1. The empirical illustration in Chapter 3 (Section 3.9) used the Normal linear regression model with natural conjugate prior with the house price data set.

Please refer to this illustration for data definitions.

(a) Use the house price data set and the partial linear model to investigate whether the effect of lot size on house price is nonlinear. Experiment with different priors (including empirical Bayes methods).

(b) Calculate the Bayes factor comparing the partial linear model to the Normal linear regression model for this data set.

(c) Carry out a prior sensitivity analysis to investigate how robust your answer in part

(b) is to prior choice.