Classification Trees and k-NN

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2

>Data

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1

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792 68 1 1 1 6 2 4 4 3 1 0 1 0 1 1 1 0 0 1

t

39 1 1 3 48 2 4 3 2 2 0 4 0 1 0 1 0 0 2

t

30 2 1 1 6 2 3 1 3 1 1 4 0 0 0 1 0 0 4

2,063 659 t

795 38 0 0 1 12 2 4 0 3 1 0 4 0 0 1 1 0 0 1

509 t

796 37 2 1 3 9 4 4 4 1 1 0 2 0 0 1 0 0 1 4

692 41 v

797 54 0 1 1 15 2 2 4 3 1 1 4 0 1 0 1 0 0 4

3,568 1,238 t

798 42 2 0 2 18 3 2 4 2 1 0 4 0 0 1 0 0 0 6

485 v

799 64 0 2 1 13 2 4 0 2 1 0 2 0 0 1 0 0 1 4

845 197 v

800 38 0 1 1 12 2 4 4 2 1 0 4 0 0 1 0 0 0 4 804 402 61 t
801 61 0 4 1 12 2 4 3 1 1 0 2 0 0 1 0 0 1 4

540 t

802 44 2 1 1 24 2 2 4 3 1 0 4 0 0 0 1 0 0 2

t

34 2 1 1 7 2 2 2 2 1 0 3 1 0 1 0 0 1 4 2,415 2,173 578 t

804 37 3 1 1 10 2 2 2 2 1 0 2 0 0 1 1 0 0 0

612 102 t

805 39 0 1 2 11 4 4 2 1 1 0 1 0 0 1 0 0 0 1

1,165 t

806 23 3 1 1 18 2 2 4 3 1 0 3 0 0 1 0 0 0 1

1,961 659 t

807 37 0 1 1 36 2 4 2 2 1 0 4 0 1 0 1 0 0 5

909

v

808 39 0 0 1 54 0 2 2 1 2 0 2 0 0 1 0 0 0 2

t

30 1 2 1 18 2 3 3 3 2 0 4 0 0 1 1 0 0 1

421 v

810 36 2 1 1 36 4 4 4 2 1 0 4 0 0 1 0 0 1 4

2,337 698 t

811 30 1 0 1 24 2 2 1 2 1 0 1 0 0 1 1 1 0 3

993 v

812 23 1 3 2 33 4 4 2 2 1 0 1 0 0 1 0 0 0 3

2,996

t

813 34 2 1 2 12 4 2 0 3 1 0 4 0 0 1 1 0 0 2

211 t

814 35 2 0 3 15 4 2 3 2 1 0 4 1 1 1 1 0 1 4

2,728 362 v

28 1 1 2 36 4 2 2 2 1 0 3 1 0 1 0 0 0 3

1,137 t

816 38 2 2 2 24 2 3 3 2 1 0 2 0 1 1 1 0 0 1

3,160 561 t

817 25 0 1 1 24 2 4 3 2 1 1 2 0 0 0 1 0 0 3

396 t

818 31 0 1 2 12 2 2 3 3 2 1 4 0 0 0 1 0 0 4

172 t

819 20 1 2 1 12 2 1 3 2 1 0 4 0 0 1 0 0 0 4 674 606

t

820 36 2 0 1 24 2 4 4 2 1 0 4 0 1 0 1 0 0 2

394 v

21 1 1 1 24 2 2 2 1 1 0 2 0 1 1 0 0 0 6

1,750 v

822 24 1 1 1 24 2 2 2 1 1 1 2 0 0 0 0 0 1 3

402 t

823 22 0 1 1 9 2 2 3 2 1 0 4 0 0 1 0 0 0 4

t

824 35 0 1 2 12 4 2 2 2 1 0 4 0 0 1 0 0 0 4 1,291

173 t

825 26 3 1 1 24 2 2 2 2 1 0 2 0 0 1 0 0 1 3 1,925

535 t

826 23 0 2 1 15 2 4 1 2 1 0 1 0 0 1 1 0 0 2

3,812

t

827 45 1 1 1 14 2 4 4 3 1 0 1 0 0 1 1 1 0 1

t

828 32 0 1 1 6 2 4 1 2 1 0 1 0 0 1 0 0 0 3 4,611

v

829 49 2 1 2 12 2 4 2 2 1 0 4 1 0 1 1 0 1 4 1,092 764 94 v
830 43 0 1 1 18 2 4 2 2 1 0 3 0 0 1 1 0 1 3

235 v

831 24 2 1 1 8 2 4 2 2 1 0 3 0 0 1 0 0 1 3 1,237 989

t

832 32 0 1 2 12 4 2 2 2 1 0 4 0 0 1 0 0 0 5 701 350 49 v
833 31 3 1 1 36 2 2 4 2 1 0 4 0 0 1 0 0 0 4

4,473 1,355 t

28 1 1 1 24 2 4 2 2 1 0 4 0 0 1 0 0 0 3

599 t

835 34 0 2 2 6 3 2 2 1 1 0 1 0 0 1 0 0 1 6

1,045 135 v

836 28 0 1 1 12 2 2 2 2 1 0 4 0 0 1 0 0 1 4 776 543 104 v
837 42 1 1 1 36 2 2 4 2 2 0 4 0 0 1 0 0 0 3

t

838 57 2 1 1 36 2 2 4 3 1 0 4 0 0 0 1 0 0 1

v

839 27 2 3 1 15 4 4 2 2 1 0 2 0 1 1 0 0 0 6 2,326 1,860 519 t

46 2 1 2 12 2 1 4 2 1 1 1 0 0 0 0 0 1 1 1,223

v

841 26 0 3 1 24 2 2 4 3 1 0 3 0 0 1 1 0 0 4

1,617 258 t

842 31 0 3 1 21 2 2 3 3 1 0 1 0 1 1 0 0 0 1

366 t

843 20 0 1 1 9 2 4 4 2 1 0 1 0 0 1 0 0 0 3

787 154 v

844 65 1 1 2 42 4 4 0 0 1 0 4 0 0 1 0 0 0 0

258 t

845 55 3 0 1 12 2 4 4 3 1 0 3 0 0 1 1 0 1 3 1,424 854 199 t
846 27 1 1 1 6 2 1 1 2 1 0 4 0 0 1 0 0 1 0 343 308 98 t

26 0 1 2 33 3 2 2 2 1 0 2 0 0 1 1 0 0 6

189 v

848 39 2 2 1 12 2 4 3 1 1 0 3 0 0 1 0 0 1 6

622 116 t

35 0 2 1 10 2 2 2 1 1 1 3 0 0 0 0 1 1 1

992 206 v

850 32 2 1 1 18 2 2 4 1 1 0 4 1 0 1 0 0 1 4

650 121 t

851 28 0 1 1 24 2 2 2 2 1 0 4 0 0 1 0 0 0 4

1,413 426 t

852 43 1 2 1 6 2 2 4 2 1 0 3 0 0 1 1 0 0 1 1,203 842 162 t
853 31 1 1 1 36 2 4 2 2 1 1 4 0 0 0 0 0 0 4

