Linear classification
The linear regression model discussed so far assumes a quantitative response variable. In this section, we will focus on approaches to modeling qualitative output variables for inference and prediction, a process that is known as classification and that occurs even more frequently than regression in practice.
Predicting a qualitative response for a data point is called classifying that observation because it involves assigning the observation to a category, or class. In practice, classification methods often predict probabilities for each of the categories of a qualitative variable and then use this probability to decide on the proper classification.
We could approach this classification problem by ignoring the fact that the output variable assumes discrete values, and then applying the linear regression model to try to predict a categorical output using multiple input variables. However, it is easy to construct examples where this method performs very...
