Proposal to Investigate the Dependence of New Car Sales on Advertising, Sales Force
and Incentives for Mark Twain Motors.
Darrell Freeman
Mark Twain Motors is a dealership serving the Greater Sacramento area(1). New car sales
are important to Mark Twain Motors, as 40 percent of revenue is generated by new car
sales. Other important sources of revenue include warranty service, which is follow on
service to new car purchases from Mark Twain and other dealers in the area, and used
car sales. Most cars taken in trade are wholesaled, but a select few are retained for resale
on the companies nearby used car lot.
Monthly data will be supplied by the dealership for NewCarSales in $ millions,
SalesForce (average number of sales people on the floor during the month), advertising
expenditures in $ 000 and indications of whether manufacturer incentives were on during
the month. Months in which new models were introduced were also flagged by the
dealership.
An initial model of the form,
NewCarSales = 0 + 1*Advertising + 2* SalesForce + 3*Incentives
is proposed. “Incentives” is a dummy variable having a value 0 everywhere except for
those months where incentives were offered by the manufacturer.
The initial model will be tried, inspected and adjusted until a final model is obtained.
Steps in generating and evaluating the model will be documented in the report of the
study results.
Mark Twain had a 50% increase in its sales force in month 28. It may be necessary to
model this jump in sales force as a “before and after” event. Management has also noted
a decrease in sales in those months immediately following termination of an incentive
program. This may need to be included in the model.
Mark Twain has a policy of increasing advertising just prior to and during incentive and
new model events in expectation of maximizing the benefit to the dealership of the
manufacturer sponsored events.
1. Data and analysis was constructed for instructional purposes only, and does not
represent an actual company.
The Dependence of New Car Sales on Advertising,
Sales Force and Incentives for Mark Twain Motors
Inspection of Sales Data
New car sales by month is shown for the period from Jan., 2000 through March, 2005 in
Figure 1. Two features stand out. First, the data is clearly trending upward. Secondly,
the data shows significant variability around the trend. Inspection of the data shows that
the peaks in sales are associated with manufacturers incentives. This can be seen by
comparing the peak months in Figure 1 with the incentive months in Figure 2.
Figure1
Time Series Plot for NewCarSales
NewCarSales
20
16
12
8
4
0
0
20
40
60
80
Figure 2
Time Series Plot for Incentives
Incentives
1
0.8
0.6
0.4
0.2
0
0
20
40
60
80
Trending in NewCarSales may be due to an underlying growth effect not included in the
model, such as population growth in the area, or expansion of the area served. To
investigate the trend the autocorrelation coefficients were computed for NewCarSales.
Results are shown in Figure 3.
Figure 3
Estimated Autocorrelations for NewCarSales
Autocorrelations
1
0.6
0.2
-0.2
-0.6
-1
0
4
8
12
16
20
24
lag
The autocorrelation coefficient is nearly 0.8 with a lag of one, suggesting that prior
period sales are a strong indicator of sales in the current period. A one period lag of
NewCarSales will likely be needed in the model.
To investigate the explanatory content of advertising and sales force, the crosscorrelation
of these variables with new car sales was determined. Results for advertising crossed
with new car sales is shown in Figure 4.
Figure 4
Crosscorrelations
Estimated Crosscorrelations for NewCarSales with Advertising
1
0.6
0.2
-0.2
-0.6
-1
-21
-11
-1
9
lag
19
29
The high values of the crosscorrelation coefficient at lags of 0,1 and 2 suggest that
advertising has a cumulative effect on sales. All three lags show a strong positive
correlation with sales. These lagged variables will likely be needed in the model.
The crosscorrelation coefficients of NewCarSales with SalesForce are shown in Figure 5.
Figure 5
Crosscorrelations
Estimated Crosscorrelations for NewCarSales with SalesForce
1
0.6
0.2
-0.2
-0.6
-1
-21
-11
-1
9
19
29
lag
Figure 5 shows that sales and sales force are positively correlated, but no particular lag
stands out as dominant. SalesForce can probably enter the model with zero lag, since that
is the peak value.
Inspection of the sales force data shows a general increase in sales force after week 28.
To account for the effect of a non-stationary sales force the dummy variable
SalesForceIncr was created. This variable has a value of zero prior to the increase and a
value of 1 following the increase. The sales force is relatively volatile and may have
limited explanatory value for this reason. (The volatility of the sales force data may mask
any dependency of new car sales on sales force.)
