The Marketing Book 5th Edition

Residual (error)

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X

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a(intercept)

b(regression coefficient)

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208 The Marketing Book

By way of an introduction we will begin with
OLS regression, a technique which is very
common and fairly easy to understand.

Ordinary least-squares regression

Simple OLS regression

Simple OLS regression attempts to represent
the relationship between two variables using a
line. This line is computed using the least-
squares method and provides a line of best fit.
For two variables, the OLS regression equation
is equivalent to Y=+X+(Figure 9.5).
Using this graph, we are able to define the
relationship between the two variables YandX,
and also how strong the relationship is.
The important thing to note from this
demonstration is that GLMs can be used to
model non-linear relationships even though
they are linear techniques. This makes the
techniques particularly useful in the social
sciences, where relationships are rarely linear.

Multivariate OLS regression

OLS regression can also be used when there are
more than two variables. It is important to be

able to include a number of variables into a

model, as more than one source of information

is often required to account for a particular

variable.

Take, for example, a situation where a

particular company employs on the basis of

educational achievement and not on the basis

of gender. If this company recruits in a region

where males and females do not have equal

access to education, it is likely that a simple

regression model that predicts wages from

gender will show a significant relationship

between the two. On the basis of this relation-

ship, it would appear that the company is

breaking the law, as it is paying different rates

to males and females. This conclusion might

be unjust in this case, as it is possible that it

is a bias in the provision of education that has

resulted in males being more highly educated

and, consequently, better paid. In this case, the

relationship between gender and wage is a

consequence of the relationship between gen-

der and education. To adequately model

wages, both pieces of information need to be

included in a model. Such a model can be

represented in the form of a Venn diagram

(Figure 9.6).

Figure 9.5 Plot of the OLS regression equation