Tayko is a software catalog firm that sells games and educational software. It started out as a software manufacturer and later added third-party titles to its offerings. It has recently put together a revised collection of items in a new catalog, which it is preparing to roll out in a mailing.
In addition to its own software titles, Tayko’s customer list is a key asset. In an attempt to expand its customer base, it has recently joined a consortium of catalog firms that specialize in computerand software products. The consortium affords members the opportunity to mail catalogs to names drawn from a pooled list of customers. Members supply their own customer lists to the pool and can “withdraw” an equivalent number of names in each quarter. Members are allowed to do predictive modeling on the records in the pool so they can do a better job of selecting names from the pool.
The Mailing Experiment Tayko has supplied its customer list of 200,000 names to the pool, which totals over 5,000,000 names, so it is now entitled to draw 200,000 names for a mailing.
Tayko would like to select the names that have the best chance of performing well, so it conducts a test—it draws 20,000 names from the pool and does a test mailing of the new catalog.
This mailing yielded 1065 purchasers, a response rate of 0.053. To optimize the performance of the machine learning techniques, it was decided to work with a stratified sample that contained equal numbers of purchasers and nonpurchasers. For ease of presentation, the dataset for this case includes just 1000 purchasers and 1000 nonpurchasers, an apparent response rate of 0.5. Therefore, after using the dataset to predict who will be a purchaser, we must adjust the purchase rate back down by multiplying each case’s “probability of purchase”
by 0.053/0.5, or 0.107.
Data There are two target attributes in this case. Purchase indicates whether or not a prospect responded to the test mailing and purchased something. Spending indicates, for those who made a purchase, how much they spent. The overall procedure in this case will be to develop two models. One will be used to classifyrecords as purchase or no purchase. The second will be used for those cases that are classified as purchase and will predict the amount they will spend.
Table 23.6 shows the first few rows of data. Table 23.7 provides a description of the attributes available in this case.

1. Each catalog costs approximately $2 to mail (including printing, postage, and mailing costs). Estimate the gross profit that the firm could expect from the remaining 180,000 names if it selects them randomly from the pool.
2. Develop a model for classifying a customer as a purchaser or nonpurchaser.

a. Partition the data randomly into a training set (800 records), validation set (700 records), and holdout set (500 records).

b. Run logistic regression using regularization with L1 penalty (setting λ
and α parameters as discussed in Section 6.4) to select the best subset of attributes, and then use this model to classify the data into purchasers and nonpurchasers. Use only the training set for running the model.
(Logistic regression is used because it yields an estimated “probability of purchase,” which is required later in the analysis.)
3. Develop a model for predicting spending among the purchasers.

a. Create subsets of the training and validation sets for only purchasers’
records by filtering for Purchase = 1.

b. Develop models for predicting spending with the filtered datasets, using:

i. Multiple linear regression (use stepwise regression with the Iterative T-Test option in the Linear Regression operator)
ii. Regression trees

c. Choose one model on the basis of its performance on the validation data.
4. Return to the original holdout data partition. Note that this holdout data partition includes both purchasers and nonpurchasers.

a. Using the Apply Model operator, generate the predicted scores from the logistic regression.

b. For the above labeled data, again use the Apply Model operator to generate the predicted spending amount from the prediction model chosen. 

c. Generate an attribute for “adjusted probability of purchase” by multiplying “predicted probability of purchase” by 0.107. This is to adjust for oversampling the purchasers (see earlier description).

d. Generate an attribute for expected spending: adjusted probability of purchase × predicted spending. Sort the data in descending order of expected spending.

e. Plot the lift chart (cumulative gains chart) of the expected spending (cumulative expected spending as a function of number of records targeted). 

f. Using this lift chart, estimate the gross profit that would result from mailing to the 180,000 names on the basis of your machine learning models.