the least
### number of hours.  

x <- c(1,99,25.8, 
				1,152,20.5,
				1,293,14.3, 
				1,155,23.2, 
				1,196,20.6, 
				1,53,31.1, 
				1,184,20.9, 
				1,171,20.9, 
				1,52,30.4,
				2,376,16.3, 
				2,385,11.6, 
				2,402,11.8, 
				2,29,32.5, 
				2,76,32,
				2,296,18, 
				2,151,24.1, 
				2,177,26.5, 
				2,209,25.8, 
				3,119,28.8, 
				3,188,22, 
				3,115,29.7, 
				3,88,28.9, 
				3,58,32.8, 
				3,49,32.5, 
				3,150,25.4,
				3,107,31.7, 
				3,125,28.5)

H <- matrix(x, ncol=3, byrow=T)		# create data matrix

# create the variables

lot <- H[,1]
hrs <- H[,2]
amount <- H[,3]

# plot the data ignoring lot

plot(amount,hrs)

# fit the linear model hrs = a + b*amount + e

hormone <- data.frame(hrs,amount)

H.lm <- lm(amount ~ hrs, hormone)
summary(H.lm)

# bootstrap the linear model

hormone.boot <- bootstrap(hormone, coef(lm(amount ~ hrs, hormone))
summary(hormone.boot)
plot(hormone.boot)

# Next, the jackknife after the bootstrap is used to assess the accuracy of the3 standard 
# error estimates, and the influence of each observation on these estimates.

hormone.jack <- jack.after.bootstrap(hormone.boot,"SE")
hormone.jack
plot(hormone.jack)