1,841

v

854 42 1 1 1 48 2 4 4 3 1 0 4 0 1 0 0 0 0 1

t

855 24 1 1 1 12 1 4 2 1 1 0 4 0 1 1 0 0 1 4 626 563

t

856 27 1 1 1 24 1 4 3 2 1 0 3 0 1 1 0 0 0 3

t

857 41 2 0 2 48 2 1 3 2 2 0 4 0 0 1 1 0 0 4

481 t

858 27 2 1 2 36 4 4 1 2 1 0 4 0 0 1 0 0 0 1

t

859 47 1 1 1 18 2 3 2 1 1 0 4 0 0 1 1 0 1 0

973

t

860 31 0 1 2 18 4 2 3 2 1 0 2 0 1 1 0 0 0 1

t

33 0 1 1 18 2 1 1 2 1 0 4 0 0 1 0 0 1 4 2,051

343 t

862 21 2 2 1 30 2 4 2 2 1 1 2 0 0 0 0 0 0 3

t

863 36 0 3 2 42 4 4 2 2 1 0 4 0 0 1 1 0 1 3 4,042

650 v

864 34 0 1 1 12 2 3 1 2 2 0 4 0 0 1 0 0 0 4 1,493 1,045 266 t
865 38 3 1 1 24 2 3 3 2 2 0 4 0 1 0 0 0 0 1 947 947

t

866 28 2 1 2 30 0 1 2 2 1 0 2 0 0 1 0 0 0 6

414 v

867 43 1 1 2 12 4 4 4 2 1 1 3 0 0 0 1 0 0 1

t

868 64 1 1 1 24 2 4 4 1 1 1 4 0 1 0 0 0 1 4

322 t

869 35 0 2 1 9 2 4 4 2 1 0 3 0 0 1 1 0 0 4

503 t

870 24 0 1 2 18 4 2 2 2 1 0 4 0 0 1 0 0 0 4

1,440 233 t

25 2 1 1 9 2 4 4 2 1 0 4 0 0 1 0 0 1 4

296 t

872 31 3 0 2 24 4 2 2 2 1 0 3 0 0 1 1 0 0 4

1,574 135 t

59 2 1 1 48 1 3 4 2 1 1 4 0 0 0 0 0 0 6

6,416

t

874 45 0 1 2 6 4 3 3 3 2 0 1 0 0 1 1 0 0 1

1,037 t

875 26 0 0 1 21 2 3 2 2 1 0 1 0 0 1 0 0 0 2

2,624 487 t

876 31 0 1 1 24 2 2 2 2 1 0 2 1 0 1 1 0 1 1 1,393 835 178 v

28 2 1 3 12 4 4 4 2 1 1 1 0 0 0 1 0 0 3

535 v

878 38 0 4 2 36 4 2 4 3 1 0 4 0 0 1 1 0 0 2

987 t

879 50 2 1 1 48 3 4 4 2 1 0 4 0 0 0 0 0 0 5

v

880 54 0 0 2 24 3 4 4 2 1 0 4 0 0 1 1 0 0 1 717 501 83 t
881 55 2 1 1 42 1 2 0 3 1 0 1 0 1 0 1 0 0 2

t

882 43 1 1 1 36 2 3 0 3 1 0 2 0 0 1 0 0 0 0

15,857

v

47 1 0 1 36 2 4 4 2 1 0 3 0 0 0 0 0 0 2

t

884 63 1 1 2 24 4 4 4 2 1 0 4 0 0 1 1 0 0 2

277 t

885 59 1 1 1 9 2 4 3 2 1 0 3 0 0 1 0 0 1 4

1,091 276 v

886 29 1 1 1 15 2 2 2 2 1 0 3 0 0 1 1 0 0 1 3,959

t

887 37 0 0 2 36 2 2 4 2 1 0 3 0 0 1 0 0 0 6

671 v

888 27 1 1 1 9 2 2 1 3 1 0 3 0 0 0 1 0 0 1

995

v

889 34 0 1 2 36 4 4 4 3 1 0 4 0 0 1 1 0 0 1

261 v

890 33 0 0 1 15 2 4 3 1 1 1 1 0 1 0 0 0 1 3

374 v

46 0 1 2 15 3 2 1 1 1 0 1 0 0 1 0 0 0 2

3,594 824 t

892 33 1 2 1 24 2 1 0 2 1 0 1 0 0 1 0 0 0 3 2,359

t

893 58 0 0 1 30 2 4 4 2 1 0 4 0 0 1 1 0 0 4

242 v

894 42 2 1 1 60 2 4 2 2 1 0 4 0 0 0 0 0 0 5

t

43 0 1 1 18 2 1 1 1 2 0 4 0 0 1 0 0 0 3 1,533 1,073

t

896 45 1 1 1 28 2 2 2 1 1 0 3 0 0 1 0 0 0 1

2,804

t

897 29 0 0 1 42 2 4 3 2 1 1 2 0 0 0 1 0 0 4

v

898 47 0 1 2 24 3 4 4 1 2 0 4 0 0 1 0 0 0 1

2,284

t

899 29 1 1 1 24 2 2 0 3 1 0 4 0 0 0 1 0 0 2

794 t

900 23 1 1 1 45 2 4 2 2 1 0 4 0 0 0 1 0 0 4

t

901 28 2 1 2 30 4 2 0 3 1 0 4 0 0 1 0 0 0 1

t

902 31 0 3 1 24 2 2 4 2 2 0 3 0 0 1 1 0 0 4

637 t

903 63 1 1 2 60 3 4 4 2 1 0 3 0 0 1 1 0 0 6

t

904 24 2 1 1 9 2 3 2 2 1 0 4 0 0 1 0 0 1 4 458 412 127 t
905 28 0 2 1 12 2 2 2 2 1 0 4 0 0 1 0 0 1 4

1,243 224 t

23 1 1 2 36 4 4 1 1 1 1 4 0 0 0 1 0 0 3

t

907 25 0 0 1 36 2 4 2 2 1 0 4 0 0 1 0 0 0 4 2,394

283 t

908 22 2 1 1 30 2 1 1 2 1 0 2 0 0 1 0 0 0 3

857 t

909 28 1 1 2 12 0 3 3 2 1 0 4 0 0 1 0 0 1 0

1,108 -368 t

910 36 2 0 2 20 3 4 3 3 2 1 3 0 1 0 1 0 0 2

807 t

911 35 2 3 1 14 2 2 4 2 1 0 1 0 0 1 1 0 1 6

846 144 t

912 36 2 3 1 12 4 3 3 3 1 0 3 0 0 1 1 0 0 1

2,366 810 v

913 29 1 1 2 12 4 2 2 2 1 0 3 0 0 1 0 0 1 1

3,149

t

914 44 3 1 1 12 2 2 2 1 1 1 2 0 0 0 1 0 0 4

264 v

915 46 0 4 2 18 4 4 4 2 1 0 4 0 0 1 0 0 0 4

1,582 344 t

916 34 0 0 2 6 4 2 2 1 2 0 1 0 0 1 0 0 1 4

1,328 218 v

31 2 1 2 24 4 4 4 2 1 0 4 0 0 1 1 0 1 6 1,935 967

t

918 65 1 1 2 21 4 4 4 2 1 0 4 0 0 1 0 0 1 1 571 456 87 t
919 33 2 1 2 18 0 4 2 2 1 0 1 0 1 1 1 0 0 3

702 t

920 40 2 1 1 18 3 3 4 3 1 0 4 0 0 1 1 0 0 3

t

921 55 0 4 1 12 2 2 3 2 1 0 3 0 0 1 0 1 0 2 1,413 1,271 384 t
922 64 0 1 1 10 2 4 2 2 1 0 2 0 0 1 1 0 0 1 1,364 1,364 373 t
923 22 1 1 1 24 2 1 1 2 1 0 4 0 1 0 0 0 0 3 3,149

