PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 PROFIT VERSION 3.20 ORIGINATOR: J. DOUGLAS CARROLL AND J-J. CHANG, BELL LABORATORIES, MURRAY HILL, NEW JERSEY 07974, U.S.A. +-------------------------------------------------------------------------------------------+ | | | M D S (X) PROGRAMS | | | | AN INTEGRATED SERIES OF MULTIDIMENSIONAL SCALING PROGRAMS WITH A COMMON COMMAND | | LANGUAGE. | | | | PROGRAMS AND SUPPORTING DOCUMENTATION OTHER ENQUIRIES SHOULD | | ARE DISTRIBUTED FROM BE ADDRESSED TO | | | | MDS(X) PROJECT, MDS(X) PROJECT, | | PROGRAM LIBRARY UNIT, SOCIOLOGICAL RESEARCH UNIT, | | UNIVERSITY OF EDINBURGH, UNIVERSITY COLLEGE, | | 18 BUCCLEUCH PLACE, P.O. BOX 78, | | EDINBURGH EH8 9LN, CARDIFF CF1 1XL, | | U.K. U.K. | | | | USERS ARE EXPECTED TO CITE THE PROGRAM ORIGINATOR AND THE MDS(X) SERIES WHEN | | PUBLISHING RESULTS. | | | +-------------------------------------------------------------------------------------------+ 1. RUN NAME PROFIT TEST DATA. 2. TASK NAME ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. 3. PRINT DATA YES 4. # OF SUBJECTS 4 5. # OF STIMULI 20 6. DIMENSIONS 4 7. PARAMETERS REGRESSION(3) 8. PLOT FINAL,RESIDUALS ,SHEPARD ,INITIAL 9. PUNCH SPSS,SOLUTION 10. PRINT INITIAL,RESIDUALS 11. COMMENT 12. PARAMETER DEFINITIONS. 13. ---------------------- 14. 15. 2) REGRESSION TYPE (DEFAULT VALUE 1) 16. 1: LINEAR REGRESSION ONLY. 17. 2: NON-LINEAR REGRESSION ONLY. 18. 3: BOTH REGRESSIONS (INDEPENDENTLY). 19. 4) MATFORM (DEFAULT VALUE 0) 20. 0: THE INPUT CONFIGURATION IS PUNCHED STIMULI(ROWS) 21. BY DIMENSIONS(COLUMNS). 22. 1: THE INPUT CONFIGURATION IS PUNCHED DIMENSIONS 23. (ROWS) BY STIMULI(COLUMNS). 24. 5) WEIGHT (DEFAULT VALUE 0) 25. SEE CARROLL AND CHANG WRITE UP 26. 6) BCO (DEFAULT VALUE 0) 27. SEE CARROLL AND CHANG WRITE UP 28. 29. INPUT FORMAT (2X,4F7.3) 30. READ CONFIG INPUT INITIAL CONFIGURATION 1 2 3 4 1 0.3090 -0.4760 1.1260 0.7500 2 0.5880 -0.2940 -2.2510 0.2500 3 0.8090 0.4760 2.6940 -0.8500 4 0.9510 0.2940 -1.8640 -0.4500 5 1.0000 -0.2940 2.1180 0.8500 6 0.9510 -0.4760 -0.3520 -0.1500 7 0.8090 0.2940 0.6990 -0.2500 8 0.5880 -0.4760 -2.1350 -0.9500 9 0.3090 0.0000 1.5970 0.6500 10 0.0000 -0.2940 -2.0060 0.4500 11 -0.3090 0.4760 -1.1310 -0.6500 12 -0.5880 -0.2940 -0.6380 0.5500 13 -0.8090 0.0000 3.3300 0.9500 14 -0.9510 -0.4760 -1.3420 0.1500 15 -1.0000 0.0000 -0.0360 0.3500 16 -0.9510 0.4760 0.3130 0.0500 17 -0.8090 0.0000 -0.8960 -0.7500 18 -0.5880 0.2940 -1.7070 -0.5500 19 -0.3090 0.2940 -1.5340 -0.3500 20 0.0000 0.4760 4.0330 -0.0500 31. INPUT FORMAT (20F3.1) 32. READ MATRIX INPUT PROPERTY MATRICES PROPERTY : PROPERTY NUMBER ONE. 0.100000 0.200000 0.300000 0.400000 0.500000 0.600000 0.700000 0.800000 0.900000 1.000000 1.100000 1.200000 1.300000 1.400000 1.500000 1.600000 1.700000 1.800000 1.900000 2.000000 PROPERTY : PROPERTY NUMBER TWO. 1.800000 0.600000 0.200000 0.400000 0.900000 1.700000 1.100000 0.700000 2.000000 1.600000 1.200000 1.900000 0.500000 0.800000 1.000000 1.300000 1.500000 0.100000 1.400000 0.300000 PROPERTY : PROPERTY NUMBER THREE. 