Remember that in regression
we have a dependent variable that we try to explain using
one or more predictor (independent) variables. In the example used
in this chapter, we wish to explain why and how customers buy more
or fewer services by looking at predictors such as satisfaction and
trust. This is desirable either because such explanation has intrinsic
value to our analysis, or because explaining it helps us to predict the
dependent variable in the future.
What do we mean by “explaining”
a dependent variable? This question is at the absolute heart of understanding
regression.
Saying that the aim
is to explain the dependent variable (sales) is all very well, but
exactly what do we want to
explain about it? In fact, in regression what we are trying to explain
is why, when or how the dependent variable occurs
at different levels, in other words why, when
and how it spreads away from the center. Why do some customers have
high sales, while some have low or medium sales?
In other words, in regression
our aim is to explain the spread of the dependent variable. Precisely,
we want to explain the statistical variance of the dependent variable
based on given levels of independent variables.
Remember, the variance is
the standard deviation squared. Therefore, if the dependent variable
has a variance of 120, we want to see if other variables can explain
this spread, that is, accurately explain when one observation will
be low, another medium, and another high on the dependent variable.
A second question is
how we phrase the effects of an independent variable on the dependent
variable. What we wish to be able to say is that when the independent
variable increases by 1 unit
in whatever metric it is measured, the dependent variable changes
by so-many of its units.
For example, we want
to be able to say something like “if trust increases by 1 unit
(an increase of 1 unit in the independent variable) then the dependent
variable Sales is expected to increase by $203,764.” (This
is only an example; the actual association measure might be bigger
or smaller than this.)