323 v

924 39 1 1 1 30 2 3 4 2 2 0 1 1 0 1 0 0 0 4

376 t

925 22 0 1 1 18 2 4 0 2 1 1 3 0 0 0 0 0 1 4 433 346

t

926 57 0 2 3 11 4 4 0 1 1 0 4 0 0 1 0 0 1 4 1,154 1,154 219 t
927 25 0 0 2 24 2 2 4 2 1 0 4 0 0 1 0 0 0 4 999 999 197 t
928 29 0 2 1 24 2 4 2 3 1 1 4 0 0 0 1 0 0 4

1,330 310 t

929 48 1 1 1 24 3 4 1 2 1 0 4 0 1 1 0 0 1 4

614 -325 v

930 32 2 4 2 21 4 2 3 2 1 0 3 0 0 1 1 0 0 3

1,647 171 v

931 22 2 1 1 9 2 4 2 1 1 1 4 0 0 0 0 0 1 1 276 220 50 t
932 27 1 1 2 15 3 4 4 1 1 0 1 0 0 1 0 0 0 3

3,643 855 t

933 28 2 1 1 6 2 4 4 2 2 0 4 0 0 1 0 0 0 4

640 152 v

934 31 2 1 1 10 2 2 2 1 1 0 4 0 0 1 0 0 0 3

912 207 t

935 32 2 4 2 9 4 3 4 2 2 0 4 0 0 0 0 0 0 5

681 -538 t

936 23 1 1 1 30 2 4 3 2 1 1 4 0 0 0 0 0 1 3 2,406 1,924

v

937 40 2 1 1 18 2 4 3 2 1 1 2 0 0 0 0 0 1 3

699 v

938 52 0 2 2 6 4 4 2 1 1 0 4 0 0 1 0 0 0 1 362 253 41 t

27 0 1 2 9 2 2 3 2 1 0 3 0 0 1 0 0 0 6

1,159 200 v

940 43 0 4 2 24 4 1 2 1 1 0 4 0 0 1 0 0 1 4

1,061 172 t

941 28 3 3 3 12 4 2 3 2 1 0 4 0 0 1 1 0 1 1 939 751

t

942 33 2 0 1 18 2 2 2 2 1 0 4 0 0 1 0 0 0 1

729

t

943 55 1 1 3 18 4 4 0 0 2 0 2 0 0 0 0 0 0 0

833

t

944 26 3 1 1 12 1 1 1 0 1 0 4 0 0 1 0 0 1 6 609 548

t

945 61 2 4 2 15 3 3 2 2 1 0 3 0 1 1 0 0 0 0

907

v

946 32 0 1 1 18 2 2 1 2 1 0 3 0 0 1 1 0 0 4

556 t

947 35 0 1 2 24 3 3 3 1 1 0 3 0 0 1 1 0 0 2

3,275 604 t

948 44 1 1 2 15 4 4 4 2 2 0 4 0 0 1 1 0 0 3 1,478 886 137 v
949 26 0 1 1 6 2 3 2 2 1 1 2 1 0 0 0 0 0 1

3,518

t

950 28 3 2 2 6 4 4 4 2 2 0 2 0 0 1 1 0 0 1

166 t

951 45 0 2 1 39 2 2 4 3 1 0 4 0 0 1 1 0 0 2

5,152 948 t

952 36 0 0 2 6 4 4 4 2 1 0 4 0 0 0 0 0 0 4 700 350 29 t
953 41 1 1 1 6 2 4 1 1 2 0 3 0 0 1 1 0 1 1 662 595 182 v
954 45 3 1 1 18 2 1 1 1 1 0 1 0 1 1 0 0 0 3

3,049 902 v

955 35 0 0 2 48 4 1 3 2 1 0 2 0 0 0 1 0 0 2

1,010 v

956 31 2 1 2 18 4 2 1 1 1 0 2 0 0 1 0 0 1 3

v

957 31 1 1 1 48 2 2 2 2 1 0 3 0 0 1 1 0 0 4

v

958 27 0 1 2 24 2 3 1 1 1 0 4 0 0 1 0 0 0 0 937 655 103 t
959 60 1 1 2 12 4 3 4 2 1 0 3 0 0 1 0 0 0 3

1,572

t

960 32 0 1 1 24 3 2 2 2 1 0 1 0 0 0 0 0 0 6

975 t

961 45 0 0 1 15 2 4 4 2 2 0 4 0 1 0 0 0 0 2

780 130 v

962 49 0 1 1 12 2 2 2 1 1 0 4 0 0 1 0 0 1 1 640 320 44 t
963 64 0 0 1 9 2 4 4 1 1 0 1 0 0 1 0 0 1 5 3,832

323 v

964 26 1 1 2 42 3 2 3 2 2 0 3 0 1 1 1 0 0 4

v

965 40 1 1 1 12 2 4 2 1 2 1 4 0 0 0 0 0 0 5 684 615

v

966 41 2 1 1 18 4 1 4 2 1 0 2 0 0 1 1 0 0 3

1,098 t

967 47 3 1 1 30 4 4 4 2 1 0 4 0 0 1 0 0 0 4 3,017

323 t

968 26 0 1 1 18 2 1 1 2 1 0 3 0 0 1 0 0 1 4

293 v

969 31 1 4 1 12 2 3 2 2 2 0 1 0 0 1 0 0 0 1

882 t

970 40 3 1 1 15 2 4 4 3 1 1 4 0 0 0 1 0 0 5

208 v

37 2 1 1 9 2 2 2 1 2 0 2 0 0 1 0 0 1 4

2,118 630 t

972 31 2 2 2 20 0 4 4 2 1 0 3 0 1 1 1 0 0 2

809 t

973 36 3 4 2 24 4 4 2 2 1 0 2 0 0 1 1 0 1 6 1,275 892 116 t
974 26 2 2 2 30 0 4 2 1 1 1 4 0 0 0 0 0 0 6

t

975 33 0 1 1 15 2 2 3 2 1 0 2 0 0 1 0 0 0 2

366 v

976 35 1 1 2 12 4 3 4 2 1 0 4 0 0 1 0 0 0 1 691 414

t

977 63 0 1 2 12 4 4 4 1 1 0 2 0 0 1 1 0 1 4

288 t

978 67 2 1 1 18 2 4 0 2 1 0 2 0 0 1 1 0 0 0

3,872 1,149 v

979 27 1 1 1 40 4 3 2 2 1 0 4 0 1 1 1 0 0 5

t

980 35 2 0 1 9 2 2 1 0 1 0 4 0 0 1 0 0 1 1

929 192 t

981 26 2 1 2 15 0 1 1 0 1 1 2 0 0 0 0 0 1 1

-428 v

26 1 1 1 18 2 3 2 2 1 0 4 0 1 1 0 0 1 4

807 -352 t

983 38 2 0 1 48 3 4 2 2 2 0 4 0 0 0 1 0 0 6

t

984 46 0 1 2 24 4 3 4 2 1 0 4 0 0 1 0 0 1 4

482 t

985 57 1 1 1 12 2 4 4 1 1 0 4 0 1 1 0 0 1 4 709 425

v

26 0 2 1 9 2 2 2 2 2 1 1 1 0 0 0 1 1 1

2,146 481 t

987 24 1 1 1 12 2 4 4 2 1 1 4 0 0 0 0 0 0 3 652 456 112 v
988 36 0 0 2 30 4 3 3 2 1 0 2 0 0 1 0 0 0 4

