PREDICTIVE
MARKETING
ANALYSIS FOR
A SPORTING
GOODS MANUFACTURER
We’re
looking for a
professional consultant
who can help us
forecast sales
volume based on
the manipulation
of marketing variables
such as advertising
and the number
of outside sales
representatives. We
also need to assess
the contribution
of these variables
in terms of their
effect on sales. How
can ARI help us? Please
give an example.
A
well known sporting
goods manufacturer
contacted ARI because
they wanted to develop
a model which would
help
them predict sales
volume based on
the manipulation
of advertising expenditures
and
the number of employees
working in a sales
territory. An
approach based
on regression
analysis
was utilized because
the client was
interested in
the relationship
between sales and
marketing variables
which were frequently
manipulated by the
company.
Regression
analysis is based
on a procedure for
deriving a mathematical
relationship in
the form of an equation
between
a single dependent
variable and one
or more independent
variables. The
equation used to
predict sales based
on advertising
and the number
of employees working
in a sales territory
is shown below.
y = a + b_{1}x_{1} + b_{2}x_{2}
Where:
y =
sales, the dependent
variable
a =
the intercept
x_{1} =
advertising, an
independent variable
x_{2} =
number of employees,
an independent variable
b_{1} =
the slope for independent
variable x_{1}
b_{2} =
the slope for independent
variable x_{2}
Advertising
and the number of
employees working
in a sales territory
are the independent
variables and they
are represented
by x_{1} and x_{2} in
this equation. The
intercept, a,
is the point on
the yaxis
that the regression
line hits when x =
0. The slope, b,
is the change in
sales for any 1unit
change in x_{1} and x_{2}. In
this context the
terms independent
and dependent are
arbitrary designations
because this is
not a casual relationship. In
other words, there
is no causeandeffect
relationship between
the dependent
and independent
variables.
Unlike
other consulting
projects, a survey
was not needed because
relevant
marketing data was
archived by the company. The
matrix shown below
was compiled from
sales records within
the company’s
management information
system.
TERRITORY

SALES
($
Thousands)
y

ADVERTISING
($
Hundreds)
x1

NUMBER
OF
SALES
REPS
x2

1

81

27

2

2

94

92

2

3

110

103

4

4

125

115

5

5

90

94

1

6

84

79

1

7

112

105

4

8

99

94

2

9

93

85

2

10

78

54

3

11

114

106

4

12

132

120

6

13

129

118

5

14

79

75

1

15

97

77

3

In
most cases the
slope and intercept
are unknown,
therefore they
must be estimated
with separate
equations. These
formulas are
complex, however
the slope and
intercept can
be automatically
calculated with
statistical software
using data from
the matrix shown
above. The
values for these
parameters are
shown below
in the coefficients
column.

Coefficients

Std.
Error

Beta

t

Sig.

Constant

49.36

4.46


11.07

0.000

Advertising

0.35

0.06

0.48

5.76

0.000

Sales
Reps

6.84

0.95

0.60

7.23

0.000

ARI
understands that
many marketing
managers are
not statistically
orientated, therefore
an interpretation
of this needs
to be offered
in plain English. The
computer has
estimated the
intercept and
slope for advertising
and number of
sales representatives. These
are the independent
variables. In
this example,
.35 denotes
the change
in
sales per unit
change in advertising
when number
of sales representatives
is held constant.
Similarly
6.84 denotes
the change in
sales per unit
change in number
of sales representatives
when advertising
is held constant. The
estimated intercept
is 49.36. This
is the predicted
value of sales
when the independent
variables equal
zero. The t values,
shown in the
third column,
are used to
test the statistical
significance
of the relationship
between sales
and the independent
variables;
advertising
and number
of
sales representatives. The t value
is calculated
by dividing
the slope
by
the standard
error. i.e.
6.84/.95
= 7.23. This
number is
greater
than the
critical
value from
the t distribution
which is
used
to reject
or
not reject
the null
hypothesis. The
null hypothesis
implies that
there is
no
linear relationship
between sales
and the independent
variables.
Since
7.23 is greater
than 2.16 (2.16
is the critical
value from the t distribution)
the null hypothesis
for advertising
was rejected. In
other words,
there is a significant
linear relationship
between number
of sales representatives
and sales. The t value
for advertising
also exceeds
2.16
which means
that it is
also
a statistically
significant
variable. The
Sig. abbreviation
in the far
right column
is also a measure
of statistical
significance. Values
less than
.05 are statistically
significant. In
this example
the Sig.
values for
both variables
are 0.00,
hence they
are statistically
significant.
Advertising
and number of
sales representatives
were shown to
be statistically
significant however
the client
also wanted to
determine the relative
importance of
these variables
on sales. Focus
your attention
on the beta values
in the fourth
column of the
table. Since
most independent
variables are
measured with
different units,
specialized
computer software
was used to automatically
standardize
these values
which enabled
the client to
make direct comparisons
between advertising
and size of sales
force. The
larger the
absolute value
of the beta
number, the
more relative
importance
it assumes in
predicting the
dependent variable. Thus
number of sales
representatives
has a greater
effect on sales
than advertising.
The
equation for
predicting sales
based on advertising
expenditures
and number of
sales representatives
is shown below.
y =
49.36 + .35x_{1} +
6.84x_{2}_{ }
How
can you use
this equation
to make a marketing
decision? Imagine
you’re
the marketing
director for
the sporting
goods manufacturer
and you’re
faced with declining
sales in a western
territory. Should
you hire additional
sales people
or increase your
advertising budget? How
might sales be
affected in territory
one if you hired
two additional
sales reps and
tripled your
advertising budget? The
numbers in parenthesis
represent proposed
changes.
y =
49.36 + .35(81)
+ 6.84(4)
y =
49.36 + 28.35
+ 27.36
y =
105.07
The
calculated prediction
is about $105,000
assuming you
manipulate the
variables as
indicated. What
if you wanted
to make some
changes in the
opposite direction? In
other words,
what might you
expect if you
reduced the advertising
budget in territory
twelve from $12,000
to $7,500 and
transferred one
sales rep from
the same territory
to a different
region? The
same equation
can be used
to make the sales
prediction and
it is shown
below.
y =
49.36 + .35(7.5)
+ 6.84(5)
y =
86.19
Regression
analysis is
a powerful tool
within the realm
of predictive
research because
it can be utilized
for many marketing
applications. In
addition to sales,
regression analysis
can be used to
predict satisfaction,
likelihood of
brand purchase
and consumer
loyalty. In
spite of this, predictions
derived from
regression analysis
do not imply
causality because
this statistic
is an extension
of a correlation. Finally
regression analysis
should not be
used to make
predictions
outside the boundaries
of the data
used to develop
the equation. In
other words,
advertising
values between
$2,700 and $12,000
offer the greatest
validity.
What
you have just
read is a brief example of
applied marketing
research.
The
data shown in
the matrix is
fictitious. ARI
will never reveal
the identity
of a client
or the actual
results of a
project under
any circumstances
without a client’s
consent. This
example was
developed
to help potential
clients fathom
an application
of regression
analysis which
might be useful
to their profession.