CHAPTER 13 Simple Linear Regression

512 CHAPTER THIRTEEN Simple Linear Regression
Using Statistics @ Sunflowers Apparel
The sales for Sunflowers Apparel, a chain of upscale clothing stores for
women, have increased during the past 12 years as the chain has
expanded the number of stores open. Until now, Sunflowers managers
selected sites based on subjective factors, such as the availability of a
good lease or the perception that a location seemed ideal for an apparel
store. As the new director of planning, you need to develop a systematic
approach that will lead to making better decisions during the site selection
process. As a starting point, you believe that the size of the store significantly
contributes to store sales, and you want to use this relationship
in the decision-making process. How can you use statistics so that you
can forecast the annual sales of a proposed store based on the size of that
store?
In this chapter and the next two chapters, you learn how regression analysis enables you to
develop a model to predict the values of a numerical variable, based on the value of other
variables.
In regression analysis, the variable you wish to predict is called the dependent variable.
The variables used to make the prediction are called independent variables. In addition to
predicting values of the dependent variable, regression analysis also allows you to identify the
type of mathematical relationship that exists between a dependent and an independent variable,
to quantify the effect that changes in the independent variable have on the dependent
variable, and to identify unusual observations. For example, as the director of planning, you
may wish to predict sales for a Sunflowers store, based on the size of the store. Other examples
include predicting the monthly rent of an apartment, based on its size, and predicting the
monthly sales of a product in a supermarket, based on the amount of shelf space devoted to the
product.
This chapter discusses simple linear regression, in which a single numerical independent
variable, X, is used to predict the numerical dependent variable Y, such as using the size of a
store to predict the annual sales of the store. Chapters 14 and 15 discuss multiple regression
models, which use several independent variables to predict a numerical dependent variable, Y.
For example, you could use the amount of advertising expenditures, price, and the amount of
shelf space devoted to a product to predict its monthly sales.
13.1 TYPES OF REGRESSION MODELS
In Section 2.5, you used a scatter plot (also known as a scatter diagram) to examine the relationship
between an X variable on the horizontal axis and a Y variable on the vertical axis. The
nature of the relationship between two variables can take many forms, ranging from simple to
extremely complicated mathematical functions. The simplest relationship consists of a straightline,
or linear relationship. An example of this relationship is shown in Figure 13.1.