We will use the Energy efficiency dataset from the UCI Machine Learning repository for the illustration of Bayesian regression (reference 2 in the References section of this chapter). The dataset can be downloaded from the website at http://archive.ics.uci.edu/ml/datasets/Energy+efficiency. The dataset contains the measurements of energy efficiency of buildings with different building parameters. There are two energy efficiency parameters measured: heating load (Y1) and cooling load (Y2).

The building parameters used are: relative compactness (X1), surface area (X2), wall area (X3), roof area (X4), overall height (X5), orientation (X6), glazing area (X7), and glazing area distribution (X8). We will try to predict heating load as a function of all the building parameters using both ordinary regression and Bayesian regression, using the glm functions of the arm package. We will show that, for the same dataset, Bayesian regression gives significantly smaller prediction intervals.