Big Ten Expansion From 1946 to 1990, the Big Ten Conference consisted of the University of Illinois, Indiana University, University of Iowa, University of Michigan, Michigan State University, University of Minnesota, Northwestern University, Ohio State University, Purdue University, and University of Wisconsin. In 1990, the conference added Pennsylvania State University. In 2011, the conference added the University of Nebraska. In 2014, the University of Maryland and Rutgers University were added to the conference with speculation of more schools being added in the future. The file BigTenExpand contains data on the football stadium capacity, latitude, longitude, endowment, and enrollment of 59 National Collegiate Athletic Association (NCAA) Football Bowl Subdivision (FBS) schools. Treat the 10 schools that were members of the Big Ten from 1946 to 1990 as being in a cluster and the other 49 schools as each being in their own cluster. 1. Create a scatterplot matrix in JMP to show the five variables for the Big Ten schools using the tab Big Ten. Comment on the scatterplot. Steps: a. Graph > Scatterplot Matrix > Add all variables except School in the Y columns section > Click OK b. Once the Scatterplot matrix is formed, click on the red triangle, and select Density Ellipses > Shaded Ellipses. You can also change the color of the shaded ellipses if you want to. 2. Using the data in the Big Ten tab, standardize all five variables for each school in JMP. Steps: a. Cols > New Column > Change the Column Name to Std Stadium Cap. b. Click on Column Properties > Select Formula > From the list of functions in the formula editor select Statistical > Col Standardize c. Add the Stadium Capacity to the formula by dragging it into the parenthesis. d. Repeat the above steps to create a standardized column for all five variables. 3. Add new rows to your data table in JMP for Pittsburg and Temple. 4. Recreate the scatterplot matrix, this time with the 12 rows and use the standardized columns as Y. Comment on whether you think Pittsburgh or Temple should be added to the Big Ten cluster based on the scatterplots. 5. Export this data table to Excel. (File > Export) 6. Using Euclidean distance to measure dissimilarity between observations, and Michigan as the point of comparison, determine which school out of Pittsburgh and Temple you would recommend integrating into the Big Ten Conference. That is, which school is the most similar with respect to complete linkage (Using Michigan) to the cluster of ten schools that were members of the Big Ten from 1946 to 1990? 7. Run a Hierarchical clustering algorithm on the 12 rows of data to check which school would have been added the last to the Big Ten Cluster if all 12 were competing to be added at the same time? Submit your dendrogram to support your answer. Steps: a. Analyze > Clustering > Hierarchical Cluster b. Fill out the clustering platform as shown below