1.500000 0.100000 1.800000 0.400000 1.700000 1.100000 1.400000 0.200000 1.600000 0.300000 0.800000 1.000000 1.900000 0.700000 1.200000 1.300000 0.900000 0.500000 0.600000 2.000000 PROPERTY : PROPERTY NUMBER FOUR. 1.800000 1.300000 0.200000 0.600000 1.900000 0.900000 0.800000 0.100000 1.700000 1.500000 0.400000 1.600000 2.000000 1.200000 1.400000 1.100000 0.300000 0.500000 0.700000 1.000000 33. COMPUTE * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * L I N E A R R E G R E S S I O N * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. NORMALIZED CONFIGURATION ------------------------ 1 0.3090 0.5880 0.8090 0.9510 1.0000 0.9510 0.8090 0.5880 0.3090 0.0000 -0.3090 -0.5880 -0.8090 -0.9510 -1.0000 -0.9510 -0.8090 -0.5880 -0.3090 0.0000 2 -0.4760 -0.2940 0.4760 0.2940 -0.2940 -0.4760 0.2940 -0.4760 0.0000 -0.2940 0.4760 -0.2940 0.0000 -0.4760 0.0000 0.4760 0.0000 0.2940 0.2940 0.4760 3 1.1251 -2.2519 2.6931 -1.8649 2.1171 -0.3529 0.6981 -2.1359 1.5961 -2.0069 -1.1319 -0.6389 3.3291 -1.3429 -0.0369 0.3121 -0.8969 -1.7079 -1.5349 4.0321 4 0.7500 0.2500 -0.8500 -0.4500 0.8500 -0.1500 -0.2500 -0.9500 0.6500 0.4500 -0.6500 0.5500 0.9500 0.1500 0.3500 0.0500 -0.7500 -0.5500 -0.3500 -0.0500 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 2 PLOTTED AGAINST DIMENSION 1 DIMENSION 2 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.06 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 ! 28 0.97 ! 6 7 3 ! 24 0.81 ! ! 20 0.65 ! 8 2 ! 16 0.48 ! ! 12 0.32 ! 1 9 ! 8 0.16 ! ! 4 DIMENSION 1 + -0.16 ! 10 20 ! -4 -0.32 ! 19 11 ! -8 -0.48 ! ! -12 -0.65 ! 12 18 ! -16 -0.81 ! ! -20 -0.97 ! 14 17 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.06 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 17 OVERLAYS POINT(S) 13 POINT 7 OVERLAYS POINT(S) 4 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 3 PLOTTED AGAINST DIMENSION 1 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.06 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 ! 28 0.97 ! 6 7 3 ! 24 0.81 ! ! 20 0.65 ! 8 ! 16 0.48 ! ! 12 0.32 ! 1 9 ! 8 0.16 ! ! 4 DIMENSION 1 + -0.16 ! 10 20 ! -4 -0.32 ! 19 11 ! -8 -0.48 ! ! -12 -0.65 ! 18 12 ! -16 -0.81 ! ! -20 -0.97 ! 14 17 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.06 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 8 OVERLAYS POINT(S) 2 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 4 PLOTTED AGAINST DIMENSION 1 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.06 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 ! 28 0.97 ! 3 7 6 ! 24 0.81 ! ! 20 0.65 ! 8 ! 