459 t

989 40 0 0 2 28 1 4 1 2 2 1 3 1 1 0 1 0 1 2

v

990 42 1 1 1 18 2 3 2 2 1 0 2 0 0 1 0 0 0 3

3,322

v

991 33 2 0 1 9 2 2 2 1 1 0 1 0 0 1 0 0 1 1

679 v

992 39 1 1 1 24 2 2 4 3 1 1 4 0 0 0 1 0 0 3

2,676

v

993 43 1 1 2 12 3 2 2 1 2 0 4 0 0 1 0 0 1 1 1,344 940 158 v
994 46 0 0 2 24 4 4 2 3 2 0 2 0 0 1 1 0 0 2

894 t

995 31 0 2 2 24 2 4 4 2 1 0 2 0 0 1 0 0 0 4

t

996 30 2 2 1 24 2 4 4 2 1 0 4 0 0 0 0 0 0 3

1,841 322 t

997 40 1 1 2 11 4 2 2 1 2 0 1 0 0 1 0 0 1 1

324 t

998 25 2 2 1 15 1 2 2 2 1 1 2 0 0 0 0 0 0 1 1,264 884

t

999 48 2 1 2 24 4 2 4 1 1 0 4 0 0 1 0 0 0 4 1,743

202 t

27 2 2 1 45 4 4 0 2 1 0 3 0 0 1 0 0 0 2

1,200 v

OBS# AGE CHK_ACCT SAV_ACCT NUM_CREDITS DURATION HISTORY PRESENT_RESIDENT EMPLOYMENT JOB NUM_DEPENDENTS RENT INSTALL_RATE GUARANTOR OTHER_INSTALL OWN_RES TELEPHONE FOREIGN REAL_ESTATE TYPE AMOUNT_REQUESTED CREDIT_EXTENDED NPV Splitting Variable
1 6 7 0 4 1,

