4. Use the house price data set and the Normal linear regression model which is partly nonlinear and partly linear described in Exercise 2. You may use whatever prior you wish for þ andšprovided it is informative. Normal priors will be the most convenient.

(a) Using your results from Exercise 2, write and run a program for posterior simulation which allows for the explanatory variables lot size and number of bedrooms to have a nonlinear effect on house price. Assume the other explanatory variables enter linearly and f ./ has a CES form

(see (5.1)).

(b) Do posterior results indicate that lot size and number of bedrooms have a nonlinear effect on house price?

(c) Use the Savage–Dickey density ratio to calculate the Bayes factor for testing whether there is nonlinearity in the regression relationship (see the discussion at the beginning of Section 5.7).

(d) Re-do part

(d) using the Gelfand–Dey method.