Question

Rob’s Market (RM) is a regional food store chain in the southwest United States. David White, director of Business Intelligence for RM, would like to initiate a study of the purchase behavior of customers who use the RM loyalty card (a card that customers scan at checkout to qualify for discounted prices). The use of the loyalty card allows RM to capture what is known as “point-of-sale” data, that is, a list of products purchased by a given customer as he/she checks out of the market. David feels that better understanding of which products tend to be purchased together could lead to insights for better pricing and display strategies as well as a better understanding of sales and the potential impact of different levels of coupon discounts. This type of analysis is known as market basket analysis, as it is a study of what different customers have in their “shopping baskets” as they check out of the store.

As a prototype study, David wants to investigate customer buying behavior with regard to bread, jelly, and peanut butter. RM’s Information Technology (IT) group, at David’s request, has provided a data set of purchases made by 1000 customers over a one-week period. The data set contains the following variables for each customer:

Bread—wheat, white, or none
Jelly—grape, strawberry, or none
Peanut Butter—creamy, natural, or none

The variables appear in the above order from left to right in the data set, where each row is a customer. For example, the first record of the data set is:

white grape none
which means that customer #1 purchased white bread, grape jelly, and no peanut butter. The second record is:

white strawberry none
which means that customer #2 purchased white bread, strawberry jelly, and no peanut butter. The sixth record in the data set is:

none none none
which means that the sixth customer did not purchase bread, jelly, or peanut butter.

Other records are interpreted in a similar fashion.

David would like you to do an initial study of the data to get a better understanding of RM customer behavior with regard to these three products.

Managerial Report

Prepare a report that gives insight into the purchase behavior of customers who use the RM loyalty card. At a minimum your report should include estimates of the following:

1. The probability that a random customer does not purchase any of the three products (bread, jelly, or peanut butter).

2. The probability that a random customer purchases white bread.

3. The probability that a random customer purchases wheat bread.

4. The probability that a random customer purchases grape jelly given that he/she purchases white bread.

5. The probability that a random customer purchases strawberry jelly given that he/she purchases white bread.

6. The probability that a random customer purchases creamy peanut butter given that he/she purchases white bread.

7. The probability that a random customer purchases natural peanut butter given that he/she purchases white bread.

8. The probability that a random customer purchases creamy peanut butter given that he/she purchases wheat bread.

9. The probability that a random customer purchases natural peanut butter given that he/she purchases wheat bread.

10. The probability that a random customer purchases white bread, grape jelly, and creamy peanut butter.