Question $1$

Shop A only sells three products, namely, product X$,$ product Y and product Z to the customers. Last week, $4000$ customers shopped in Shop A$,$ and each customer purchased at least one product. Customers are divided into $4$ demographic segments which are displayed in table $1$:

Customer Segment ID Gender Marital Status Number of Customers

$1$ Male Single $1000$

$2$ Male Married $1000$

$3$ Female Single $1000$

$4$ Female Married $1000$

The purchase patterns in each segment is displayed in Table $2,$ Table $3,$ Table $4$ and Table $5$ respectively:

Table $2$: Purchase patterns of Customers in Segment $1($Male and Single$)$

Choose X $=100$

Choose Y $=200$

Choose Z $=100$

Choose X and Y $=100$

Choose Y and Z $=50$

Choose X and Z$=50$

Choose X$,$Y$,$Z $=400$

$($Interpretation: In Pattern $1,100$ male and single customers purchased product A only. Similarly, in pattern $7,400$ male and single customers purchased all products$)$

Table $3$: Purchase patterns of Customers in Segment $2($Male and Married$)$

Choose X $=100$

Choose Y $=200$

Choose Z $=100$

Choose X and Y $=400$

Choose Y and Z $=50$

Choose X and Z$=50$

Choose X$,$Y$,$Z $=100$

Table $4$: Purchase patterns of Customers in Segment $3($Female and Single$)$

Choose X $=100$

Choose Y $=200$

Choose Z $=100$

Choose X and Y $=50$

Choose Y and Z $=50$

Choose X and Z$=400$

Choose X$,$Y$,$Z $=100$

Table $5$: Purchase patterns of Customers in Segment $4($Female and Married$)$

Choose X $=100$

Choose Y $=200$

Choose Z $=100$

Choose X and Y $=50$

Choose Y and Z $=400$

Choose X and Z$=50$

Choose X$,$Y$,$Z $=100$

Consider four targeting rules below for selling product Z to customers:

Rule $1$: IF $$X$$ THEN $$Z$.$

Rule $2$: IF $$Female $$ and $$X$$ and $$Y$$ THEN $$Z$.$

just consider the female tables

Rule $3$: IF $$Married$$ and $($X$$ or $$Y$)$ THEN $$Z$.$

just consider the married tables

Rule $4$: IF $$Male$$ and $$Single$$ THEN $$Z$.$

just consider the male and single table

Question A:

Compute the confidence, the support and the lift of all the rules above and summarize the results in table $6$ on page $7.$ You can show me the calculation steps.

Question B

Which one of these four rules is the best targeting rule you recommend? Please justify your answer