16 0.48 ! ! 12 0.32 ! 9 1 ! 8 0.16 ! ! 4 DIMENSION 1 + -0.16 ! 20 10 ! -4 -0.32 ! 11 19 ! -8 -0.48 ! ! -12 -0.65 ! 18 12 ! -16 -0.81 ! ! -20 -0.97 ! 17 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.06 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 16 OVERLAYS POINT(S) 14 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 3 PLOTTED AGAINST DIMENSION 2 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.06 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! ! 28 0.97 ! ! 24 0.81 ! ! 20 0.65 ! ! 16 0.48 ! 11 16 3 20 ! 12 0.32 ! 18 19 7 ! 8 0.16 ! ! 4 DIMENSION 2 + -0.16 ! 17 15 9 13 ! -4 -0.32 ! 2 10 12 5 ! -8 -0.48 ! 8 14 6 1 ! -12 -0.65 ! ! -16 -0.81 ! ! -20 -0.97 ! ! -24 -1.13 ! ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.06 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 18 OVERLAYS POINT(S) 4 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 4 PLOTTED AGAINST DIMENSION 2 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.06 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! ! 28 0.97 ! ! 24 0.81 ! ! 20 0.65 ! ! 16 0.48 ! 3 11 20 16 ! 12 0.32 ! 18 19 ! 8 0.16 ! ! 4 DIMENSION 2 + -0.16 ! 17 15 9 13 ! -4 -0.32 ! 10 12 5 ! -8 -0.48 ! 8 6 14 1 ! -12 -0.65 ! ! -16 -0.81 ! ! -20 -0.97 ! ! -24 -1.13 ! ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.06 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 19 OVERLAYS POINT(S) 7 POINT 10 OVERLAYS POINT(S) 2 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 4 PLOTTED AGAINST DIMENSION 3 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! 20 ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! 13 ! 84 3.23 ! ! 80 3.06 ! ! 76 2.90 ! ! 72 2.74 ! 3 ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! 5 ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! 9 ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 1 ! 28 0.97 ! ! 24 0.81 ! 7 ! 20 0.65 ! ! 16 0.48 ! ! 12 0.32 ! 16 ! 8 0.16 ! ! 4 DIMENSION 3 + -0.16 ! 15 ! -4 -0.32 ! ! -8 -0.48 ! 6 ! -12 -0.65 ! 12 ! -16 -0.81 ! ! -20 -0.97 ! 17 ! -24 -1.13 ! ! -28 -1.29 ! 11 ! -32 -1.45 ! 14 ! -36 -1.61 ! 19 ! -40 -1.77 ! 18 ! -44 -1.94 ! 4 ! -48 -2.10 ! 10 ! -52 -2.26 ! 8 2 ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.06 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 MINOR PRODUCT MOMENT MATRIX --------------------------- 1 10.0004 -0.6819 2.2658 -0.9825 2 -0.6819 2.5041 3.6204 -1.7066 3 2.2658 3.6204 70.3083 7.9682 4 -0.9825 -1.7066 7.9682 6.6500 XMAT ---- 1 0.0183 0.0899 0.0464 0.1397 0.1063 0.0616 0.0958 -0.0009 0.0501 0.0300 -0.0123 -0.0532 -0.0881 -0.1255 -0.0943 -0.0669 -0.1247 -0.0469 -0.0053 -0.0200 2 -0.1831 0.0786 -0.0194 0.3104 -0.0292 -0.2738 0.1671 -0.4083 0.0998 0.0627 0.2124 -0.0641 -0.0462 -0.2946 0.0091 0.2479 -0.2271 0.1247 0.1961 0.0368 3 0.0198 -0.0544 0.0603 -0.0587 