Incentives show a pattern of crosscorrelation with sales similar to advertising for lags of
0, 1 and 2. Results are shown in Figure 6. There will be multicollinearity between
advertising and incentives since the company policy is to increase advertising before and
during incentive programs. This means that much of the explanatory value of the
Incentives dummy variable will be contained in the Advertising variable.
Figure 6
Crosscorrelations
Estimated Crosscorrelations for NewCarSales with Incentives
1
0.6
0.2
-0.2
-0.6
-1
-21
-11
-1
9
19
29
lag
Initial Model and Evaluation
Based on the inspection of the data, the initial model has been expanded to include the
two lagged Advertising variables in addition to the unlagged advertising and sales force
data. The model now has the form:
NewCarSales = 0 + 1*SalesForce + 2*SalesForceIncr + 3*Advertising +
4*Lag(Advertising;1) + 5*Lag(Advertising;2) + 6*Incentives
This model was used to compute regression coefficients with the results shown below.
Multiple Regression Analysis
----------------------------------------------------------------------------Dependent variable: NewCarSales
----------------------------------------------------------------------------Standard
T
Parameter
Estimate
Error
Statistic
P-Value
----------------------------------------------------------------------------CONSTANT
0.470374
0.842182
0.558518
0.5789
SalesForce
0.0199789
0.0224612
0.889484
0.3778
SalesForceIncr
-0.220484
0.326803
-0.674668
0.5029
Advertising
0.0915136
0.0127663
7.16837
0.0000
lag(Advertising;1
0.107852
0.0111636
9.66111
0.0000
lag(Advertising;2
0.0865742
0.0158959
5.44631
0.0000
lag(NewCarSales;1
0.284103
0.0537414
5.28649
0.0000
Incentives
0.713168
0.248074
2.87481
0.0058
----------------------------------------------------------------------------Analysis of Variance
----------------------------------------------------------------------------Source
Sum of Squares
Df Mean Square
F-Ratio
P-Value
----------------------------------------------------------------------------Model
591.569
7
84.5099
270.87
0.0000
Residual
16.2235
52
0.31199
----------------------------------------------------------------------------Total (Corr.)
607.792
59
R-squared = 97.3308 percent
R-squared (adjusted for d.f.) = 96.9714 percent
Standard Error of Est. = 0.558561
Mean absolute error = 0.411079
Durbin-Watson statistic = 2.4895 (P=0.0098)
Lag 1 residual autocorrelation = -0.344262
The high p values for SalesForce and SalesForceIncr indicate that these variables are not
significant to the analysis and may be removed. This was anticipated because of the
volatility of the sales force. The initial model accounts for 97.33 percent of the variation
in sales.
Inspection of the residual error shows that months immediately following an incentive
program have reduced sales. To model this effect, those months were flagged with a
dummy variable, PostEvent. The new model includes this dummy variable. The sales
force related variables have been removed. In addition, a dummy variable representing
those months when new car models were introduced, NewModel, was included in the
model.
These additions may seem superfluous since the model already explains over 97% of the
variability in sales, however computation of a coefficient for these dummy variables is
justified on two grounds. First, the post incentive slow down in sales and the boost in
sales related to new model introduction are observed phenomenon, directly related to the
economic activity of the firm. Therefore, it will be beneficial to the model to include
these effects directly and compute coefficients for their effects on new car sales. The
coefficient will be a direct readout of the effects of these events on new car sales in
millions of dollars.
Secondly, by including these effects directly in the model we disentangle their effects
from the effects of the other independent variables, and the coefficients of those variables
will provide more accurate representation of their influence on new car sales.
Results of the regression analysis with new model are shown below.
Multiple Regression Analysis
----------------------------------------------------------------------------Dependent variable: NewCarSales
----------------------------------------------------------------------------Standard
T
Parameter
Estimate
Error
Statistic
P-Value
----------------------------------------------------------------------------CONSTANT
0.835062
0.217213
3.84444
0.0003
lag(NewCarSales;1
0.454145
0.0459942
9.87396
0.0000
Advertising
0.105232
0.00944438
11.1423
0.0000
lag(Advertising;1
0.0664449
0.0118868
5.58981
0.0000
lag(Advertising;2
0.0378722
0.0135615
2.79263
0.0073
Incentives
0.87747
0.176113
4.98243
0.0000
NewModel
1.6593
0.272169
6.09658
0.0000
PostEvent
-0.20551
0.250053
-0.821865
0.4149
----------------------------------------------------------------------------Analysis of Variance
----------------------------------------------------------------------------Source
Sum of Squares
Df Mean Square
F-Ratio
P-Value
----------------------------------------------------------------------------Model
598.946
7
85.5637
502.93
0.0000
Residual
8.84673
52
0.17013
----------------------------------------------------------------------------Total (Corr.)
