Homework Problem 26, Due Monday May 12.
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Use the data "Rubber" from the MASS library within R, 
together with your prediction methods developed from the
last HW. 

Do a small bootstrap study (preferably of many more than 1000
replications) designed to find a 95% confidence interval for the 
probability  P(loss > 165 | hard, tens)  by each of your three methods
in (i) from HW 25, for several (say, the first 5) of the (hard, tens)
combinations actually occurring in the data. There are a few different
ways to do such a study. Do the study TWO DIFFERENT WAYS chosen from
among the following: 
     (a) bootstrap the triples (loss, hard, tens) directly (ie,
directly sample with replacement from the set of 30 triples); OR
     (b) do a parametric bootstrap of the data, by simulating 
with replacement from only the pairs (hard, tens) and generating the
additive regression errors from the normal linear regression model
with parameters fitted to the dataset of all 30 points; OR
     (c) form the residuals from the linear regression model (fitted
to the original dataset), and bootstrap them (ie repeatedly select
with replacement), each time adding them back to the orginal
linear-regression predictors to get a `pseudo-data' sample 
(pseudo-loss, hard, tens) of size 30 on which you can check the
behavior of your prediction methods in (i).