0.0148 0.0192 -0.0046 0.0217 0.0013 -0.0495 -0.0249 -0.0124 0.0454 0.0095 -0.0030 -0.0152 0.0283 -0.0262 -0.0363 0.0651 4 0.0448 0.1362 -0.1982 0.1029 0.1183 -0.1067 0.0250 -0.2737 0.1292 0.1475 -0.0152 0.0732 0.0637 -0.0830 0.0446 0.0794 -0.2233 -0.0262 0.0404 -0.0790 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 1 PROPERTY NAME : PROPERTY NUMBER ONE. SSQ= 0.52193 XL= 0.72245 ORIGINAL VALUES ON PROPERTY NO : 1 PROPERTY NAME : PROPERTY NUMBER ONE. 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000 PROJECTIONS ON FITTED VECTORS -0.6060 -0.8033 -0.1808 -0.6978 -1.1366 -0.9889 -0.5094 -0.5220 -0.3850 -0.3267 0.5772 0.2306 0.6031 0.5687 0.7867 1.0154 0.8899 0.7045 0.4079 0.3724 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 1 IS 0.836 , RSQ= 0.699 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 1 PROPERTY NAME : PROPERTY NUMBER ONE. OBTAINED VALUES 2.06 ! * ! ! 1.93 ! * ! ! 1.84 ! * ! 1.76 ! * ! 1.71 ! * * 1.58 ! * ! ! 1.54 ! * 1.41 ! * ! ! 0.97 ! * ! ! ! ! ! ! ! ! ! 0.83 ! * ! ! 0.79 ! * 0.66 ! * ! ! 0.61 ! * 0.57 ! * 0.44 !* ! ! 0.35 ! * ! 0.18 ! * ! ! ! 0.04 ! * ! ! ! +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 2 PROPERTY NAME : PROPERTY NUMBER TWO. SSQ= 0.21334 XL= 0.46189 ORIGINAL VALUES ON PROPERTY NO : 2 PROPERTY NAME : PROPERTY NUMBER TWO. 1.8000 0.6000 0.2000 0.4000 0.9000 1.7000 1.1000 0.7000 2.0000 1.6000 1.2000 1.9000 0.5000 0.8000 1.0000 1.3000 1.5000 0.1000 1.4000 0.3000 PROJECTIONS ON FITTED VECTORS 0.6784 0.6461 -1.4029 -0.3431 0.4341 0.1539 -0.5478 -0.1614 0.2337 0.8145 -0.6019 0.7460 0.3111 0.6930 0.3591 -0.2235 -0.3649 -0.3033 -0.2022 -0.9189 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 2 IS 0.474 , RSQ= 0.225 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 2 PROPERTY NAME : PROPERTY NUMBER TWO. OBTAINED VALUES ! 2.17 ! * 2.13 ! * 2.08 ! * 1.86 ! * * ! ! ! ! 1.76 ! * ! 1.72 ! * 1.67 ! * 1.58 ! * ! 1.27 ! * ! ! ! ! ! ! 1.22 ! * 1.13 ! * * ! 1.09 !* 1.04 ! * 0.86 ! * ! ! ! 0.81 ! * 0.50 ! * ! ! ! ! ! ! 0.05 ! * ! ! ! ! ! ! ! ! ! ! +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 3 PROPERTY NAME : PROPERTY NUMBER THREE. SSQ= 0.09171 XL= 0.30283 ORIGINAL VALUES ON PROPERTY NO : 3 PROPERTY NAME : PROPERTY NUMBER THREE. 1.5000 0.1000 1.8000 0.4000 1.7000 1.1000 1.4000 0.2000 1.6000 0.3000 0.8000 1.0000 1.9000 0.7000 1.2000 1.3000 0.9000 0.5000 0.6000 2.0000 PROJECTIONS ON FITTED VECTORS 1.0957 -2.3015 2.4787 -2.0167 1.9621 -0.5054 0.5409 -2.2376 1.5503 -1.9548 -1.0980 -0.5058 3.4548 -1.1554 0.1432 0.4609 -0.7836 -1.6135 -1.4801 3.9659 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 3 IS 0.972 , RSQ= 0.944 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 3 PROPERTY NAME : PROPERTY NUMBER THREE. OBTAINED VALUES ! 5.88 ! * ! ! 4.86 ! * ! ! ! ! ! ! ! 4.35 ! * ! ! ! 3.97 ! * ! ! 