The Marketing Book 5th Edition

B

A

C

Education

Gender

Wage level

Quantitative methods in marketing 209

Many variables can be added to a regres-
sion analysis. We merely add more terms into
the model. A multiple OLS regression model
with k variables can be represented by the
equation:

Y=+ 1 X 1 + 2 X 2 + 3 X 3 + 4 X 4

+... + kXk+

In the above equation, the variable Yis

predicted using information from all of the X

variables. This could be wages predicted by

gender, education, type of work, location,

experience, etc. The effect that each variable has

on wage is assessed whilst controlling for all

other variables. The output from an OLS

regression is given in Tables 9.2 and 9.3, and

shows how such a model can be interpreted.

Which data can be used in OLS regression?

OLS regression can be used to model response

variables (Yvariables) which are recorded on at

least an interval scale (i.e. continuous variables

such as age, output and wages). Explanatory

variables (the Xvariables) can be continuous or

ordered and unordered categorical data pro-

vided that they are coded appropriately). In

short, OLS regression is used to model con-

tinuous data from all other types of data.

Conclusions

 OLS regression uses linear equations, as these

are relatively easy to formulate and work with.

 Non-linear relationships can be modelled using

linear equations if transformations are applied

to the data.

Single regressions:
Wage level
=a +  Education
Area = A + B:R^2 = 0.76

Wage level = a + Gender
Area = B + C:R^2 = 0.47

Multivariate regression:

Wage level

=a +  1 Education =  2 Gender

Area = A + B + C:R^2 = 0.79

Figure 9.6 Venn diagram representing multivariate
OLS regression

Table 9.2 ANOVAa

Model Sum of

squares

df Mean

square

F Sig.

1 Regression 123.581 8 15.448 9.919 0.000b

Residual 722.617 464 1.557

Total 846.199 472

aDependent Variable: SSAT.

bPredictors (Constant): SH_TESC, REGR factor score 3 for analysis 1, REGR factor score 2 for analysis 1,

SH_SOLO, SH_ASDA, REGR factor score 4 for analysis 1, REGR factor score 1 for analysis 1, SH_SAINS.