Homework Problem 25, Due Wednesday May 7.
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Access the data "Rubber" from the MASS library within R. 
This dataset has 3 variables: loss (the amount of rubber wear, 
the response variable) and two predictors, "hard" and "tens".

The objective of this exercise is to compare the predictive 
success of different methods of "predicting" above-median 
rubber-loss (ie, loss > 165).

(i) Develop three methods of predicting above-median rubber loss from
the variables "hard" and "tens":
--- using a linear-regression model (normal errors)
--- using a logistic regression model
--- using a nonparametric regression model (kernel density estimator
with a single bandwidth b=40) for "loss" as a function of the 
linear-regression fitted linear combination of "hard" and "tens". 

You should code a function which does the model-fitting and defines 
predictions based on a dataset of the same structure as "Rubber", but
with size n between 25 and 30. Note that each prediction method is 
an algorithm mapping the dataset to a logical vector of the same 
size n (where T corresponds to "> 165" and F to "<= 165"). For
convenience, you should probably write your function to calculate the
numbers or proportions of correct predictions on a test dataset input
to the same function.

(ii) Do a small cross-validation study (say, of 1000 replications), 
by repeatedly leaving out 5 observations chosen at random from the
original dataset of 30, designed to estimate the accuracy of
prediction of [loss > 165] by each of the three prediction methods 
you developed in (i).