Problem Set 2
(Due before Week 5’s 1st class, submit SAS code, copy and paste results into a Word File)
1. In the data “CustomerAcquisitionData.xlsx”, there are two worksheets (60 points).
(1) Use the “EstimationData” to estimate the models for customer acquisition (logistic regression) and first purchase quantity. Interpret the results.
(2) Use the model estimates to answer the following two questions:
(a) Suppose you want to acquire all the prospects in the “PredictionData”, i.e., make
them become your customers. Note that, at this moment, they are PROSPECTS and you only observe their demographics. What is the minimum acquisition budget you should have? (There is a minimum for each prospect and the sum is the global minimum.) (Hint: You observe the prospects’ characteristics – Industry, Revenue and Employees. You need an acquisition budget for each prospect such that the prospect can be pushed to become a customer. The minimum acquisition cost is the expense you need to push a prospect to cross the cutoff probability—it is 0.5 in our case. Think about the equation of the logistic probability.)
(b) Suppose you are given $1,000 to acquire customers. What prospects should you target to have the maximum net contributions? (For simplicity, you only look at their first purchases.)
2. Use the gymUsage and gymMembership data to do the following (limit to those members between 15 and 74). The gym’s operation hours are from 8:00am-9:59pm, Mon to Sun. (40 points)
(1) Do there exist any time trend and seasonality within a day, within a week, and within a year in gyn usage duration per session?
(2) Do the above time trend and seasonality differ by gender?
(3) Does the total number of gym users exhibit any time trend and seasonality within a day, within a week, and within a year?
(4) Do the above (3) time trend and seasonality within a day, within a week, and within a year differ by gender?
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