3.45 ! * ! ! ! 2.94 ! * ! ! ! 2.81 ! * 2.56 ! * ! 1.92 ! * ! ! ! ! 1.53 ! * * ! ! 1.28 ! * ! 1.15 ! * 0.90 ! * ! 0.77 ! * 0.38 ! * ! ! 0.13 ! * * ! 0.13 ! * +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 4 PROPERTY NAME : PROPERTY NUMBER FOUR. SSQ= 1.00000 XL= 1.00000 ORIGINAL VALUES ON PROPERTY NO : 4 PROPERTY NAME : PROPERTY NUMBER FOUR. 1.8000 1.3000 0.2000 0.6000 1.9000 0.9000 0.8000 0.1000 1.7000 1.5000 0.4000 1.6000 2.0000 1.2000 1.4000 1.1000 0.3000 0.5000 0.7000 1.0000 PROJECTIONS ON FITTED VECTORS 0.7500 0.2500 -0.8500 -0.4500 0.8500 -0.1500 -0.2500 -0.9500 0.6500 0.4500 -0.6500 0.5500 0.9500 0.1500 0.3500 0.0500 -0.7500 -0.5500 -0.3500 -0.0500 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 4 IS 1.000 , RSQ= 1.000 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 4 PROPERTY NAME : PROPERTY NUMBER FOUR. OBTAINED VALUES ! 1.82 ! * ! 1.71 ! * ! ! 1.63 ! * ! 1.51 ! * ! ! 1.43 ! * ! 1.32 ! * ! ! 1.20 ! * ! ! 1.12 ! * ! 1.01 ! * ! ! 0.93 ! * ! 0.81 ! * ! ! 0.74 ! * ! 0.62 ! * ! ! 0.50 ! * ! ! 0.43 ! * ! 0.31 ! * ! ! 0.23 ! * ! 0.12 ! * ! ! 0.04 ! * ! ! +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. ============================================ RESULTS OF THE LINEAR REGRESSION PROCEDURE ============================================ TABLE 1. THE MAXIMUM CORRELATION BETWEEN THE PROPERTY AND THE PROJECTIONS ON FITTED VECTOR RHO PROPERTY 1 0.8360 PROPERTY NUMBER ONE. 2 0.4740 PROPERTY NUMBER TWO. 3 0.9715 PROPERTY NUMBER THREE. 4 1.0000 PROPERTY NUMBER FOUR. TABLE 2. DIRECTION COSINES OF FITTED VECTORS IN NORMALIZED SPACE DIMENSION VECTOR 1 2 3 4 1 -0.8880 0.3585 0.0465 -0.2843 2 -0.0895 -0.6335 -0.1437 0.7550 3 -0.1643 -0.0107 0.9854 0.0436 4 0.0000 0.0000 0.0000 1.0000 TABLE 3. COSINE OF ANGLES BETWEEN VECTORS VECTOR 1 2 3 4 2 -0.3690 3 0.1755 -0.0872 4 -0.2843 0.7550 0.0436 STIMULUS SPACE IN 4 DIMENSIONS 1 0.3090 -0.4760 1.1260 0.7500 2 0.5880 -0.2940 -2.2510 0.2500 3 0.8090 0.4760 2.6940 -0.8500 4 0.9510 0.2940 -1.8640 -0.4500 5 1.0000 -0.2940 2.1180 0.8500 6 0.9510 -0.4760 -0.3520 -0.1500 7 0.8090 0.2940 0.6990 -0.2500 8 0.5880 -0.4760 -2.1350 -0.9500 9 0.3090 0.0000 1.5970 0.6500 10 0.0000 -0.2940 -2.0060 0.4500 11 -0.3090 0.4760 -1.1310 -0.6500 12 -0.5880 -0.2940 -0.6380 0.5500 13 -0.8090 0.0000 3.3300 0.9500 14 -0.9510 -0.4760 -1.3420 0.1500 15 -1.0000 0.0000 -0.0360 0.3500 16 -0.9510 0.4760 0.3130 0.0500 17 -0.8090 0.0000 -0.8960 -0.7500 18 -0.5880 0.2940 -1.7070 -0.5500 19 -0.3090 0.2940 -1.5340 -0.3500 20 0.0000 0.4760 4.0330 -0.0500 TABLE OF RESIDUALS ------------------ 1 2 3 4 1 0.7060 1.1216 0.4043 1.0500 2 1.0033 -0.0461 2.4015 1.0500 3 0.4808 1.6029 -0.6787 1.0500 4 1.0978 0.7431 2.4167 1.0500 5 1.6366 0.4659 -0.2621 1.0500 6 1.5889 1.5461 1.6054 1.0500 7 1.2094 1.6478 0.8591 1.0500 8 1.3220 0.8614 2.4376 1.0500 9 