Proposal to Investigate the Dependence of New …



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 = β0 + β1*Advertising + β2* SalesForce + β3*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[pic]

Figure 2

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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

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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

[pic]

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

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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

[pic]

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 = β0 + β1*SalesForce + β2*SalesForceIncr + β3*Advertising + β4*Lag(Advertising;1) + β5*Lag(Advertising;2) + β6*Incentives

This model was used to compute regression coefficients with the results shown below.

[pic]

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.

[pic]

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.

[pic]

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 |5.07 |10.5 |0 |0 |32 |0 |0 |0 | |May-00 |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 |6.46 |11.8 |0 |0 |33 |0 |0 |0 | |May-01 |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 |8.96 |26.7 |1 |0 |43 |1 |0 |0 | |May-02 |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 |14.85 |45.1 |1 |0 |51 |1 |0 |0 | |May-03 |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 |13.12 |16.9 |0 |1 |47 |1 |0 |0 | |May-04 |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 | |

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