The Marketing Book 5th Edition

210 The Marketing Book

 When there are a number of factors affecting
the variable we wish to model, a multiple
regression can be used.
 Response variables need to be interval, but
with appropriate coding, any explanatory
variables can be included.

Logistic regression

Quite often we may wish to model a binary
variable, such as male–female, etc. For such
analyses, it is not appropriate to use OLS
regression as the data are not linear – we have
to use logistic regression.
Similar to OLS regression, a whole range of
useful statistics can be computed, including
standard errors, confidence and prediction
intervals. We are not limited by the traditional
statistics which can only provide group
comparisons.

The logistic regression model

As with OLS regression, we can use any
number of explanatory variables, variables
which can be interval or categorical. The same

considerations apply to the data as with mul-

tiple OLS regression. All the power that is

available in traditional OLS regression is also

available in logistic regression – there should be

no need to ever compute a test which assesses

group differences (t-test, Mann–Whitney, Wil-

coxon, ANOVA, etc.).

The basic form of the model is identical to

OLS regression. The only difference is in the

interpretation of the parameters. A logistic

regression can be represented as:

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

+... + kXk+

An example of a logistic regression

The data in Tables 9.4–9.6 are taken from a

recent study into consumer behaviour. The

variables have been selected for the purpose of

demonstration and not to provide a ‘good’

model.

Conclusions

 Binary response variables have a non-linear

S-shaped distribution.

Table 9.3 Coefficientsa

Model Unstandardized coefficients

B Std. Error

Standardized

Coefficients

Beta

t Sig.

1 (Constant) 4.888 0.102 48.115 0.000

Quality 0.308 0.061 0.234 5.017 0.000

Other Services –3.06E-03 0.062 –0.002 –0.050 0.961

Value brands 4.524E-03 0.059 0.003 0.077 0.939

Car facilities –3.44E-02 0.064 –0.026 –0.534 0.594

SH_ASDA 0.851 0.277 0.142 3.076 0.002

SH_SAINS 0.795 0.214 0.178 3.710 0.000

SH_SOLO 9.928E-02 0.253 0.018 0.393 0.694

SH_TESC 0.725 0.137 0.270 5.297 0.000

aDependent Variable: SSAT.