do test only use techniqes found in files
roberto pulpo
QUAN4630takehomeFA25.xlsxCluster
| Normalized Data | ||||||
| School | Type | Median SAT | Acceptance Rate (%) | Expenditures/Student | Top 10% HS | Graduation % |
| Claremont | Lib Arts | -0.0494928859 | -0.1572009316 | -0.6262131232 | -0.4578388107 | -1.2411725587 |
| Colby | Lib Arts | -1.0067894943 | 0.5906481606 | -0.7235402915 | -1.6385810067 | 0.1013761251 |
| Colgate | Lib Arts | -0.0814027728 | -0.0076311132 | -0.8109730699 | -0.9744135215 | 0.2356309935 |
| Columbia | University | 0.0781466619 | -0.6806952962 | 1.0229811922 | 0.2801250618 | 0.9069053354 |
| Cornell | University | 0.2696059836 | -0.605910387 | 0.4576429165 | 0.7966997726 | -0.0328787433 |
Please note that the data is already normalized. 1. Perform cluster analysis on the above schools using the values in columns C through G. Recall from class that this can theoretically continue until all are grouped into a single cluster. However, you can stop one step before that occurs (just like in class). 2. Based on the above, which clusters would you use to group these schools?
Discriminant
| length | left | right | bottom | top | diag | type |
| 214.8 | 131 | 131.1 | 9 | 9.7 | 141 | real |
| 214.6 | 129.7 | 129.7 | 8.1 | 9.5 | 141.7 | real |
| 214.8 | 129.7 | 129.7 | 8.7 | 9.6 | 142.2 | real |
| 214.8 | 129.7 | 129.6 | 7.5 | 10.4 | 142 | real |
| 215 | 129.6 | 129.7 | 10.4 | 7.7 | 141.8 | real |
| 215.7 | 130.8 | 130.5 | 9 | 10.1 | 141.4 | real |
| 215.5 | 129.5 | 129.7 | 7.9 | 9.6 | 141.6 | real |
| 214.5 | 129.6 | 129.2 | 7.2 | 10.7 | 141.7 | real |
| 214.9 | 129.4 | 129.7 | 8.2 | 11 | 141.9 | real |
| 215.2 | 130.4 | 130.3 | 9.2 | 10 | 140.7 | real |
| 215.3 | 130.4 | 130.3 | 7.9 | 11.7 | 141.8 | real |
| 215.1 | 129.5 | 129.6 | 7.7 | 10.5 | 142.2 | real |
| 215.2 | 130.8 | 129.6 | 7.9 | 10.8 | 141.4 | real |
| 214.7 | 129.7 | 129.7 | 7.7 | 10.9 | 141.7 | real |
| 215.1 | 129.9 | 129.7 | 7.7 | 10.8 | 141.8 | real |
| 214.5 | 129.8 | 129.8 | 9.3 | 8.5 | 141.6 | real |
| 214.6 | 129.9 | 130.1 | 8.2 | 9.8 | 141.7 | real |
| 215 | 129.9 | 129.7 | 9 | 9 | 141.9 | real |
| 215.2 | 129.6 | 129.6 | 7.4 | 11.5 | 141.5 | real |
| 214.7 | 130.2 | 129.9 | 8.6 | 10 | 141.9 | real |
| 215 | 129.9 | 129.3 | 8.4 | 10 | 141.4 | real |
| 215.6 | 130.5 | 130 | 8.1 | 10.3 | 141.6 | real |
| 215.3 | 130.6 | 130 | 8.4 | 10.8 | 141.5 | real |
| 215.7 | 130.2 | 130 | 8.7 | 10 | 141.6 | real |