1.2850 1.7663 0.0497 1.0500 10 1.3267 0.7855 2.2548 1.0500 11 0.5228 1.8019 1.8980 1.0500 12 0.9694 1.1540 1.5058 1.0500 13 0.6969 0.1889 -1.5548 1.0500 14 0.8313 0.1070 1.8554 1.0500 15 0.7133 0.6409 1.0568 1.0500 16 0.5846 1.5235 0.8391 1.0500 17 0.8101 1.8649 1.6836 1.0500 18 1.0955 0.4033 2.1135 1.0500 19 1.4921 1.6022 2.0801 1.0500 20 1.6276 1.2189 -1.9659 1.0500 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. HISTOGRAM OF LOG RESIDUALS FREQUENCY 23! *** 22! *** 21! *** 20! *** 19! *** 18! *** 17! *** 16! *** 15! *** 14! *** 13! *** 12! *** 11! *** 10! *** 9! *** *** 8! *** *** 7! *** *** 6! ****** ********* 5! ****** ********* 4! *************** ********* 3! ****************************** 2!*** *** *** ****************************** 1!*** *** *** *** ********************************************* !!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=! LOG -1.337 -1.040 -0.742 -0.445 -0.148 0.149 0.446 ACTUAL 0.046 0.091 0.181 0.359 0.711 1.410 2.795 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 2 PLOTTED AGAINST DIMENSION 1 DIMENSION 2 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 ! 28 0.97 ! 6 7 3 ! 24 0.81 ! ! 20 0.65 ! 8 2 ! 16 0.48 ! ! 12 0.32 ! 1 9 ! 8 0.16 ! ! 4 DIMENSION 1 + -0.16 ! 22 10 24 20 ! -4 -0.32 ! 23 19 11 ! -8 -0.48 ! ! -12 -0.65 ! 12 18 ! -16 -0.81 ! ! -20 -0.97 ! 14 17 21 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 17 OVERLAYS POINT(S) 13 POINT 7 OVERLAYS POINT(S) 4 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 3 PLOTTED AGAINST DIMENSION 1 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 ! 28 0.97 ! 6 7 3 ! 24 0.81 ! ! 20 0.65 ! 2 8 ! 16 0.48 ! ! 12 0.32 ! 1 9 ! 8 0.16 ! ! 4 DIMENSION 1 + -0.16 ! 10 24 20 ! -4 -0.32 ! 19 11 23 ! -8 -0.48 ! ! -12 -0.65 ! 18 12 ! -16 -0.81 ! ! -20 -0.97 ! 14 17 21 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 24 OVERLAYS POINT(S) 22 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 4 PLOTTED AGAINST DIMENSION 1 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 ! 28 0.97 ! 3 7 6 ! 24 0.81 ! ! 20 0.65 ! 8 2 ! 16 0.48 ! ! 12 0.32 ! 9 1 ! 8 0.16 ! ! 4 DIMENSION 1 + -0.16 ! 20 10 24 ! -4 -0.32 ! 11 19 23 ! -8 -0.48 ! ! -12 -0.65 ! 18 12 ! -16 -0.81 ! ! -20 -0.97 ! 17 21 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 16 OVERLAYS POINT(S) 14 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 3 PLOTTED AGAINST DIMENSION 2 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! ! 28 0.97 ! ! 24 0.81 ! ! 20 0.65 ! ! 16 0.48 ! 11 21 16 3 20 ! 12 0.32 ! 18 19 7 ! 8 0.16 ! ! 4 DIMENSION 2 + -0.16 ! 17 24 23 9 13 ! -4 -0.32 ! 2 10 12 5 ! -8 -0.48 ! 8 14 6 1 ! -12 -0.65 ! 22 ! -16 -0.81 ! ! -20 -0.97 ! ! -24 -1.13 ! ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 24 OVERLAYS POINT(S) 15 POINT 18 OVERLAYS POINT(S) 4 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 4 PLOTTED AGAINST DIMENSION 2 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! ! 