Question $2(25$ points$)-$ Association Rules

You are analyzing transaction data from a large e$-$commerce website using association rule mining. After applying the A$-$priori algorithm, you obtain the following frequent itemsets and their corresponding support values:

$-\backslash \{$Laptop$\backslash \}$: Support $=10\backslash \%$

$-\backslash \{$Phone$\backslash \}$: Support $=8\backslash \%$

$-\backslash \{$Laptop$,$ Phone$\backslash \}$: Support $=4\backslash \%$

$-\backslash \{$Headphones$\backslash \}$: Support $=6\backslash \%$

$-\backslash \{$Laptop$,$ Headphones$\backslash \}$: Support $=3\backslash \%$

$-\backslash \{$Phone$,$ Headphones$\backslash \}$: Support $=2\backslash \%$

$-\backslash \{$Laptop$,$ Phone, Headphones$\backslash \}$: Support $=1\backslash \%$

The minimum support threshold is set to $\backslash (5\backslash \%\backslash )$ and the minimum confidence threshold to $\backslash (60\backslash \%\backslash ).$

$1.$ Calculate the support, confidence and lift for the rule $\backslash \{$Laptop$,$ Phone $\backslash (\backslash \}\backslash$rightarrow $\backslash )\backslash \{$Headphones$\backslash \},$ and interpret the results. $(10$ pts $)$

$2.$ Discuss whether the rule $\backslash (\backslash \{\backslash )$ Laptop, Phone $\backslash (\backslash \}\backslash$rightarrow $\backslash )\backslash \{$Headphones $\backslash (\backslash \}\backslash )$ is useful for a marketing campaign, given the calculated metrics. $(15$ pts$)$