This problem uses the data set in HairCare-Product.xlsx, courtesy of SAS. In this hypothetical case, a promotion for a hair care product was sent to some members of a buyers club. Purchases were then recorded for both the members who got the promotion and those who did not.

a. What is the purchase propensity i. among those who received the promotion?

ii. among those who did not receive the promotion?

b. Partition the data into training \((60 \%)\) and validation \((40 \%)\) and fit a model of your choice, with Purchase as the target. Report the predicted class and propensities for the first 10 records in the validation set.

c. Copy the validation data to a new worksheet and reverse the values of the Promotion variable (call it Promotion- \(R\) to avoid confusion). This means that for every record, if the original had Promotion \(=1\), the copy will have Promotion \(R=0\), and vice versa.

Score the model to the new copy of the validation data. In XLMiner you can do this either with the Score function, or by re-running the model and selecting the copy as new data in the Score New Data area. You will need to match Promotion to Promotion-R. Report the predicted class and propensities for the first 10 records in the validation set.

d. In a new worksheet, copy the purchase propensities from the original validation data alongside those from the reversed-promotion validation data. Subtract the purchase propensity when Promotion \(=0\) from the purchase propensity when Promotion \(=1\). This is the uplift. Report the uplift for the first 10 records in your validation set.