Database Reference
In-Depth Information
the speciic relationship is between the two variables. So, we now introduce Regres-
sion Analysis, which will determine the best itting slope and intercept of this linear
relationship based on the data. Using the scenario from this chapter, it will tell us,
for example, how much an increased assessment of the usefulness of the ability to
perform a Boolean search, say by one unit, will increase the likelihood of adoption
of the search engine.
Onward!
9.4
LINEAR REGRESSION
The fundamental purpose of regression analysis and correlation analysis is to study
the relationship between a “dependent variable” (which can be thought of as an
output
variable) and one or more “independent variables” (which can be thought
of as
input
variables). In this chapter, we will have one independent variable—
this form of regression is called “simple regression”; in the next chapter, we will
have several input/independent variables (i.e., X's)—this will be called “multiple
regression.”
Let's return to the illustrative data set we used in the correlation section. This
data set is shown in
Table 9.2
, but, for convenience, we repeat it in
Table 9.3
. We will
illustrate the principles of regression analysis using this data set and then apply the
methodology to the Behemoth.com data.
We traditionally refer to the “Y” as the
dependent variable
, and the “X” as the
independent variable
. In fact, you shall see that SPSS uses those terms.
Let us consider a straight-line (i.e., “linear”) relationship between the two vari-
ables in
Table 9.3
. We usually start off considering a straight-line relationship irst,
unless the (Y, X) graph of the data points (similar to the graphs in
Figure 9.1
)
strongly indicates that the relationship is clearly curved. The graph of the data in
Table 9.3
is in
Figure 9.13
. The graph in
Figure 9.13
is referred to as a “scatter
diagram.”
It is evident that a straight line its the data pretty well, and that there is no mean-
ingful indication of curvature. In
Figure 9.14
, we add a line that, intuitively, its the
data well.
Thus, we can pretty safely consider a straight-line relationship between X
and Y, and not be concerned about more complex relationships. In fact, let us
Table 9.3
Illustrative Data
Y
X
5
4
4
4
2
1
3
3
4
3
Search WWH ::
Custom Search