In this question, you will use the K-means algorithm to cluster the US states, based on their 2018 US News & World Report rankings. US News and World Report ranks all 50 states, according to each of the following criteria: Healthcare, Education, Economy, Opportunity, Infrastructure, Crime and Corrections, Fiscal Stability, Quality of Life. (Iowa was ranked as the best state overall, in case you are curious.) The file, StateRankings.csv, summarizes the data. (Please note that lower rank is better.) To begin your work on this question, please read the data in StateRankings.csv into a data frame called Rankings. Please include set.seed(1) once at the beginning of your code, so we all get the same results.

(a) Perform K-means clustering of all 50 states, using the Healthcare and Economy rankings only. Use five clusters and 20 different initializations. Answer the following questions: What are the sizes of the five clusters you obtained? What is average Healthcare ranking for each cluster? What is the average Economy ranking for each cluster?

(b) Provide a plot of the states with Economy ranking on the x-axis, Healthcare ranking on the y-axis, using a different shape and color for each cluster, and including the state names on the plot.