CHAPTER 13 Simple Linear Regression

514 CHAPTER THIRTEEN Simple Linear Regression
FIGURE 13.2
Examples of types
of relationships found
in scatter plots
Y
Y
Panel A
Positive linear relationship
X
Panel B
Negative linear relationship
X
Y
Y
X
Panel C
Positive curvilinear relationship
Y
X
Panel D
U-shaped curvilinear relationship
Y
X
Panel E
Negative curvilinear relationship
X
Panel F
No relationship between X and Y
decreases as the individual becomes more proficient at the task, but then it increases beyond a
certain point because of factors such as fatigue and boredom.
Panel E indicates an exponential relationship between X and Y. In this case, Y decreases
very rapidly as X first increases, but then it decreases much less rapidly as X increases further.
An example of an exponential relationship could be the resale value of an automobile and its
age. In the first year, the resale value drops drastically from its original price; however, the
resale value then decreases much less rapidly in subsequent years.
Finally, Panel F shows a set of data in which there is very little or no relationship between
X and Y. High and low values of Y appear at each value of X.
In this section, a variety of different models that represent the relationship between two
variables were briefly examined. Although scatter plots are useful in visually displaying the
mathematical form of a relationship, more sophisticated statistical procedures are available to
determine the most appropriate model for a set of variables. The rest of this chapter discusses
the model used when there is a linear relationship between variables.
13.2 DETERMINING THE SIMPLE LINEAR REGRESSION EQUATION
In the Using Statistics scenario on page 512, the stated goal is to forecast annual sales for all
new stores, based on store size. To examine the relationship between the store size in square feet
and its annual sales, a sample of 14 stores was selected. Table 13.1 summarizes the results for
these 14 stores, which are stored in the file site.xls.