28 0.97 ! ! 24 0.81 ! ! 20 0.65 ! ! 16 0.48 ! 3 11 21 20 16 ! 12 0.32 ! 18 19 ! 8 0.16 ! ! 4 DIMENSION 2 + -0.16 ! 17 23 9 24 ! -4 -0.32 ! 10 12 5 ! -8 -0.48 ! 8 6 14 1 ! -12 -0.65 ! 22 ! -16 -0.81 ! ! -20 -0.97 ! ! -24 -1.13 ! ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 24 OVERLAYS POINT(S) 13 POINT 19 OVERLAYS POINT(S) 7 POINT 10 OVERLAYS POINT(S) 2 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 4 PLOTTED AGAINST DIMENSION 3 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! 20 ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! 13 ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! 3 ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! 5 ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! 9 ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 23 1 ! 28 0.97 ! ! 24 0.81 ! 7 ! 20 0.65 ! ! 16 0.48 ! ! 12 0.32 ! 16 ! 8 0.16 ! 21 ! 4 DIMENSION 3 + -0.16 ! 15 22 24 ! -4 -0.32 ! ! -8 -0.48 ! 6 ! -12 -0.65 ! 12 ! -16 -0.81 ! ! -20 -0.97 ! 17 ! -24 -1.13 ! ! -28 -1.29 ! 11 ! -32 -1.45 ! 14 ! -36 -1.61 ! 19 ! -40 -1.77 ! 18 ! -44 -1.94 ! 4 ! -48 -2.10 ! 10 ! -52 -2.26 ! 8 2 ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINTS 1 TO 20 ARE STIMULI, POINTS 21 TO 24 ARE SUBJECT VECTORS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * N O N - L I NE A R R E G R E S S I O N * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. BASIC STRUCTURE --------------- 1 0.1411 -0.2595 0.3096 -0.2193 0.2626 -0.0423 0.0833 -0.2640 0.1976 -0.2304 -0.1402 -0.0710 0.4004 -0.1617 -0.0033 0.0363 -0.1189 -0.2085 -0.1843 0.4746 2 0.0386 0.1617 0.3051 0.3203 0.2372 0.3035 0.2607 0.2573 0.0417 -0.0316 -0.0464 -0.2175 -0.3200 -0.2937 -0.3292 -0.2956 -0.1851 -0.1365 -0.0680 -0.0023 3 0.3244 0.2615 -0.3976 -0.0642 0.3461 0.1266 -0.0962 -0.1086 0.1871 0.2725 -0.2909 0.2119 0.1381 0.1069 0.0373 -0.1586 -0.2846 -0.2269 -0.1437 -0.2418 4 -0.1486 0.1560 -0.1103 0.3637 0.0425 -0.2971 0.1817 -0.5098 0.1604 0.1370 0.1910 -0.0320 -0.0313 -0.3324 0.0154 0.2589 -0.3372 0.0992 0.2040 -0.0129 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 2 PLOTTED AGAINST DIMENSION 1 DIMENSION 2 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 0.51 ! ! 100 0.49 ! 20 ! 96 0.47 ! ! 92 0.45 ! ! 88 0.43 ! ! 84 0.41 ! 13 ! 80 0.39 ! ! 76 0.37 ! ! 72 0.35 ! ! 68 0.33 ! 3 ! 64 0.31 ! ! 60 0.29 ! ! 56 0.27 ! 5 ! 52 0.24 ! ! 48 0.22 ! ! 44 0.20 ! 9 ! 40 0.18 ! ! 36 0.16 ! ! 32 0.14 ! 1 ! 28 0.12 ! ! 24 0.10 ! 7 ! 20 0.08 ! ! 16 0.06 ! ! 12 0.04 ! 16 ! 8 0.02 ! ! 4 DIMENSION 1 + -0.02 ! 15 ! -4 -0.04 ! ! -8 -0.06 ! 6 ! -12 -0.08 ! 12 ! -16 -0.10 ! ! -20 -0.12 ! 17 ! -24 -0.14 ! 11 ! -28 -0.16 ! 14 ! -32 -0.18 ! ! -36 -0.20 ! 19 ! -40 -0.22 ! 