Linear Regression as a Classifier

We covered linear regression in the context of predicting continuous variable output in the previous chapter, but it can also be used to predict the class that a set of data is a member of. Linear regression classifiers are not as powerful as other types of classifiers that we will cover in this chapter, but they are particularly useful in understanding the process of classification. Let's say we had a fictional dataset containing two separate groups, Xs and Os, as shown in Figure 4.1. We could construct a linear classifier by first using linear regression to fit the equation of a straight line to the dataset. For any value that lies above the line, the X class would be predicted, and for any value beneath the line, the O class would be predicted. Any dataset that can be separated by a straight line is known as linearly separable, which forms an important subset of data types in machine learning problems. While this may not be particularly helpful in the...