| 215.1 | 129.7 | 129.9 | 7.4 | 10.8 | 141.1 | real |
| 215.3 | 130.4 | 130.4 | 8 | 11 | 142.3 | real |
| 215.5 | 130.2 | 130.1 | 8.9 | 9.8 | 142.4 | real |
| 215.1 | 130.3 | 130.3 | 9.8 | 9.5 | 141.9 | real |
| 215.1 | 130 | 130 | 7.4 | 10.5 | 141.8 | real |
| 214.8 | 129.7 | 129.3 | 8.3 | 9 | 142 | real |
| 215.2 | 130.1 | 129.8 | 7.9 | 10.7 | 141.8 | real |
| 214.8 | 129.7 | 129.7 | 8.6 | 9.1 | 142.3 | real |
| 215 | 130 | 129.6 | 7.7 | 10.5 | 140.7 | real |
| 215.6 | 130.4 | 130.1 | 8.4 | 10.3 | 141 | real |
| 215.9 | 130.4 | 130 | 8.9 | 10.6 | 141.4 | real |
| 214.6 | 130.2 | 130.2 | 9.4 | 9.7 | 141.8 | real |
| 215.5 | 130.3 | 130 | 8.4 | 9.7 | 141.8 | real |
| 215.3 | 129.9 | 129.4 | 7.9 | 10 | 142 | real |
| 215.3 | 130.3 | 130.1 | 8.5 | 9.3 | 142.1 | real |
| 213.9 | 130.3 | 129 | 8.1 | 9.7 | 141.3 | real |
| 214.4 | 129.8 | 129.2 | 8.9 | 9.4 | 142.3 | real |
| 214.8 | 130.1 | 129.6 | 8.8 | 9.9 | 140.9 | real |
| 214.9 | 129.6 | 129.4 | 9.3 | 9 | 141.7 | real |
| 214.9 | 130.4 | 129.7 | 9 | 9.8 | 140.9 | real |
| 214.8 | 129.4 | 129.1 | 8.2 | 10.2 | 141 | real |
| 214.3 | 129.5 | 129.4 | 8.3 | 10.2 | 141.8 | real |
| 214.8 | 129.9 | 129.7 | 8.3 | 10.2 | 141.5 | real |
| 214.8 | 129.9 | 129.7 | 7.3 | 10.9 | 142 | real |
| 214.6 | 129.7 | 129.8 | 7.9 | 10.3 | 141.1 | real |
| 214.5 | 129 | 129.6 | 7.8 | 9.8 | 142 | real |
| 214.6 | 129.8 | 129.4 | 7.2 | 10 | 141.3 | real |
| 215.3 | 130.6 | 130 | 9.5 | 9.7 | 141.1 | real |
| 214.5 | 130.1 | 130 | 7.8 | 10.9 | 140.9 | real |
| 215.4 | 130.2 | 130.2 | 7.6 | 10.9 | 141.6 | real |
| 214.5 | 129.4 | 129.5 | 7.9 | 10 | 141.4 | real |
| 215.2 | 129.7 | 129.4 | 9.2 | 9.4 | 142 | real |
| 215.7 | 130 | 129.4 | 9.2 | 10.4 | 141.2 | real |
| 215 | 129.6 | 129.4 | 8.8 | 9 | 141.1 | real |
| 215.1 | 130.1 | 129.9 | 7.9 | 11 | 141.3 | real |
| 215.1 | 130 | 129.8 | 8.2 | 10.3 | 141.4 | real |
| 215.1 | 129.6 | 129.3 | 8.3 | 9.9 | 141.6 | real |
| 215.3 | 129.7 | 129.4 | 7.5 | 10.5 | 141.5 | real |
| 215.4 | 129.8 | 129.4 | 8 | 10.6 | 141.5 | real |
| 214.5 | 130 | 129.5 | 8 | 10.8 | 141.4 | real |
| 215 | 130 | 129.8 | 8.6 | 10.6 | 141.5 | real |
| 215.2 | 130.6 | 130 | 8.8 | 10.6 | 140.8 | real |
| 214.6 | 129.5 | 129.2 | 7.7 | 10.3 | 141.3 | real |
| 214.8 | 129.7 | 129.3 | 9.1 | 9.5 | 141.5 | real |
| 215.1 | 129.6 | 129.8 | 8.6 | 9.8 | 141.8 | real |
| 214.9 | 130.2 | 130.2 | 8 | 11.2 | 139.6 | real |
