Data Modeling I – Basics

Abstract

In this chapter, we introduce methods for modeling data. We refer to these methods as “basics” since they form the foundation for many of the more advanced ideas and concepts discussed in later chapters. The most basic concept is that of a model itself. You may ask: “What is a model? And why do we need models at all?” We will give answers to these fundamental questions in Section 3.1. In Section 3.2, we will discuss linear regression models as one of the most widespread and versatile types of models. The name “linear” implies that we will discuss models that assume that the relationship follows a straight line. For instance, you may argue that the more you eat, the more weight you gain – and you may gain an additional pound of body weight for every pound of food that you eat. That’s exactly what we mean by a linear model: every unit of “input” has the same (proportional) impact on the “output.” If I eat 2 pounds of food, I will gain 2 pounds in body weight; and if I eat 4 pounds, I will gain 4 pounds of body weight, and so on – the relationship between input and output is always the same (1 to 1 in this case). You will quickly realize that while the concept of linear models is extremely powerful, it also has its limitations. For instance, do you really believe that the entire world follows linear relationships? If, for instance, human growth was linear and increased by the same rate every year, why is it that by the time we reach the age of 50, we are not 50 feet tall? In that sense, we will also discuss limitations of linear regression throughout this chapter. Some of these limitations will be addressed immediately, while others will be our motivation for more advanced methods discussed in subsequent chapters.