607.792
59
R-squared = 98.5444 percent
R-squared (adjusted for d.f.) = 98.3485 percent
Standard Error of Est. = 0.412468
Mean absolute error = 0.297911
Durbin-Watson statistic = 2.32459 (P=0.0779)
Lag 1 residual autocorrelation = -0.300737
The PostEvent variable is not statistically significant, and will therefore be removed from
the model.
Inspection of the graphs of NewCarSales with Advertising and with Lag(NewCarSales,1)
indicated that row 3 of the data might be an outlier needing special intervention. At this
point we have explained over 98% of the variability in new car sales with the model, so
further investigation will not buy us much there, however, because the row in question is
at the edge of the range of data, it may have an undue influence on the results. This is
corroborated by the analysis which shows row 3 to be an infuential point. To investigate
this, an intervention dummy variable was used to flag only row 3 and assess its effects
separately. Results with this addition to the model and PostEvent removed are shown
below.
Multiple Regression Analysis
----------------------------------------------------------------------------Dependent variable: NewCarSales
----------------------------------------------------------------------------Standard
T
Parameter
Estimate
Error
Statistic
P-Value
----------------------------------------------------------------------------CONSTANT
1.14176
0.205173
5.56488
0.0000
lag(NewCarSales;1
0.398617
0.0432463
9.21737
0.0000
Advertising
0.105947
0.00786235
13.4752
0.0000
lag(Advertising;1
0.0688236
0.00980002
7.0228
0.0000
lag(Advertising;2
0.0489577
0.0124836
3.92177
0.0003
Incentives
0.827725
0.157614
5.25158
0.0000
NewModel
1.57382
0.236124
6.66524
0.0000
Interv
-1.4864
0.400935
-3.70734
0.0005
----------------------------------------------------------------------------Analysis of Variance
----------------------------------------------------------------------------Source
Sum of Squares
Df Mean Square
F-Ratio
P-Value
----------------------------------------------------------------------------Model
600.704
7
85.8149
629.55
0.0000
Residual
7.08814
52
0.13631
----------------------------------------------------------------------------Total (Corr.)
607.792
59
R-squared = 98.8338 percent
R-squared (adjusted for d.f.) = 98.6768 percent
Standard Error of Est. = 0.369202
Mean absolute error = 0.273094
Durbin-Watson statistic = 2.57652 (P=0.0066)
Lag 1 residual autocorrelation = -0.348445
The R-squared value has been increased to 98.83 percent. The economic activities as
described by management have been fully incorporated into the model, or in the case of
sales force effects have been investigated and excluded. The autocorrelation and
crosscorrelation effects have been accounted for. It remains to examine the coefficients
to assess whether they make sense economically.
The coefficients associated with events (dummy variables) provide a direct read out of
the effects of these events. Incentives increase sales by $828,000 per month.
The NewModel effect is to increase sales by $1,574,000 in the month of new model
introduction.
Advertising is positively correlated with sales, with the prior months accounting for over
half the total advertising effect. The total effect is about $223,000 in sales per $1000 of
advertising. The current period advertising contributes about $105,000 in sales per
$1000 in advertising. Nearly 40% of the new car sales comes from the inertia of sales
from the prior month.
Row 3 had a negative $1,500,000 effect on sales. The intervention had an observable
effect on all of the other coefficients, and it raised the R-squared value to nearly 99%.
Therefore, the row 3 intervention was retained in the model.
The above results are taken to be the final model.
Discussion of Results
The final model may be used as a starting point for an ongoing effort to track new car
sales with advertising and sales events. It may also be used to forecast near term sales
with a variety of inputs for advertising.
Since a great deal of inertia seems to be a part of new car sales, it might be useful to
explore ways of enhancing this inertia. For example, obtaining sales leads from satisfied
customers through a customer service survey might give an early indication of either
satisfaction or trouble, and possibly give a boost to the sales inertia by identifying
qualified buyers.