| 213.8 | 129.8 | 129.5 | 8.4 | 11.1 | 140.9 | real |
| 215.2 | 129.9 | 129.5 | 8.2 | 10.3 | 141.4 | real |
| 215 | 129.6 | 130.2 | 8.7 | 10 | 141.2 | real |
| 214.4 | 129.9 | 129.6 | 7.5 | 10.5 | 141.8 | real |
| 215.2 | 129.9 | 129.7 | 7.2 | 10.6 | 142.1 | real |
| 214.1 | 129.6 | 129.3 | 7.6 | 10.7 | 141.7 | real |
| 214.9 | 129.9 | 130.1 | 8.8 | 10 | 141.2 | real |
| 214.6 | 129.8 | 129.4 | 7.4 | 10.6 | 141 | real |
| 215.2 | 130.5 | 129.8 | 7.9 | 10.9 | 140.9 | real |
| 214.6 | 129.9 | 129.4 | 7.9 | 10 | 141.8 | real |
| 215.1 | 129.7 | 129.7 | 8.6 | 10.3 | 140.6 | real |
| 214.9 | 129.8 | 129.6 | 7.5 | 10.3 | 141 | real |
| 215.2 | 129.7 | 129.1 | 9 | 9.7 | 141.9 | real |
| 215.2 | 130.1 | 129.9 | 7.9 | 10.8 | 141.3 | real |
| 215.4 | 130.7 | 130.2 | 9 | 11.1 | 141.2 | real |
| 215.1 | 129.9 | 129.6 | 8.9 | 10.2 | 141.5 | real |
| 215.2 | 129.9 | 129.7 | 8.7 | 9.5 | 141.6 | real |
| 215 | 129.6 | 129.2 | 8.4 | 10.2 | 142.1 | real |
| 214.9 | 130.3 | 129.9 | 7.4 | 11.2 | 141.5 | real |
| 215 | 129.9 | 129.7 | 8 | 10.5 | 142 | real |
| 214.7 | 129.7 | 129.3 | 8.6 | 9.6 | 141.6 | real |
| 215.4 | 130 | 129.9 | 8.5 | 9.7 | 141.4 | real |
| 214.9 | 129.4 | 129.5 | 8.2 | 9.9 | 141.5 | real |
| 214.5 | 129.5 | 129.3 | 7.4 | 10.7 | 141.5 | real |
| 214.7 | 129.6 | 129.5 | 8.3 | 10 | 142 | real |
| 215.6 | 129.9 | 129.9 | 9 | 9.5 | 141.7 | real |
| 215 | 130.4 | 130.3 | 9.1 | 10.2 | 141.1 | real |
| 214.4 | 129.7 | 129.5 | 8 | 10.3 | 141.2 | real |
| 215.1 | 130 | 129.8 | 9.1 | 10.2 | 141.5 | real |
| 214.7 | 130 | 129.4 | 7.8 | 10 | 141.2 | real |
| 214.4 | 130.1 | 130.3 | 9.7 | 11.7 | 139.8 | fake |
| 214.9 | 130.5 | 130.2 | 11 | 11.5 | 139.5 | fake |
| 214.9 | 130.3 | 130.1 | 8.7 | 11.7 | 140.2 | fake |
| 215 | 130.4 | 130.6 | 9.9 | 10.9 | 140.3 | fake |
| 214.7 | 130.2 | 130.3 | 11.8 | 10.9 | 139.7 | fake |
| 215 | 130.2 | 130.2 | 10.6 | 10.7 | 139.9 | fake |
| 215.3 | 130.3 | 130.1 | 9.3 | 12.1 | 140.2 | fake |
| 214.8 | 130.1 | 130.4 | 9.8 | 11.5 | 139.9 | fake |
| 215 | 130.2 | 129.9 | 10 | 11.9 | 139.4 | fake |
| 215.2 | 130.6 | 130.8 | 10.4 | 11.2 | 140.3 | fake |
| 215.2 | 130.4 | 130.3 | 8 | 11.5 | 139.2 | fake |
| 215.1 | 130.5 | 130.3 | 10.6 | 11.5 | 140.1 | fake |
| 215.4 | 130.7 | 131.1 | 9.7 | 11.8 | 140.6 | fake |
| 214.9 | 130.4 | 129.9 | 11.4 | 11 | 139.9 | fake |
| 215.1 | 130.3 | 130 | 10.6 | 10.8 | 139.7 | fake |
| 215.5 | 130.4 | 130 | 8.2 | 11.2 | 139.2 | fake |