 16 9 1,0

 5 24 3 v
25 12 1,

 29 1,1

 65 –

 47
4

 8 2,

 13 1,9

 20 26
36 18 1,

 91 1,7

 21 41
30 2,

 33 1,1

 66 23
333 1,

86 48
27 1,

 39 69 11
8,

 133 6,

 50 1,

 40
44 5,9

 43 94 -1,

 82
10 56 61 55 1

 63
1,

 46 1,3

 22 37
31 1,4

 49 1,

304 2

 52
1,8

 35 9

 17 –

 508
14 8,4

 87 5,0

 92 9

 76
15 70 4

96 93
42 1,

 34 1,076 2

95
2,8

 72 2,

 58 74
950 57 -1

 88
19 28 9,

572 6,

 700 -4,

 38
54 4,

 59 4,

131 -2,

 912
936 84 1

 98
3,074 2,1

 51 2

 62
625 3

 75 90
4,

 210 2,

 526 –

 81
915 –

 337
666 466 67
1,

657 1,

491 429
32 2,

 662 1,

 863 4

 85
3,3

 68 2,

694 414
6

 45 114
672 470 116
5,

 381 1,

768
4,

 249 2,

549 -1,

157
6,

 615 3,

 307 3

 79
5,

743 4,020 674
1,

236 741 140
1,

 239 867 194
3,079 2,7

 71 811
2,

212 2,212 611
1,

820 542
1,4

 73 473 430
1,

 967 1,

 376 301
3,

 186 862
3,

 448 3,

 103 824
1,

 884 1,

 507 415
11,054 7,

 737 1,

 64
3,

620 1,

 810 334
3,092 1,

546 –

 790
3,

 573 2,

 501 590
1,

 934 1,

547 282
3,

 123 2,

 498 –

1,

330
759 53 –

305
5,507 4,

 956 848
2,

273 1,

818 350
1,

 534 920 -415
99
2,

964 1,012
3,

234 -1,

 151
1,056 –

388
60 385 308
2,

 329 1,

3

97 2

 77
518 –

 192
3,

 652 2,

 191
3,

 660 2,

928 80
750 525 –

403
7,

 476 5,

980 1,

 585
1,

297 648 137
4,

 139 3,

311 551
1,

538 1,

230 364
975
1,123 1,010 –

 535
629 440
1,337 1,

203 –

 479
6,403 3,

 841 696
2,

325 1,

 627 356
428 342
5,045 3,027
78 2,

812 1,

406 198
4,

 933 3,

 946 -2,

 365
1,

 188 594 –

 446
1,

 597 401
907 816 248
83 1,

101 990
2,

375 1,

 425 148
5,

179 4,

 143 -2,

232
2,

 235 1,

 341 –

603
5,

 804 4,

643
7,

 678 4,

 606 682
89 7,

 814 7,032 2,

 237
2,

 442 1,

 709 -10
2,625 –

1,

254
4,

 454 3,

 117 397
1,

817 1,

 453 207
1,

 747 1,572 457
3,

527 2,

468 522
3,590 2,

872 343
1,

 740 1,

 218 168
1,

514 1,

 211 296
8,

386 -3,

 751
100 3,

 565 2,

852 553
5,

 951 5,

355 -3,080
102 4,308 -2,

 807
2,

 647 770
104 3,

618 879
105 1,

 158 926 253
106 5,

965 1,508
107 1,

537 1,

 383 291
108 730 511
109 1,

213 1,091 261
110 1,

 409 1,

 268 318
111 2,

 323 1,

393
112 392 352
113 3,

 868 2,

 707 372
6,

887 6,198 -4,

 715
115 4,

 795 3,356 805
1,

924 1,

539
1,055 844 164
118 763 610 175
119 4,

455 –

2,

746
120 3,844 3,075 -2,

 447
121 1,168 251
122 3,

 835 2,301 458
1,

 200 1,080 299
124 2,507 1,

 504 262
125 1,

 595
126 2,251 1,

575 349
127 1,603 961 195
128 1,

 402 1,261
129 1,

574 1,

416
130 9,

398 6,

 578 –

2,415
3,804 2,282 -1,051
132 5,511 3,

 306 723
1,

938 1,

550 -696
134 1,

 864 -1,

183
135 3,

 599 2,

159 426
136 959 –

 247
3,

399 2,039 493
138 6,070 758
12,

 976 6,

 488 -3,

587
983 589 141
1,887 1,

 698 312
142 7,253 5,077
2,028 1,

825
144 1

1,

 328 7,

 929 -4,440
145 1,620 972
146
147 1,

721 860 163
–

 220
149 1,

 201 720 165
150 8,318 7,

486 -5,

624
5,493 4,

 394 1,032
152 4,

686 2,343 378
153 3,

190 1,

914 -1,031
154 2,

 631 1,

315 –

 459
155 2,032 1,

 219
156 1,750 1,050 229
1,546 –

813
5,

 954 4,

 167
3,124 616
160 1,965
161 918 734 –

284
162 1,

 240 744 -409
1,

530 1,

 377 –

653
1,553 931 –

 366
1,308 784
166 1,

 922 1,

 345 –

494
900 -491
5,

 742 1,198
169 2,

279
170 1,841
171 6,

331 5,

 697 -2,024
172 838 -590
173 433 389 -328
174 1,

 987 1,192 –

 693
1,048
176 683 –

 300
177 2,124 1,486 -587
178 8,065 4,

839 -3,043
1,

 940 1,746
180 6,

 313 2,

 196
181 1,795 1,615
182 484 338
3,016 2,

 412 567
184 1,

216 729 –

 266
185 2,

 993 2,095 359
4,042 2,425
187 2,169 1,

952 –

 1,355
1,343
189 9,

 277 5,

566 981
1,

829 464
3,

 485 2,

788 456
4,

 736 4,262 –

1,

718
193 12,

 749 3,442
1,

 670 1,

 503 -488
1,236 286
2,145 1,072 –

 673
197 2,

353 2,117 405
7,393 4,

435 767
199 4,844 3,

 390 -2,152
1,

569 941
2,096 1,

467
202 1,567 1,096 241
2,241 1,

 568 258
204 5,

 866 2,933 225
205 6,204 4,

 963 1,229
206 1,262 1,009 275
1,

953 1,

562 -976
208 1,164
209 363
797 717 –

 302
932
6,

260 3,

756 708
1,237
214 2,708 1,

354
215 3,416
5,848 4,093 896
217 757
2,064 1,

 651 –

 882
1,647 1,152 -610
3,915 1,

957 -1,448
221 5,117 3,

581
222 5,

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223
224 2,141 1,

712 445
4,

605 3,

 684 -1,

645
226 2,150 1,720 -683
227 5,302 4,

771 564
228 12,169 7,301 1,522
1,445 1,011
6,

 419 4,493
231 1,

 344 806 –

 348
3,749 2,624 612
233 2,

910 1,455
7,

408 5,926 -3,

545
3,213 1,

927 434
3,229 1,119
2,247 1,797
238 2,146 1,

716 320
1,

 283 898
3,249 2,599
8,648 6,918 -4,433
242 2,

 292 -1,

 437
243 958
244 1,872 1,

497
245 2,629 1,

577
246 2,759 2,207 421
3,017 2,715 656
654 -188
3,

 622 2,173
250 1,113
1,126 563
252 2,

687 791
7,119 5,

695 -2,010
1,503 427
255 6,350 3,810 –

1,

 837
256 6,

 999 4,

 899 -1,

 881
257
5,433 4,

889 1,312
259 1,388 1,249
1,100 265
1,102 –

822
3,

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 685 766
263 3,914 2,348 –

1,440
264 1,

444
4,

623 2,

 773 -2,096
2,

303 2,072 –

968
267 1,

 792
10,366 7,256
269 1,

478 1,330
270 2,896 2,027
271 1,377 688
272 2,476 1,

733
1,228 -376
274 760 608
3,160
276
2,214 1,328
278 3,275 880
1,

410 846
280 1,221 854
281 4,272 1,000
9,629 5,

 777 -1,

853
2,712
11,816 7,089 -4,581
285 1,

943 1,

360 -792
1,

471
287 2,

 439 2,195 -1,208
288 1,

382
289 2,181 1,

962 319
290 2,171 1,

 519
10,

 477 5,238 604
2,

991 2,

 691 802
1,366 1,092 –

 502
294 1,224 1,101
295 557
4,113 2,879 -1,160
3,

 556 2,844 632
298 1,193 –

 424
2,

923 1,

 753
1,936
7,882 4,729
1,199 -289
1,804 1,623 407
1,264 1,137
6,187 4,

949 997
3,378 2,026
14,421 10,094 -7,360
5,954
309 1,

755 1,053
310 3,

617 2,170
1,

919 1,535
7,

 855 4,

713 –

1,

 659
781
314 1,

 984 1,

 785
2,

462 1,231 -464
316 7,758 4,654
317 7,308 6,577 2,059
1,414
3,777 2,266 492
2,108 1,

897
321 902 -273
322 1,

908 1,526 -1,279
2,

978
324 779
1,185 592
326 4,151 2,

490 413
327 2,

748 1,648
3,060 1,

 836 -836
1,

520 1,064
4,

796 3,357 764
1,038 830
332 -256
2,659 1,329
11,590 -4,476
335 4,439 3,551
336 6,199 3,

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1,766
13,756 8,253 1,802
339 798
340 1,

369
1,277
1,

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2,058 1,

646
-280
346 2,670 1,

869
347 754 452
1,238
960
368
351 1,216 –

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3,488 1,744
1,311
2,864 –

559
1,

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1

2,389 8,672 -3,366
358 725
2,

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2,718 1,

 630 –

831
361 3,349 2,344 -1,215
362 3,632 2,179
1,

858
1,980 1,188 -398
1,

851 1,

665
8,086 4,043 -1,

774
367 735
2,080
5,103 4,592
370 4,716 4,244
371 2,503 2,002
1,138
373
374 2,603 1,822
2,

483 2,234
5,771 5,193 1,122
12,

680 6,340 -2,

703
2,223 1,333
379 -192
380 2,

 892 2,313
3,051 1,830 –

555
731 438
5,084 3,

558
1,559
1,442 -573
387 4,526 4,073
874
1,098 658
5,

800 4,

 640
391 1,386
2,142 1,

 499
1,

 801 465
395
396 10,

974 6,

584 -2,

 944
2,397 1,

677 -538
7,297 3,648 -2,507
8,229 6,

583 -2,272
400 3,959 3,167 916
4,

870 2,922 -1,742
1,403
2,069 1,862
404 1,

474 1,474
6,143 3,685 -1,770
2,225 1,

 780 -747
3,181 2,

544 598
1,

977 1,383 -961
2,315 2,083
1,318 1,186
411 2,445
1,680 1,344
1,924 –

843
10,144 8,115 2,159
2,288
6,967 4,

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417 909 727
418 3,414 2,048 –

1,278
-134
420 3,031 2,424 -997
1,

495 1,196
422 3,342 2,673
423 4,657 4,191 1,287
1,544 1,235
3,447 2,412 509
2,030 1,

827
11,

998 10,798 -4,141
3,

878 2,326
7,629 6,103
10,127 6,076 -2,454
432 1,494
1,028 925
4,110 3,

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3,949 3,159
436
2,473 1,978 -1,048
14,

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2,563
2,406
441 2,899 2,

 609 826
1,381 1,242 –

443
2,

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638
2,136 1,708
5,096 4,076 -1,

739
4,817 2,

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 679
1,950 1,170
1,245 996 -453
449 1,163
450 2,122 1,061
451 1,207 -375
2,255
3,105
1,255
1,079
4,712 3,298
1,082 973
2,133 600
460 1,358
461 1,275 765
1,

808 1,265 -751
463 2,600 1,

560 -557
948 -325
1,880 1,316
2,346 1,407
1,047 523
2,

 580 1,290 -805
469 9,

 857 6,899
2,284
2,

528 1,

 769
472 14,027 7,013 –

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2,

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1,039
3,380 2,

704
475 14,179
1,555 -545
1,

480 1,036
6,468 2,006
3,062 1,

531
7,472 5,230 1,339
482 3,931 3,537 -1,

985
3,780 1,890
2,327 –

772
3,422
10,

875 7,612 1,341
487 2,210 1,989 -948
3,231
489 4,057 2,839 -918
1,169 701
1,022
3,161 -2,801
6,872 6,184 -2,721
1,498
1,

 845 1,660
496 1,

893
2,831 2,264
1,419
500 2,390 2,151
9,055
1,282 -352
1,374
4,746 3,322 -1,100
505 1,393
506 783 626
5,190
1,412 988
510 15,

945 7,972 -6,114
11,938 8,356 -3,313
512 3,578 2,862
513 2,121
1,240
515 3,566 2,139
516 -302
517
7,485 5,988 -2,232
1,360 1,088
1,501 1,200 -764
521 10,623 6,373
2,

613
524 1,

823 1,093 -648
1,258
7,418 5,192 1,304
561 -263
2,697
529 10,

 722 9,

649 2,569
9,960 7,968 -2,393
1,

 543 1,234
532 2,196 -989
533 3,398 819
3,384 -1,846
1,459 1,021
536 1,246 1,121 -569
1,542
7,685 4,611 -3,379
2,238 1,342
540 11,760 7,056 1,248
541 1,631 -926
5,

