Homework 16. Due IN CLASS Friday Nov.11.
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Enter the data from 

http://www-users.math.umd.edu/~evs/s430.old/Data/cigcanc.dat

into an R data.frame. The data concern various cancer 
incidence rates and levels of cigarette smoking from some 
years ago, by state. Take LUNG cancer rates as the desired 
response variable, and the others as predictors.

A simple forward stepwise analysis shows that  LUNG ~ CIG + BLAD
is the best simple model.

(a) Set up a Bayesian analysis for a normal linear regression model
based on these data: define a prior for the rho = 1/sigma^2  and 
nu = beta-coeff/sigma^2 parameters, as in the BayesConjug.pdf
Lecture-notes file (as close to "noninformative" as you like).

Find the posterior mean of the vector of coefficient estimators 
beta for your regression.

(b) For the Bayesian analysis you set up in part (a), find 
the posterior probability that the CIG and BLAD parameters
simultaneously lie within their frequentist 95% confidence intervals
CIG in (0.13056, 0.57282)  and  BLAD in (0.17891, 2.73342).

(c) Find and plot a histogram of the predictive maximum absolute
standardized residual from a dataset of the same size (n=44) 
simulated with the same predictors (X_CIG,X_BLAD) as the 
cigcanc.dat  dataset. (Do this based on a Bayesian predictive 
posterior simulation of 1000 datasets.)