The following contingency table summarizes supermarket transaction data, where hot dogs refers to the transactions containing hot dogs, \(\overline{\text { hot dogs }}\) refers to the transactions that do not contain hot dogs, hamburgers refers to the transactions containing hamburgers, and \(\overline{\text { hamburgers }}\) refers to the transactions that do not contain hamburgers.

a. Suppose that the association rule "hot dogs \(\Rightarrow\) hamburgers" is mined. Given a minimum support threshold of \(25 \%\) and a minimum confidence threshold of \(50 \%\), is this association rule strong?

b. Based on the given data, is the purchase of hot dogs independent of the purchase of hamburgers? If not, what kind of correlation relationship exists between the two?

c. Compare the use of the all_confidence, max_confidence, Kulczynski, and cosine measures with lift and correlation on the given data.

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hotdogs hot dogs 500 hamburgers 2000 hamburgers 1000 Ecol 3000 1500 2000 2500 2500 5000