1. What is the Apriori property?

2. Following is a list of five transactions that include items A, B, C, and D:

â€¢ Tl: {A, B, C}

â€¢ T2: {A, B}

â€¢ T3: {B}

â€¢ T4: {A, C}

â€¢ TS: {A, C, D}

Which itemsets satisfy the minimum support of 0.5?

(Hint: An item set may include more than one item.)

3. How are interesting rules distinguished from coincidental rules?

4. A local retailer has a database that stores 10,000 transactions of last summer. After analyzing the data, a data science team has identified the following statistics:

â€¢ {battery} appears in 4,000 transactions.

â€¢ {sunscreen} appears in 3,000 transactions.

â€¢ {sandals} appears in 4,000 transactions.

â€¢ {bowls} appears in 1,000 transactions.

â€¢ {battery, sunscreen} appears in 1,500 transactions.

â€¢ {battery, sandals} appears in 1,000 transactions.

â€¢ {battery, bowls} appears in 1250 transactions.

â€¢ {battery, sunscreen, sandals} appears in 600 transactions.

a. What are the support values of the preceding itemsets?

b. Assuming the minimum support is 0.05, which itemsetsare considered frequent?

c. What are the confidence values of {battery}->{ sunscreen} and {battery, sunscreen}->{ sandals} ?

d. Which of the two rules is more interesting?

5. In the use of a categorical variable with n possible values, explain the following:

a. Why only n – 1 binary variables are necessary

b. Why using n variables would be problematic

6. If the probability of an event occurring is 0.4, then

a. What is the odds ratio?

b. What is the log odds ratio?