Refer to the Presidential election data in Section 10.4.3.

a. Use a Bayesian approach to fit model (10.7), with independent N(0, 100)

priors for {????i}. Find corresponding estimates of {????i}, and evaluate their performance by finding the MSE and comparing with the ordinary sample proportions.

b. Use a Bayesian approach to fit model (10.7), taking the population percentage qi voting for Obama in the 2008 election (shown in the data file)

as prior information by using a N[logit(qi), 1] prior for ????i in model (10.7).

Find corresponding estimates of {????i}, and compare their MSE with the values in (a).