What is the lift of the association rule:

{coffee} - {milk, bagel}?

Question

What is the lift of the association rule:

{coffee} -> {milk, bagel}?

BlackTom AI · Accepted Answer

To understand the lift of an association rule, we need the formula lift(A -> B) = support(A ∪ B) / (support(A) * support(B)). Here, the rule is {coffee} -> {milk, bagel}, and the given supports are: support({coffee}) = 0.67, support({milk, bagel}) = 0.5, and presumably support({coffee, milk, bagel}) = 0.5 as the joint support in the numerator.

Option 1: None of the above. This claim would be true if none of the listed expressions matched the lift correctly. However, the third option provides the correct lift value using the proper numerator and denominator, so claiming "none of the above" is inaccurate because there is a correct expression among the options.

Option 2: 0.75/(0.67*0.33) = 3.4. In this expression, the numerator 0.75 does not correspond to the joint support of {coffee} ∪ {milk, bagel} (which is given as 0.5 elsewhere), and the denominator uses 0.33 as support({milk, bagel}) instead of the stated 0.5. Since both numbers in the fraction are inconsistent with the provided data, this calculation does not reflect the true lift for the rule.

Option 3: 0.5/(0.67*0.5) = 1.5. Here, the numerator 0.5 matches the joint support of {coffee, milk, bagel} (A ∪ B), and the denominator uses support({coffee}) = 0.67 and support({milk, bagel}) = 0.5. Multiplying 0.67 by 0.5 gives 0.335, and 0.5 divided by 0.335 indeed equals approximately 1.49, which rounds to 1.5. This aligns with the standard lift calculation for the given rule.

In summary, evaluating each option against the lift formula and the provided supports shows that the third option correctly applies the lift computation, while the first is incorrect because a valid option exists, and the second is incorrect due to mismatched supports in both the numerator and denominator.

What is the lift of the association rule: {coffee} -> {milk, bagel}?Single choice

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