First exercise for Mon Nov ¡­

First exercise for Mon Nov 24 (more to be posted here within a day or two):

Go to http://lib.stat.cmu.edu/DASL/Stories/cigcancer.html, access the data set to create data vectors x = CIG (number of cigarettes sold per capita) and y = LUNG (death rate per 100,000) for 44 American states. Carry out a Bayesian linear-normal regression analysis for y on x. For sigma, let 1/sigma^2 have a Gamma prior such that sigma has 0.10 and 0.90 quantiles equal to 1.0 and 5.0. For alpha and beta, let these for given sigma be independent normals N(15, (2.0 sigma)^2) and N(0, (2.0 sigma)^2). Give 95% credibility intervals for the three parameters. Display the predictive distribution for ynew associated with a different state that has cigarette consumption xnew = 45.00.

Re-do the analysis with a noninformative prior.