Chapter Preview. A regression analyst collects data, selects a model and then reports on the findings of the study, in that order. This chapter considers these three topics in reverse order, emphasizing how each stage of the study is influenced by preceding steps. An application, determining a firm’s characteristics that influence its effectiveness in managing risk, illustrates the regression modeling process from start to finish.
Studying a problem using a regression modeling process involves a substantial commitment of time and energy. One must first embrace the concept of statistical thinking, a willingness to use data actively as part of a decision making process. Second, one must appreciate the usefulness of a model that is used to approximate a real situation. Having made this substantial commitment, there is a natural tendency to “oversell” the results of statistical methods such as regression analysis. By overselling any set of ideas, consumers eventually become disappointed when the results do not live up to their expectations. This chapter begins in Section 6.1 by summarizing what we can reasonably expect to learn from regression modeling.
Models are designed to be much simpler than relationships among entities that exist in the real world. A model is merely an approximation of reality. As stated by George Box (1979), “All models are wrong, but some are useful.” Developing the model, the subject of Chapter 5, is part of the art of statistics. Although the principles of variable selection are widely accepted, the application of these principles can vary considerably among analysts. The resulting product has certain aesthetic values and is by no means predetermined. Statistics can be thought of as the art of reasoning with data. Section 6.2 will underscore the importance of variable selection.
Model formulation and data collection form the first stage of the modeling process. Students of statistics are usually surprised at the difficulty of relating ideas about relationships to available data. These difficulties include a lack of readily available data and the need to use certain data as proxies for ideal information that is not available numerically. Section 6.3 will describe several types of difficulties that can arise when collecting data. Section 6.4 will describe some models to alleviate these difficulties.