ABSTRACT
DATA represents the basic scores or observations, usually but not always numerical, that we want to analyze. MODEL is a more compact description or representation of the data. Our data are usually bulky and of a form that is hard to communicate to others. The compact description provided by the model is much easier to communicate, say, in a journal article, and is much easier to think about when trying to understand phenomena, to build theories, and to make predictions. To be a representation of the data, all the models we consider will make a specific prediction for each observation or element in DATA. Models range from the simple (making the same prediction for every observation in DATA) to the complex (making differential predictions conditional on other known attributes of each observation). To be less abstract, let us consider an example. Suppose our data were, for each state in the United States, the percentage of households that had internet access in the year 2000; these data are listed in Exhibit 1.1. A simple model would predict the same percentage for each state. A more complex model might adjust the prediction for each state according to the age, educational level, and income of the state’s population, as well as whether the population is primarily urban or rural. The amount by which we adjust the prediction for a particular attribute (e.g., educational level) is an unknown parameter that must be estimated from the data.