 842 4,089
2,779 1,

667
1,484 -456
1,244
2,679
2,924 2,046
548 3,114 2,802 -1,133
1,209 -475
2,996 2,696 -1,242
1,309 -396
552
7,

966 4,779
554 2,319 1,159 -874
-474
1,331 -277
2,230
1,223 -517
-441
2,

828 1,696
12,204
1,

979 1,781
7,980 5,

586 -3,503
3,973 2,781
6,314 5,682
4,530 593
6,527 2,161
571 5,324 3,194
7,

596 4,557
3,990 1,326
576 1,285 1,156 -424
1,155
1,371 -388
1,941
9,271 6,489 –

 3,149
582 7,432 4,459
1,

602
-337
3,976
2,221 1,554
588 1,322
-413
8,

 947 6,262
1,107 885
18,424 12,896 -6,960
-173
-892
8,358 7,522
738
1,715 1,029
1,006
1,433 859
1,736
601 2,835 1,984
1,212
6,110 4,

 888 1,392
2,299
4,527 -2,129
607
3,965 2,

775 –

1,203
1,295
2,012
6,458 –

2,804
7,174 5,739 -3,167
614 8,613 7,751
1,288
1,131 -313
2,577 2,061
619 5,129 3,077 -1,488
1,382 1,243
621 1,

935 1,548
3,104 2,483 724
10,961 7,672 -3,241
14,555 11,

644 -5,406
2,684
6,304 4,412 681
628 2,404 1,923
4,788 2,394
4,

 675 2,805
4,811 3,848
633 5,801 3,480
634 2,101
635
636 2,331 1,165
637 3,

850 2,695
2,320 2,088
639
2,578
641 2,197
642 2,579 2,321 –

1,291
2,743 2,194
1,842 1,289 -599
3,

905 3,514
1,493 -819
2,312
2,769
650 9,034 7,227 -3,545
2,360 1,652
1,361
1,532
655 2,022 1,617
2,278 -868
1,372 -428
2,

 930 2,051
2,799 1,399
-595
661 2,263
9,157 2,

 992
663 2,116 1,

 692
664 1,376
4,583 3,208
-311
3,496 2,796
668 5,150 3,605
669 1,347 942
1,103
671 6,560 5,

904 -2,623
1,538
921
11,560 9,248 -4,648
2,511 1,757
676 1,299
3,108 2,797 -1,444
3,535 710
2,675 1,605
7,511 5,257 -1,602
1,338
3,966 3,569 -1,

 955
886
6,

761 4,056 -1,421
894
970
689 2,825 2,260
690 2,606 2,084
3,763 1,324
2,848 1,993
1,049
745 -200
2,009 -615
3,656 3,290
2,520 2,016 -647
6,289 3,144
3,857 3,471 1,057
6,948 4,863
702 8,072 5,650
2,100 –

832
705 1,352
706 9,566 7,652
1,007
3,816
12,612 6,306 -4,459
2,622 2,359
711 6,078 5,470 1,702
2,132 1,492
-330
714 -368
1,577
1,175
1,424
3,

913 3,130
7,

865 5,505 -2,364
2,767 2,490 –

2,105
1,204
726 2,149 -1,220
1,533 1,379
728
7,582 6,065
1,158
-340
732 4,351 3,045
1,525
-222
3,758 2,254
4,463 -1,012
3,650 2,920
7,374 6,636
1,408
8,471 4,235
1,149
2,576 2,318
3,386 3,047 -1,723
7,238 5,790
5,152
3,757
1,585 1,268
6,850 3,425 -1,718
752 7,127 4,988 -1,596
1,202
3,612 3,250 1,045
1,552
5,003 3,502 -1,636
4,241 –

2,676
2,671 -927
3,676 2,940
1,437 1,005 -356
15,653 7,826 937
1,247 -605
10,222 9,199 2,951
3,609 2,165
5,595 3,916 -2,321
2,

969
1,505 1,354
1,882 1,317 -576
4,380 3,504
1,274 -268
776 1,271
2,

901 1,740
778 3,509
2,751 1,925
4,165 3,748 -3,135
786 3,343 1,671
787 3,331
3,595 2,876
789 15,672 14,104 -12,029
1,592
3,711 2,597
14,896 13,406 -7,231
793 10,297 7,207 -4,283
794 2,063
2,859 2,287
1,154
3,568
2,427 2,184
1,409
3,059 2,447
12,579 10,063 -3,320
803
1,225
7,228 6,505
1,961
1,819 -637
9,436 7,548 1,677
809 2,249 1,574
2,337
7,721 4,632
4,281 -1,312
1,860 1,302
2,728
815 5,371 4,

 833
3,512
3,972 2,383
1,963 1,177
-211
2,760 1,656
821 6,568 5,

911
3,021 2,114
1,478 1,034 -372
903
1,732
3,812 1,205
8,978 7,182 -3,830
2,766 -1,336
2,515 1,257
-430
4,473
834 4,169 2,501
1,743
3,446 3,101 -1,708
14,318 11,454 -5,352
840 856 -335
3,235
2,782 1,669
1,313
3,394 2,036
847 2,764 1,658
1,037
849 1,418
1,301
1,413
2,302 -888
7,763 5,434 -2,226
-231
3,552 1,776 -894
3,979 2,785
2,820 2,256 -1,037
1,217 -395
2,775 2,220 -689
861 1,435
3,441 2,752 -1,151
3,233
-411
4,221 2,954
4,843 4,358 -1,482
2,384 1,430
2,753 2,202
1,800
871 1,206 1,085
3,148
873 6,416 -3,914
6,761 6,084
5,248
877 3,617 3,255
5,711 4,568
6,224 4,979 -4,477
9,283 8,354 2,423
15,857 4,387
883 8,335 5,001 -2,571
2,957 1,774
1,364
2,771 –

1,073
7,409 4,445
1,422 -316
6,614 3,307
2,186 1,530
891 3,594
2,123 -1,023
1,867 1,120
6,288 5,659 -3,

994
895 -566
4,006 -1,282
7,166 5,016 1,013
2,538 -904
6,579 3,947
1,845 1,476 -884
5,234 4,187 -1,605
3,430 2,401
6,836 3,418 -2,339
2,073
906 6,229 3,737 -1,801
1,436
3,832 3,448
1,108
7,057 5,645
1,410
2,366
3,499 -1,351
1,881 1,128
1,582
1,898
917 -865
3,244 2,919
4,297 3,437 -1,255
1,889
2,522 1,765
-116
1,901
1,024
2,745
3,643
1,068
1,521
1,136
-1,024
3,001 2,700
939 1,449
1,516
-250
1,042 -364
1,190 -394
-349
1,512 -338
4,594 2,756
4,679
3,518 1,046
1,323 1,058
8,588
3,049
8,858 7,086
1,928 1,735 -849
6,758 4,054 -1,503
2,246 -654
3,863 3,476
1,300
1,916
4,370 3,933 -1,461
-487
6,361 5,088
1,810
1,453 1,162
3,651 3,285
1,905 1,143
971 2,118
6,148 4,918
4,280 2,568 -1,974
3,029 1,817
-225
1,655 1,489
3,872
5,998 4,198 -3,572
1,549
1,778 1,066
982 1,345
6,681 6,012 1,714
2,611 2,349
-142
986 3,577
6,742 4,045
7,824 7,041 1,536
4,153 -1,278
3,195 2,556
3,345 -971
6,842 5,473
3,621 3,258 -1,327
3,069
3,939 2,363
-286
1,394
1000 4,576 4,118

