1. In this problem, use R-studio to perform K-means clustering on the data set "data-hw.csv", which is available at the link below, or you can find the data by searching library mass on line. (Notice that the last column "x.label" is the label for each observation and should be excluded in the clustering analysis.)

1. Perform K-means clustering of the observations with K = 3. How well do the clusters that you obtained in K-means clustering compare to the true class labels?

2, Perform K-means clustering with K = 2. Describe your results.

1. Now perform K-means clustering with K = 4, and describe your results.
2. Using the scale() function, perform K-means clustering with K = 3 on the data after scaling each variable to have standard deviation one. How do these results compare to those obtained in (b)? Explain.

data-hw:

https://www.dropbox.com/scl/fi/mhiavkpmevpgzk7uhk2p9/HW-data.docx?dl=0&rlkey=p98ls04k5dxdh7tdp5kqzgu91