$1.[$Association: affinity analysis$]$ Home Basics is a home improvement retail store selling all manner of products that are needed by home owners to repair, remodel, and redecorate their homes. The management of Home Basics is analyzing buying patterns of its customers to evaluate the layout of its stores. Products within a Home Basics store are organized into the following categories: Paint, Wallpaper, Lawn Care, Flooring, Hardware, Plumbing, Tools, Electrical, Building Materials, Cleaning, and Appliances. The file named HomeBasics.xlsm $($in the range A$4$:K$1504)$ contains a sample of $1,500$ recent transactions from a Home Basics store. Management would like to determine what, if any, categories of products tend to be purchased together.

a$.$ Use affinity analysis to create association rules for the data using a minimum support of $150$ records and a $50\%$ minimum confidence percent.

b$.$ What managerial implications might be suggested by the rules at the top, say with a minimum lift ratio of at least $2?$

$2.[$Clustering: k$-$means clustering, hierarchical clustering$]$ Colleges and universities are often interested in identifying their peer institutions. The file named Colleges.xlsm $($in the range A$1$:L$308)$ contains a number of $($artificial$)$ metrics for $307$ higher education institutions in the U$.$S$.$

a$.$ Use k$-$means clustering to create $4$ clusters for this data $($with normalized input data and $50$ iterations$).$

b$.$ How many schools are in each cluster?

c$.$ Draw a line graph of the cluster centers. How would you characterize each of the clusters?

d$.$ Now use hierarchical clustering $($with normalized input data, Euclidean distance, Ward$$s method, $2$ clusters$)$ for this data and produce a dendrogram.

e$.$ If four clusters are desired, how many schools would be in each cluster?