_x000D__x000D_

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Data Dictionary

1 OBS#

2 AGE

Numerical

3 CHK_ACCT

4 SAV_ACCT

Categorical

5 NUM_CREDITS

Numerical

6 DURATION

Numerical

7 HISTORY

Categorical

8 PRESENT_RESIDENT

Categorical

9 EMPLOYMENT

Categorical

10 JOB

Categorical

11 NUM_DEPENDENTS

Numerical

12 RENT

13 INSTALL_RATE

Numerical

14 GUARANTOR

Binary 0: No, 1: Yes

15 OTHER_INSTALL

Binary 0: No, 1: Yes

16 OWN_RES

Binary 0: No, 1: Yes

17 TELEPHONE

Binary 0: No, 1: Yes

18 FOREIGN

Binary 0: No, 1: Yes

19 REAL_ESTATE

Binary 0: No, 1: Yes

20 TYPE

Categorical

21 AMOUNT_REQUESTED

Numerical

22 CREDIT_EXTENDED

Numerical

23 NPV

Numerical

24 Splitting Variable

Categorical

Var. # Variable Name Description Variable Type Code Description
Observation No. Numerical Sequence number in dataset
Age in years
Checking account status Categorical 0 : < 0
1: 0 < ...< 200
2 : => 200
3: no checking account
Average balance in savings account 0 : < 100
1 : 100<= ... < 500
2 : 500<= ... < 1000
3 : =>1000
4 : unknown/ no savings account
Number of existing credits
Duration of credit in months
Credit history 0: no credits taken
1: all credits at this bank paid back duly
2: existing credits paid back duly till now
3: delay in paying off in the past
4: critical account
Present resident since – years 0: <= 1 year
1<…<=2 years
2<…<=3 years
3:>4years
Present employment since 0 : unemployed
1: < 1 year
2 : 1 <= ... < 4 years
3 : 4 <=... < 7 years
4 : >= 7 years
Nature of job 0 : unemployed/ unskilled – non-resident
1 : unskilled – resident
2 : skilled employee / official
3 : management/ self-employed/highly qualified employee/ officer
Number of people for whom liable to provide maintenance
Applicant rents Binary 0: No, 1: Yes
Installment rate as % of disposable income
Applicant has a guarantor
Applicant has other installment plan credit
Applicant owns residence
Applicant has phone in his or her name
Foreign worker
Applicant owns real estate
Purpose of Credit 0: Other
1: New Car
2: Used Car
3: Furniture
4: Durable
5: Education
6: Retraining
Credit Amount Applied for
Credit Made
Net Profit from the Loan (Net Loss if Negative)
A variable added to ensure a balanced partition t: training record, v: validation record

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Classification Trees and k-NN applied to Bank Credit

This assignment concludes the analysis of the credit data, exploring whether we can improve on our earlier analysis that utilized linear and logistic regression. Please refer to the earlier assignments for the data description, and repeat if needed the data preparation steps, using the

credit2.xlsx

data:

In the spreadsheet under the tab “Data,” you will find data pertaining to 1,000 personal loan accounts. The tab “Data Dictionary” contains a description of what the various variables mean.

As a part of a new credit application, the company collects information about the applicant. The company then decides an amount of the credit extended (the variable CREDIT_EXTENDED). For these 1,000 accounts, we also have information on how profitable each account turned out to be (the variable NPV). A negative value indicates a net loss, and this typically happens when the debtor defaults on his/her payments.

1. Create a categorical variable that indicates whether or not a new credit extension will result in a positive NPV.

2. Create dummy variables for all categorical variables with more than two values (if appropriate).

3. Split the data into two parts using the splitting variable that is a part of the data set[footnoteRef:1]. This is to ensure a more balanced split between the validation and training samples. After the data partition you should have 666 rows in your training data and 334 in your validation data. [1: If you run into issues that your # of columns exceeds 50, you may leave out the employment variable.]

Please answer all questions. Supply supporting documentation and show calculations as needed. Please submit a single well-formatted  Word file.  In addition, please upload an Excel file with your model outputs .

Classification trees

Classify customers as profitable/not profitable with a classification tree

1. Run the Classification Tree algorithm using all the relevant independent variables (excluding as before Credit Extended, Obs# etc. ) including all the dummy variables (recall that one does not exclude base values when running classification trees), with the profitable/not profitable as the output variable. Use the validation data to prune back the tree, and select to use the best pruned tree for scoring.

a. Include the classification confusion matrix for the validation sample and a figure of the best pruned tree as Exhibits.  

2. Analyze the output.

a. How many decision nodes are in the best pruned tree?

b. What is the error rate for i) the training data and ii) the validation data in the best pruned tree?

c. What explains the difference in the error rate?

d. Which applicants for credit will get rejected by the model (using the best pruned tree)? (Describe the type of customers using the English language.)

3. Using the model for decision making.

a. Consider a 27-year-old domestic student that has $100 in her checking account but no savings account. The student has one existing credits, which has so far been paid back duly. The credit duration is 12 months. The applicant has been renting her current place for less than 12 months, does not own any real estate, just started graduate school (the present employment variable is set to 1 and nature of job to 2). The applicant has no dependents and no guarantor. The applicant wants to buy a used car and has requested $4,500 in credit, and therefore the installment rate is quite high, or 2.25%. However, the applicant does not have other installment plan credits. Finally, the applicant has a phone in her name.

How would the best pruned tree classify the student?

k-NN

Classify customers as profitable/not profitable with k-NN

4. Run the k-NN algorithm for classification, testing all values of k from 1 to 10, selecting to score the data on the best k (remember to standardize/normalize the data). Request detailed output for both the training and validation data.

a. Using the search log, plot the %Error of the validation sample. Include the plot in your assignment.

b. What is the best value of k?

c. Briefly explain why the % Error is zero for the training sample when k=1, but not for the validation sample.

5. Analyze the output.

a. What some of the main differences are between the customers identified as most likely to be profitable and the customers that are identified as least likely to be profitable? Briefly discuss. 

Method comparisons

You have now run three different classification algorithms on this data; logistic regression, classification tree and k-NN. Compare their performance in two ways. First using statistical measures and second using their possible impact on the credit extension process. Feel free to take advantage of the solutions to Individual Assignment 2 as a starting point.

Hint: Below is a potential set-up to measure the business impact. First, collect the predicted probability of being profitable for both the training and validation data as well as the true NPV into a single spreadsheet. Perhaps similar to this:

Then select a cell for a cut-off (in my case I used E1). Then for each method and each sample we can calculate the cumulative profit, for a specific cut-off using the sumifs() function in Excel. Specifically, the following formula sums up the NPV of all credit extensions that are made using the training sample and logistic regression:

You then need to extend this approach to both data samples and all three methods. Perhaps similarly to this:

You can then create data tables to investigate the best cut-off for each method and the corresponding NPV on the validation data.

Week 2 Individual Assignment 2: Quantitative Analysis of Credit – Solutions

This assignment is based on the data we used during our two live sessions, but it has been updated to include a splitting variable (

credit2.xlsx

). In the spreadsheet under the tab “Data,” you will find data

pertaining to

1

,

0

00 personal loan accounts. The tab “Data Dictionary” contains a description of what the various variables mean.

As a part of a new credit application, the company collects information about the applicant. The company then decides an amount of the credit extended (the variable CREDIT_EXTENDED). For these 1,000 accounts, we also have information on how profitable each account turned out to be (the variable

NPV

). A negative value indicates a net loss, and this typically happens when the debtor defaults on his/her payments.

The goal in this assignment is to investigate how one can use this data to better manage the bank’s credit extension program. Specifically, our goal is to develop a classification model to classify a new credit account as “profitable” or “not profitable.” Secondly we want to compare its performance in the context of decision support to a linear regression model that predicts NPV directly.