As an aside, this data was constructed from a different model in which sales force played
a significant role, and in which about 10% of the new car sales was random. The
statistical dependence is somewhat different than the dependencies upon which the data
was constructed. This should raise a warning flag against extrapolating these results, and
results from similar analyses, too far into the future. On the other hand, near term
projections using a range of possible inputs can be useful for optimizing near term
resource allocations.
Data for Mark Twain Motors
MnthYr
NewCarSales
Advertising
Incentives
NewModel
SalesForce
SalesForceIncr
PostEvent
Interv
Jan-00
4.46
10.2
0
0
35
0
0
0
Feb-00
3.95
10.3
0
0
30
0
0
0
Mar-00
3.54
10.4
0
0
28
0
0
1
Apr-00
May00
5.07
10.5
0
0
32
0
0
0
5.62
10.6
0
0
32
0
0
0
Jun-00
7.71
21.4
1
0
36
0
0
0
Jul-00
10.81
32.5
1
0
38
0
0
0
Aug-00
13.09
32.8
1
0
38
0
0
0
Sep-00
12.68
11.1
0
1
43
0
1
0
Oct-00
10.06
11.2
0
0
39
0
0
0
Nov-00
7.5
11.3
0
0
42
0
0
0
Dec-00
7.05
11.4
0
0
40
0
0
0
Jan-01
6.08
11.5
0
0
42
0
0
0
Feb-01
6.54
11.6
0
0
39
0
0
0
Mar-01
6.28
11.7
0
0
36
0
0
0
Apr-01
May01
6.46
11.8
0
0
33
0
0
0
8.63
23.9
1
0
37
0
0
0
Jun-01
10
24.2
1
0
36
0
0
0
Jul-01
11.03
24.4
1
0
33
0
0
0
Aug-01
13.39
37
1
0
29
0
0
0
Sep-01
12.56
24.9
0
0
34
0
1
0
Oct-01
12.96
12.6
0
1
35
0
0
0
Nov-01
9.43
12.7
0
0
36
0
0
0
Dec-01
7.83
12.8
0
0
35
0
0
0
Jan-02
7.01
13
0
0
32
0
0
0
Feb-02
6.65
13.1
0
0
36
0
0
0
Mar-02
6.68
13.2
0
0
38
0
0
0
Apr-02
May02
8.96
26.7
1
0
43
1
0
0
11.44
26.9
1
0
47
1
0
0
Jun-02
11.87
27.2
1
0
49
1
0
0
Jul-02
13.25
27.5
1
0
45
1
0
0
Aug-02
11.2
13.9
0
0
47
1
1
0
Sep-02
10.37
28
0
0
50
1
0
0
Oct-02
11.04
28.3
0
0
50
1
0
0
Nov-02
11.86
14.3
0
1
51
1
0
0
Dec-02
9.69
14.4
0
0
48
1
0
0
Jan-03
8.11
14.6
0
0
49
1
0
0
Feb-03
7.81
14.7
0
0
51
1
0
0
Mar-03
10.78
44.6
1
0
50
1
0
0
Apr-03
May03
14.85
45.1
1
0
51
1
0
0
18.33
30.4
1
1
50
1
0
0
Jun-03
13.86
15.3
0
0
46
1
1
0
Jul-03
11.52
15.5
0
0
45
1
0
0
Aug-03
11
31.3
0
0
47
1
0
0
Sep-03
11.7
31.6
0
0
46
1
0
0
Oct-03
12.93
16
0
1
44
1
0
0
Nov-03
10.07
16.1
0
0
49
1
0
0
Dec-03
8.89
16.3
0
0
52
1
0
0
Jan-04
7.77
16.4
0
0
56
1
0
0
Feb-04
10.03
33.2
0
0
52
1
0
0
Mar-04
11.83
33.5
0
0
51
1
0
0
Apr-04
May04
13.12
16.9
0
1
47
1
0
0
10.76
17.1
0
0
43
1
0
0
Jun-04
9.52
17.3
0
0
43
1
0
0
Jul-04
10.94
34.9
0
0
46
1
0
0
Aug-04
15.37
52.8
1
0
47
1
0
0
Sep-04
18.3
35.6
1
1
50
1
0
0
Oct-04
18.27
35.9
1
0
49
1
0
0
Nov-04
15.06
18.2
0
0
47
1
1
0
Dec-04
12.69
18.3
0
0
48
1
0
0
Jan-05
10.44
18.5
0
0
48
1
0
0
Feb-05
8.53
18.7
0
0
46
1
0
0