Luxury Car Buyers Case This continues the Luxury Car Buyers case from Keller (2008). The dataset includes Age, Income, and Education of 311 customers. Earlier, we discussed the DA of these data. Additionally, a cluster analysis was done. The cluster profiles are included. We will characterize the two clusters. The output is shown, and below that are some questions. Output of Cluster Analysis K-means Cluster Analysis: AGE, INC1000s, EDUC Final Partition Number of clusters: 2 Average Maximum distance distance Number of Within cluster from from observations sum of squares centroid centroid Cluster1 189 88520.994 18.545 70.212 Cluster2 122 134891.445 26.060 148.325 Cluster Centroids (Cluster Profiles) Grand Variable Cluster1 Cluster2 centroid AGE INC1000s EDUC 55.4603 49.9262 53.2894 114.9768 186.7370 143.1271 14.2487 16.6148 15.1768 TABLE. Statistics, by Cluster Crosstabulation of Brand and Cluster, with row percents Tabulated statistics: BRAND, LABEL Rows BRAND Columns: LABEL 1 2 All BMW 34 27 61 55.74 44.26 100.00 Cadillac 51 100.00 0.00 g 0 51 100.00 All the Cadillac buyers are in Cluster 1. Lexus 30 39 69 43.48 56.52 100.00 Lincoln 56 1 57 98.25 1.75 100.00 Almost all the Lincoln buyers are in Cluster 1. Note that Cadillac and Lincoln are the American cars. Mercedes 18 24.66 55 75.34 73 100.00 All 189 60.77 122 39.23 311 100.00 Cell Contents: Count % of Row Crosstab with column pots Tabulated statistics: BRAND, LABEL Rows BRAND Columns: LABEL (Cluster) 1 2 All BMW 34 27 61 17.99 22.13 19.61 Cadillac 51 26.98 0 0.00 51 16.40 Lexus 15.87 88 30 39 31.97 69 22.19 Lincoln 56 29.63 8 1 0.82 57 18.33 Mercedes 18 9.52 55 45.08 73 23.47 All 189 100.00 122 100.00 311 100.00 Cell Contents: Count % of Column Questions for this example Q1. What is the mean age in Cluster 1? (A) 14.2487 (B) 16.6148 (C) 49.93 (D) 55.46 Q2. What is the mean age in Cluster 2? (A) 14.2487 (B) 16.6148 (C) 49.93 (D) 55.46 Q3. What is the mean number of years of education in Cluster 1 . (A) 14.2487 (B) 16.6148 (C) 49.93 (D) 55.46 Q4. What is the mean number of years of education in Cluster 2 ? (A) 14.2487 (B) 16.6148 (C) 49.93 (D) 55.46 Q5. What percentage of BMW buyers are in Cluster 1 ? (A) 55.74 (B) 44.26 (C) 100.00 (D) 43.48 Remarks. How would you characterize the two clusters overall? More specifically, on the one hand, what are the profiles of the clusters in terms of Age, Education, and Income, and on the other, in terms of distribution of Brands, and what may be the con- nectionbetween(Age, Educ, Inc) and brand choice? ANSWER: All the Cadillac buyers are in Cluster 1 and almost all the Lincoln buyers are in Cluster 1, with both of these brands being American. Also, since Cluster 1 has the older mean age, buyers of these two brands can be assumed to be older.