Peter Lara, an aspiring college student, met with his high school college advisor to discuss potential colleges to which he might apply. He was advised to consult with the College Scorecard information on the Department of Education website. After talking to his family, he downloaded a list of 116 colleges and information on annual post-college earnings (Earnings in $), the average annual cost (Cost in $), the graduation rate (Grad in %), the percentage of students paying down debt (Debt in %), and whether or not a college is located in a city (1 denotes a city location, 0 otherwise). Peter and his family want to group these colleges based on the available information to help narrow down their choices. The accompanying table shows a portion of the data.

a. Perform agglomerative clustering based on the earnings, cost, graduation rate, and debt information, all standardized to z-scores. Use the Euclidean distance and Ward clustering method to determine appropriate cluster membership for the 116 colleges. How many clusters are generated if the minimum distance between clusters is 15?

b. Separate the colleges based on whether or not they are located in the city into two different data sets. Group the colleges that are located in the city into clusters based on the earnings, cost, graduation rate, and debt information using the Euclidean distance and Ward’s clustering method. Inspect the dendrogram. How many clusters are generated if the minimum distance between clusters is 10? 

c. Repeat the analysis for the colleges not located in the city. Inspect the dendrogram. How many clusters are generated if the minimum distance between clusters is 10?  

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School St. Ambrose Univ. Albion College 1 Wittenburg Univ. Earnings Cost Grad Debt 44800 22920 62 88 45100 23429 92 B ⠀ B 42700 26616 90 73 3 64 City 1 0 111 I