# Statistics Assignment | Professional Writing Services

Here is an example: consider the rule the frequent itemset <{ Eggs },{Tomatoes},{Vinegar}>. From this itemset we can generate sequential rule <{ Eggs },{Tomatoes}> -> <{Vinegar}> which says that if a customer bought Eggs and Tomatoes already, they are likely to buy Vinegar at a later time. Remember, the order of items in the antecedent is not important here so it is possible that customer bought first eggs and then tomatoes or the other way around.

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For given frequent 2-item sequence <AC>, there is only one rule <A> -> <C>. For 3-item sequence <ABC>, there will be two rules: <A> -> <BC> and <AB> -> <C>.

As with association rules, sequential rules have two important measures: the support and the confidence. The support of a rule A -> C is how many sequences contains the items from A followed by the items from C. For example, the support of the rule <{ Eggs },{Tomatoes}> -> <{Vinegar}> is 2 because the frequent item set <{ Eggs },{Tomatoes},{Vinegar}> appears twice while <{Tomatoes}, {Eggs },{Vinegar}> and <{ Eggs, Tomatoes},{Vinegar}> do not appear at all. The confidence of a rule A -> C is the support of the rule divided by the number of sequences containing the items from A. For example, Eggs and Tomatoes appear in three transactions so the confidence of the rule <{ Eggs },{Tomatoes}> -> <{Vinegar}> is 2/3 = 0.67 (or 67 % if written as a percentage). This means that only 67% of customers who bought Eggs and Tomatoes will buy Vinegar at a later time.

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