1. In this problem we will use the tumor data set. (a) Read the data in and remove the first column, which corresponds to the diagnosis. We now have a dataset with only X variables. (b) Conduct a PCA analysis. being sure to center and scale the variables. Provide a plot of the variation explained by each PC. How many principal components do you think should be kept? (Hint: In R pca.out = prcomp(tumor, scale=TRUE) pca.var = pca.out$sdev**2 pve = pca.var/sum(pca.var) plot(pve); plot(cumsum(pve) (c) How much of the total variation in the data is explained by 2 principal components? By 3? (d) Print the principal component loadings, which describe how all of the variables combine to form the PC variables. Interpret the first 2 principal components. (Hint: See Lab 10.4 in the book and the interpretations in the second half of Section 10.2.1 in the ISLR text. In R, pca.out$rotation) (e) Make a biplot of the first 2 principal components and interpret. (Hint: In R, biplot(pca.out, scale=0)) 2. Now, we will use K-means and hierarchical clustering on the data. (a) How many clusters do you think we should specify? Why? (b) Conduct K-means clustering with 2 clusters. What are the cluster means? (Hint, In R, set.seed(1) km.out = kmeans(tumor,2,nstart=20) (c) Make a scatterplot matrix between all variables and color the points by cluster. Describe your findings. (Hint. In R, pairs(tumor, col=km.out$cluster)) (d) Using complete linkage, perform hierarchical clustering and color the points on the scatterplot matrix as in the previous question. Is the result much different? (Hint: In R, hc.complete=hclust(dist(tumor), method="complete") cutree(hc.complete,2)