| 214.7 | 130.6 | 130.1 | 11.8 | 10.5 | 139.8 | fake |
| 214.7 | 130.4 | 130.1 | 12.1 | 10.4 | 139.9 | fake |
| 214.8 | 130.5 | 130.2 | 11 | 11 | 140 | fake |
| 214.4 | 130.2 | 129.9 | 10.1 | 12 | 139.2 | fake |
| 214.8 | 130.3 | 130.4 | 10.1 | 12.1 | 139.6 | fake |
| 215.1 | 130.6 | 130.3 | 12.3 | 10.2 | 139.6 | fake |
| 215.3 | 130.8 | 131.1 | 11.6 | 10.6 | 140.2 | fake |
| 215.1 | 130.7 | 130.4 | 10.5 | 11.2 | 139.7 | fake |
| 214.7 | 130.5 | 130.5 | 9.9 | 10.3 | 140.1 | fake |
| 214.9 | 130 | 130.3 | 10.2 | 11.4 | 139.6 | fake |
| 215 | 130.4 | 130.4 | 9.4 | 11.6 | 140.2 | fake |
| 215.5 | 130.7 | 130.3 | 10.2 | 11.8 | 140 | fake |
| 215.1 | 130.2 | 130.2 | 10.1 | 11.3 | 140.3 | fake |
| 214.5 | 130.2 | 130.6 | 9.8 | 12.1 | 139.9 | fake |
| 214.3 | 130.2 | 130 | 10.7 | 10.5 | 139.8 | fake |
| 214.5 | 130.2 | 129.8 | 12.3 | 11.2 | 139.2 | fake |
| 214.9 | 130.5 | 130.2 | 10.6 | 11.5 | 139.9 | fake |
| 214.6 | 130.2 | 130.4 | 10.5 | 11.8 | 139.7 | fake |
| 214.2 | 130 | 130.2 | 11 | 11.2 | 139.5 | fake |
| 214.8 | 130.1 | 130.1 | 11.9 | 11.1 | 139.5 | fake |
| 214.6 | 129.8 | 130.2 | 10.7 | 11.1 | 139.4 | fake |
| 214.9 | 130.7 | 130.3 | 9.3 | 11.2 | 138.3 | fake |
| 214.6 | 130.4 | 130.4 | 11.3 | 10.8 | 139.8 | fake |
| 214.5 | 130.5 | 130.2 | 11.8 | 10.2 | 139.6 | fake |
| 214.8 | 130.2 | 130.3 | 10 | 11.9 | 139.3 | fake |
| 214.7 | 130 | 129.4 | 10.2 | 11 | 139.2 | fake |
| 214.6 | 130.2 | 130.4 | 11.2 | 10.7 | 139.9 | fake |
| 215 | 130.5 | 130.4 | 10.6 | 11.1 | 139.9 | fake |
| 214.5 | 129.8 | 129.8 | 11.4 | 10 | 139.3 | fake |
| 214.9 | 130.6 | 130.4 | 11.9 | 10.5 | 139.8 | fake |
| 215 | 130.5 | 130.4 | 11.4 | 10.7 | 139.9 | fake |
| 215.3 | 130.6 | 130.3 | 9.3 | 11.3 | 138.1 | fake |
| 214.7 | 130.2 | 130.1 | 10.7 | 11 | 139.4 | fake |
| 214.9 | 129.9 | 130 | 9.9 | 12.3 | 139.4 | fake |
| 214.9 | 130.3 | 129.9 | 11.9 | 10.6 | 139.8 | fake |
| 214.6 | 129.9 | 129.7 | 11.9 | 10.1 | 139 | fake |
| 214.6 | 129.7 | 129.3 | 10.4 | 11 | 139.3 | fake |
| 214.5 | 130.1 | 130.1 | 12.1 | 10.3 | 139.4 | fake |
| 214.5 | 130.3 | 130 | 11 | 11.5 | 139.5 | fake |
| 215.1 | 130 | 130.3 | 11.6 | 10.5 | 139.7 | fake |
| 214.2 | 129.7 | 129.6 | 10.3 | 11.4 | 139.5 | fake |
| 214.4 | 130.1 | 130 | 11.3 | 10.7 | 139.2 | fake |
| 214.8 | 130.4 | 130.6 | 12.5 | 10 | 139.3 | fake |
| 214.6 | 130.6 | 130.1 | 8.1 | 12.1 | 137.9 | fake |
| 215.6 | 130.1 | 129.7 | 7.4 | 12.2 | 138.4 | fake |
| 214.9 | 130.5 | 130.1 | 9.9 | 10.2 | 138.1 | fake |
