It is June, and the manager of the retail chain PriceTrimmer wants to increase revenues during the back-to-school period. He plans to identify parents in early August whose children are entering school for the first time in September. His question for the management accountant and the data science team is how to identify and target these households whose children will need to purchase school supplies. PriceTrimmer’s data science team extracts prior-year data on 10,000 households from its customer database and trains a new model. The team partitions the sample into three subsamples: a training sample of 6,000 observations, a validation sample of 2,000 observations, and a holdout sample of 2,000 observations. The rate of households with a child entering school for the first time in each subsample is 18%.

Required:

1. Is this an interesting problem for PriceTrimmer to solve? Why?
2. What data might be available to help solve this problem?
3. Complete the confusion matrices below for the validation sample.

4. As the management accountant you have determined the following. Without doing any promotion, PriceTrimmer earns an average of $20 from every family sending a child to school for the first time. If it decides to promote the program, it will cost PriceTrimmer $10 per child in the form of mailers and promotions sent to households that are predicted to have a child entering school. This money would yield no return if the family was not sending a child to school for the first time. If, however, the family was sending a child to school for the first time, Price Trimmer would earn $50 (net of the cost of the promotion) instead of $20. Develop a payoff matrix for this situation.
5. Which cutoff probability of first-time kids would you select: 

(a) 0.3  

(b) 0.5 

Comment briefly on the results.

Transcribed Image Text:

First-Time Actual Kids Outcomes No First- Time Kids Total A Confusion Matrix (Cutoff 0.5) Predicted Outcomes First-Time No First- Kids Time Kids (TP) 100 (FP) ? 300 (FN) ? (TN) 1,440 1,700 Total 360 1,640 2,000 Actual Outcomes First-Time Kids No First- Time Kids Total B Confusion Matrix (Cutoff 0.3) Predicted Outcomes First-Time No First- Kids Time Kids Total (TP) ? (FP) 900 1,210 (FN) ? (TN) ? ? 360 1,640 2,000