Refer to the clustering problem involving the file FBS described in Problem 1. Apply hierarchical clustering with 10 clusters using football stadium capacity, latitude, longitude, endowment, and enrollment as variables. Be sure to Normalize input data in Step 2 of the XLMiner Hierarchical Clustering procedure. Use Ward's method as the clustering method.
a. Use a PivotTable on the data in the HC_Clusters1 worksheet to compute the cluster centers for the clusters in the hierarchical clustering.
b. Identify the cluster with the largest average football stadium capacity. Using all the variables, how would you characterize this cluster?
c. Examine the smallest cluster. What makes this cluster unique?
d. By examining the dendrogram on the HC_Dendrogram worksheet (as well as the sequence of clustering stages in HC_Output1), what number of clusters seems to be the most natural fit based on the distance? What is the increase in distance if 9 clusters were used instead of 10? (Use the HC_Output1 worksheet as well as the HC_Dendrogram worksheet.)