The goal of a model is to provide a simple low-dimensional summary of a dataset. In the context of this book we’re going to use models to partition data into patterns and residuals. Strong patterns will hide subtler trends, so we’ll use models to help peel back layers of structure as we explore a dataset.
However, before we can start using models on interesting, real datasets, you need to understand the basics of how models work. For that reason, this chapter of the book is unique because it uses only simulated datasets. These datasets are very simple, and not at all interesting, but they will help you understand the essence of modeling before you apply the same techniques to real data in the next chapter.
There are two parts to a model:
First, you define a family of models that express a precise, but
generic, pattern that you want to capture. For example, the pattern
might be a straight line, or a quadatric curve. You will express the
model family as an equation like
y = a_1 * x + a_2 or
y = a_1 * x ^ a_2. Here,
y are known variables from your
a_2 are parameters that can vary to capture
Next, you generate a fitted model by finding the model from the
family that is the closest to your data. This takes the generic model
family and makes it specific, like
y = 3 * x + 7 or
y = 9 * x ^ 2.
It’s important to understand that a fitted model is just the closest model from a family of models. ...