| 214.6 | 130.1 | 130 | 11.5 | 10.6 | 139.5 | fake |
| 214.7 | 130.1 | 130.2 | 11.6 | 10.9 | 139.1 | fake |
| 214.3 | 130.3 | 130 | 11.4 | 10.5 | 139.8 | fake |
| 215.1 | 130.3 | 130.6 | 10.3 | 12 | 139.7 | fake |
| 216.3 | 130.7 | 130.4 | 10 | 10.1 | 138.8 | fake |
| 215.6 | 130.4 | 130.1 | 9.6 | 11.2 | 138.6 | fake |
| 214.8 | 129.9 | 129.8 | 9.6 | 12 | 139.6 | fake |
| 214.9 | 130 | 129.9 | 11.4 | 10.9 | 139.7 | fake |
| 213.9 | 130.7 | 130.5 | 8.7 | 11.5 | 137.8 | fake |
| 214.2 | 130.6 | 130.4 | 12 | 10.2 | 139.6 | fake |
| 214.8 | 130.5 | 130.3 | 11.8 | 10.5 | 139.4 | fake |
| 214.8 | 129.6 | 130 | 10.4 | 11.6 | 139.2 | fake |
| 214.8 | 130.1 | 130 | 11.4 | 10.5 | 139.6 | fake |
| 214.9 | 130.4 | 130.2 | 11.9 | 10.7 | 139 | fake |
| 214.3 | 130.1 | 130.1 | 11.6 | 10.5 | 139.7 | fake |
| 214.5 | 130.4 | 130 | 9.9 | 12 | 139.6 | fake |
| 214.8 | 130.5 | 130.3 | 10.2 | 12.1 | 139.1 | fake |
| 214.5 | 130.2 | 130.4 | 8.2 | 11.8 | 137.8 | fake |
| 215 | 130.4 | 130.1 | 11.4 | 10.7 | 139.1 | fake |
| 214.8 | 130.6 | 130.6 | 8 | 11.4 | 138.7 | fake |
| 215 | 130.5 | 130.1 | 11 | 11.4 | 139.3 | fake |
| 214.6 | 130.5 | 130.4 | 10.1 | 11.4 | 139.3 | fake |
| 214.7 | 130.2 | 130.1 | 10.7 | 11.1 | 139.5 | fake |
| 214.7 | 130.4 | 130 | 11.5 | 10.7 | 139.4 | fake |
| 214.5 | 130.4 | 130 | 8 | 12.2 | 138.5 | fake |
| 214.8 | 130 | 129.7 | 11.4 | 10.6 | 139.2 | fake |
| 214.8 | 129.9 | 130.2 | 9.6 | 11.9 | 139.4 | fake |
| 214.6 | 130.3 | 130.2 | 12.7 | 9.1 | 139.2 | fake |
| 215.1 | 130.2 | 129.8 | 10.2 | 12 | 139.4 | fake |
| 215.4 | 130.5 | 130.6 | 8.8 | 11 | 138.6 | fake |
| 214.7 | 130.3 | 130.2 | 10.8 | 11.1 | 139.2 | fake |
| 215 | 130.5 | 130.3 | 9.6 | 11 | 138.5 | fake |
| 214.9 | 130.3 | 130.5 | 11.6 | 10.6 | 139.8 | fake |
| 215 | 130.4 | 130.3 | 9.9 | 12.1 | 139.6 | fake |
| 215.1 | 130.3 | 129.9 | 10.3 | 11.5 | 139.7 | fake |
| 214.8 | 130.3 | 130.4 | 10.6 | 11.1 | 140 | fake |
| 214.7 | 130.7 | 130.8 | 11.2 | 11.2 | 139.4 | fake |
| 214.3 | 129.9 | 129.9 | 10.2 | 11.5 | 139.6 | fake |
The data represent various measurements from a group of banknotes (currency). Column G, "type", shows whether each note is real or fake (counterfeit). Use discrimant analysis to come up with a discriminant score for each banknote. Place these scores in column H. Determine the cutoff score. Does using this cutoff score result in any errors in classification (real/fake)?
