A Short Tour of the Predictive Modeling Process

The fueleconomy.gov web site, run by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy and the U.S. Environmental Protection Agency, lists different estimates of fuel economy for passenger cars and trucks. For each vehicle, various characteristics are recorded such as the engine displacement or number of cylinders. Along with these values, laboratory measurements are made for the city and highway miles per gallon (MPG) of the car. In practice, we would build a model on as many vehicle characteristics as possible in order to find the most predictive model. However, this introductory illustration will focus high-level concepts of model building by using a single predictor, engine displacement (the volume inside the engine cylinders), and a single response, unadjusted highway MPG for 2010–2011 model year cars. The first step in any model building process is to understand the data, which can most easily be done through a graph. Since we have just one predictor and one response, these data can be visualized with a scatter plot (Fig. 2.1). This figure shows the relationship between engine displacement and fuel economy. The “2010 model year” panel contains all the 2010 data while the other panel shows the data only for new 2011 vehicles. Clearly, as engine displacement increases, the fuel efficiency drops regardless of year. The relationship is somewhat linear but does exhibit some curvature towards the extreme ends of the displacement axis.