Please answer all the questions. Supply supporting documentation and show calculations as

needed. Please submit a single, well-formatted PDF or Word file. The instructor should not need to go searching for your answers! In addition, please upload an Excel file with your model outputs – the file will not be graded, but will help the instructor give you feedback, if your model differs substantially from the solutions.

For extra assistance, you may want to access the tutorials located on the course resource center page.

Data Preparation

The data preparation repeats the steps from the live session:

a) The goal is to predict whether or not a new credit will result in a profitable account. Create a new variable to use as the dependent variable.

b) Create dummy variables for all categorical variables with more than 2 values (or if you prefer, you can sort your variables into numerical and categorical when you run the model).

c) Split the data into 2 parts using the splitting variable that has been added to the data set. This is to ensure a more balanced split between the

validation

and

training

samples.
Note

that Analytic Solver Data Mining only allows

50

columns in the analysis, so leave out your base dummies (if you created them) when partitioning. After the data partition, you should have 666 rows in your training data and 334 in your validation data.

The Assignment

1. Applying Logistic Regression

If one fits a Logistic Regression Model using all the independent variables, one observes a) a gap in the classification performance between the training data and the validation data, and b) very

high p-values for some of the variables. The performance gap between the training and validation may be a sign of overfitting, and the high p-values may be a sign of “useless” variables in the model, or of multicollinearity.

a) Our goal is to classify credit requests into “profitable” and “not profitable.” To that end, select to run “forward selection,” and set FIN down to 1.5 (this lowers the threshold for a variable to enter the model, resulting in more models to choose from). Select one of the forward selection models based on the principles discussed in the book and/or the tutorials on the course resource center and run it.

Note: Exclude Credit Extended and any other variables not appropriate for the analysis.

Include the model (the variables and the corresponding regression coefficients) as an Exhibit.

Predictor

Estimate

Intercept

–

0.1

409

AGE

0.0

350

NUM_CREDITS

–

0.3

472

DURATION

-0.0208

INSTALL_RATE

–

0.4

070

GUARANTOR

0.8

746

OTHER_INSTALL

–

0.6

841

OWN_RES

0.5

299

REAL_ESTATE

0.4792

AMOUNT_REQUESTED

-0.0001

GENDER_F

0.3894

CHK_ACCT_1

0.7

863

CHK_ACCT_2

1.3594

CHK_ACCT_3

2.1811

SAV_ACCT_4

0.8059

HISTORY_4

0.6811

PRESENT_RESIDENT_2

-0.4176

EMPLOYMENT_2

0.3505

EMPLOYMENT_3

0.7936

TYPE_2

1.9168

TYPE_3

0.5290

TYPE_4

0.6752

Please refer to the Excel solutions for additional details.

b) Why did you select this particular model?

From the feature selection output we chose to run the model with 18 coefficients. This model was chosen because it has Cp close to the number of coefficients in the model (and not higher), it has probability above .05 and the improvement in RSS if we expand the model further is relatively small.

c) Based on your model, and setting the

cut-off

value to 0.5, please provide the following information (based on the validation data):

· The sensitivity of the model: 0.88

· The specificity of the model: 0.495

In other words, at the default cut-off we correctly identify 88% of the profitable customers, but include around 50% of the unprofitable customers.

2. ROC Curves

a) We now want to compare the predictive performance of the model on the training sample and on the validation sample. Create a single figure that compares the ROC curves for both the training sample and the validation sample. Please refer to the ROC tutorials in the resource center as needed for a step-by-step guide for creating an ROC curve. Alternatively, you can combine the two curves that Analytical Solver Data Mining provides into a single plot.

Include a
clean
figure as an Exhibit.

3. Finding the “best” cut-off

a) Create a data-table to calculate the

total

NPV (assuming we extend credit to all classified as

“profitable” as a function of the cut-off based on the training data. Select the best cut- off.

Include the table as an Exhibit.

0

0

cut-off 0 0.1

0.2

 0.3 0.4 0.5 0.6 0.7 0.8

0.9

 1

NPV training

-56740

-26705

-2644

18771

45734

68023

88312

90

200

84

550

63883

NPV validation

-39141

-15636

-6309

13945

31128

36599

51636

51623

43999

32005

Please refer to the solutions for a more detailed table.

b) What is your selected cut-off? 0.725 (based on a more detailed table in the Excel file)

c) Create the same table for the validation data. Include the table as an Exhibit.

Refer to the table above

d) Apply the cut-off you selected based on the training data to the validation data. What is the total profit on the validation data? $51,330

e) Provide a figure that shows the cumulative NPV as a function of the cut-off for both the training data and the validation data.

4. Comparison with linear regression

a) Repeat our model development from our first live session (note you need to repeat the steps as we now have a new data split). Rerun a variable selection model to find a “good model” using the updated data.

Include the model (the variables and the corresponding regression coefficients) as an Exhibit.

For my linear regression model I selected to run a stepwise selection with the default

parameters. Note that this is not the only “correct” model, a careful analysis would have included both backwards, forwards and stepwise variable selection and the comparison of a couple of candidate models, before selecting one based on their performance (and you can define performance in multiple ways as we have discussed). Hopefully your model’s performance exceeds the performance of the model discussed here!

Predictor

Estimate

Intercept

INSTALL_RATE

<0.001

AMOUNT_REQUESTED

<0.001

CHK_ACCT_1

CHK_ACCT_2

CHK_ACCT_3

<0.001

SAV_ACCT_4

TYPE_2

<0.001

0.001

P-Value

594.6747

<

0.001

RENT

-288.596

0.010

-152.409

-0.17395

327.4346

0.005

396.0738

0.033

563.3212

378.5465

 0.001

525.5611

TYPE_5

-489.718

0.011

TYPE_6

-50

0

.304

b) Create a data table that summarizes the total profit as a function of the NPV cut-off for extending credit on the training data (note that now your cut-off is in $ you will need to investigate what is a good cut-off, for example -$50 or $50, or something else). Select the best cut-off.

Include the table as an Exhibit.

Please refer to the Excel file for detailed information, the table below shows some highlights.

0

total
training 		NPV
validation

–

750

74541

16890

–

700

75131

19502

–

650

73680

24582

–

600

71729

27223

-550

79911

28620
–

500

77482

30658

–

450

80913

30622

–

400

89518

33657

-350

86859

41614

–

300

78862

41014

–

250

84718

41885

-200

85475

44566

–

150

81744

39188

–

100

80865

36418
-50

75280

31917

71269

31705
50

64194

29323
100

62314

27407
150

59080

19587
200

52279

19844
250

50432

19938
300

46356

20864
350

40465

16292
400

33020

18002
450

25780

16046
500

22455

13862
550

16736

9610
600

12651

8478
650

9394

6152
700

9235

6167
750

8759

5329

c) What is your selected cut-off? -$400

d) Create the same table for the validation data and include it as an Exhibit.

Please refer to the table above

e) Apply the cut-off you found to the validation data. What is the total profit on the validation data? $33,657

f) Provide a figure that shows the cumulative NPV as a function of the cut-off for both the training data and the validation data.

5. Model comparison

a) Compare the performance of the logistic regression model and the linear regression model. How does the total profit compare for the two models? Which model would you select as the foundation of a decision support system and why?

When we compare the performance as measured by the total NPV is higher for both the training and the validation sample, as a result I would select my Logistic Regression model over the Linear Regression model (although it may be worth the effort to try to improve on the linear regression model).

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