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  Predictive Modeling
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Once the linear regression and/or multinomial logit models have been developed and a set of coefficients needed to build a predictive equation has been derived, a hold-out sample of 2,300 observations would be used to verify the models and to generate a predicted response rate to the marketing campaign.

The response rate represents the percentage of customers within the top nth percentile of the holdout sample that actually made a positive purchase decision. These response rates were then used to generate financial figures, such as revenues, marginal costs, and return on investment (ROI).

Additionally, a sensitivity analysis of net revenue to percentage of customers targeted can be conducted to optimize the model.  The graph above shows that net revenue can be optimized at $23,473.91 if 49.2% of the customer base is targeted for the mail campaign and given 15.72% positive response rate.  Hence, it may not be optimal to implement a full-scale direct marketing campaign or even a predefined decile/percentage of customers.

   
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