 What Is Statistical Learning?
In order to motivate our study of statistical learning, we begin with a
simple example. Suppose that we are statistical consultants hired by a
client to provide advice on how to improve sales of a particular product. The
Advertising data set consists of the sales of that product in 200 different
markets, along with advertising budgets for the product in each of those
markets for three different media: TV, radio, and newspaper. The data are
displayed in Figure 2.1. It is not possible for our client to directly increase
sales of the product. On the other hand, they can control the advertising
expenditure in each of the three media. Therefore, if we determine that
there is an association between advertising and sales, then we can instruct
our client to adjust advertising budgets, thereby indirectly increasing sales.
In other words, our goal is to develop an accurate model that can be used
to predict sales on the basis of the three media budgets.
In this setting, the advertising budgets are input variables while sales input
is an output variable. The input variables are typically denoted using the variable
output
variable symbol X, with a subscript to distinguish them. So X1 might be the TV
budget, X2 the radio budget, and X3 the newspaper budget. The inputs
go by different names, such as predictors, independent variables, features, predictor
independent
variable
feature
or sometimes just variables. The output variable—in this case, sales—is
variable
often called the response or dependent variable, and is typically denoted
response
dependent
variable
using the symbol Y . Throughout this book, we will use all of these terms
interchangeably.