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Book 78

This chapter discusses linear regression, a fundamental supervised learning method used for predicting quantitative responses. It emphasizes the importance of understanding linear regression as a foundation for more complex statistical learning techniques. The chapter also explores the relationship between advertising budgets and sales, highlighting key questions to assess the effectiveness of advertising expenditures.

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Book 78

This chapter discusses linear regression, a fundamental supervised learning method used for predicting quantitative responses. It emphasizes the importance of understanding linear regression as a foundation for more complex statistical learning techniques. The chapter also explores the relationship between advertising budgets and sales, highlighting key questions to assess the effectiveness of advertising expenditures.

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Linear Regression

This chapter is about linear regression, a very simple approach for super-
vised learning. In particular, linear regression is a useful tool for predicting
a quantitative response. It has been around for a long time and is the topic
of innumerable textbooks. Though it may seem somewhat dull compared to
some of the more modern statistical learning approaches described in later
chapters of this book, linear regression is still a useful and widely used sta-
tistical learning method. Moreover, it serves as a good jumping-off point for
newer approaches: as we will see in later chapters, many fancy statistical
learning approaches can be seen as generalizations or extensions of linear
regression. Consequently, the importance of having a good understanding
of linear regression before studying more complex learning methods cannot
be overstated. In this chapter, we review some of the key ideas underlying
the linear regression model, as well as the least squares approach that is
most commonly used to fit this model.
Recall the Advertising data from Chapter 2. Figure 2.1 displays sales
(in thousands of units) for a particular product as a function of advertis-
ing budgets (in thousands of dollars) for TV, radio, and newspaper media.
Suppose that in our role as statistical consultants we are asked to suggest,
on the basis of this data, a marketing plan for next year that will result in
high product sales. What information would be useful in order to provide
such a recommendation? Here are a few important questions that we might
seek to address:

1. Is there a relationship between advertising budget and sales?


Our first goal should be to determine whether the data provide evi-
dence of an association between advertising expenditure and sales. If
the evidence is weak, then one might argue that no money should be
spent on advertising!

© Springer Nature Switzerland AG 2023 69


G. James et al., An Introduction to Statistical Learning, Springer Texts in Statistics,
https://doi.org/10.1007/978-3-031-38747-0_3

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