18 4 ! -44 -0.24 ! 10 ! -48 -0.27 ! 2 8 ! -52 -0.29 ! ! -56 -0.31 ! ! -60 -0.33 ! ! -64 -0.35 ! ! -68 -0.37 ! ! -72 -0.39 ! ! -76 -0.41 ! ! -80 -0.43 ! ! -84 -0.45 ! ! -88 -0.47 ! ! -92 -0.49 ! ! -96 -0.51 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -0.51-0.46-0.41-0.36-0.31-0.25-0.20-0.15-0.10-0.05 * 0.05 0.10 0.15 0.20 0.25 0.31 0.36 0.41 0.46 0.51 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 3 PLOTTED AGAINST DIMENSION 1 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 0.51 ! ! 100 0.49 ! 20 ! 96 0.47 ! ! 92 0.45 ! ! 88 0.43 ! ! 84 0.41 ! 13 ! 80 0.39 ! ! 76 0.37 ! ! 72 0.35 ! ! 68 0.33 ! 3 ! 64 0.31 ! ! 60 0.29 ! ! 56 0.27 ! 5 ! 52 0.24 ! ! 48 0.22 ! ! 44 0.20 ! 9 ! 40 0.18 ! ! 36 0.16 ! ! 32 0.14 ! 1 ! 28 0.12 ! ! 24 0.10 ! 7 ! 20 0.08 ! ! 16 0.06 ! ! 12 0.04 ! 16 ! 8 0.02 ! ! 4 DIMENSION 1 + -0.02 ! 15 ! -4 -0.04 ! ! -8 -0.06 ! 6 ! -12 -0.08 ! 12 ! -16 -0.10 ! ! -20 -0.12 ! 17 ! -24 -0.14 ! 11 ! -28 -0.16 ! 14 ! -32 -0.18 ! ! -36 -0.20 ! 19 ! -40 -0.22 ! 18 4 ! -44 -0.24 ! 10 ! -48 -0.27 ! 8 2 ! -52 -0.29 ! ! -56 -0.31 ! ! -60 -0.33 ! ! -64 -0.35 ! ! -68 -0.37 ! ! -72 -0.39 ! ! -76 -0.41 ! ! -80 -0.43 ! ! -84 -0.45 ! ! -88 -0.47 ! ! -92 -0.49 ! ! -96 -0.51 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -0.51-0.46-0.41-0.36-0.31-0.25-0.20-0.15-0.10-0.05 * 0.05 0.10 0.15 0.20 0.25 0.31 0.36 0.41 0.46 0.51 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 4 PLOTTED AGAINST DIMENSION 1 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 0.51 ! ! 100 0.49 ! 20 ! 96 0.47 ! ! 92 0.45 ! ! 88 0.43 ! ! 84 0.41 ! 13 ! 80 0.39 ! ! 76 0.37 ! ! 72 0.35 ! ! 68 0.33 ! 3 ! 64 0.31 ! ! 60 0.29 ! ! 56 0.27 ! 5 ! 52 0.24 ! ! 48 0.22 ! ! 44 0.20 ! 9 ! 40 0.18 ! ! 36 0.16 ! ! 32 0.14 ! 1 ! 28 0.12 ! ! 24 0.10 ! 7 ! 20 0.08 ! ! 16 0.06 ! ! 12 0.04 ! 16 ! 8 0.02 ! ! 4 DIMENSION 1 + -0.02 ! 15 ! -4 -0.04 ! ! -8 -0.06 ! 6 ! -12 -0.08 ! 12 ! -16 -0.10 ! ! -20 -0.12 ! 17 ! -24 -0.14 ! 11 ! -28 -0.16 ! 14 ! -32 -0.18 ! ! -36 -0.20 ! 19 ! -40 -0.22 ! 18 4 ! -44 -0.24 ! 10 ! -48 -0.27 ! 8 2 ! -52 -0.29 ! ! -56 -0.31 ! ! -60 -0.33 ! ! -64 -0.35 ! ! -68 -0.37 ! ! -72 -0.39 ! ! -76 -0.41 ! ! -80 -0.43 ! ! -84 -0.45 ! ! -88 -0.47 ! ! -92 -0.49 ! ! -96 -0.51 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -0.51-0.46-0.41-0.36-0.31-0.25-0.20-0.15-0.10-0.05 * 0.05 0.10 0.15 0.20 0.25 0.31 0.36 0.41 0.46 0.51 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 3 PLOTTED AGAINST DIMENSION 2 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 0.51 ! ! 100 0.49 ! ! 96 0.47 ! ! 92 0.45 ! ! 88 0.43 ! ! 84 0.41 ! ! 80 0.39 ! ! 76 0.37 ! ! 72 0.35 ! ! 68 0.33 ! 4 ! 64 0.31 ! 3 6 ! 60 0.29 ! ! 56 0.27 ! 8 ! 52 0.24 ! 5 ! 48 0.22 ! ! 44 0.20 ! ! 40 0.18 ! ! 36 0.16 ! 2 ! 32 0.14 ! ! 28 0.12 ! ! 24 0.10 ! ! 20 0.08 ! ! 16 0.06 ! 9 ! 12 0.04 ! 1 ! 8 0.02 ! ! 4 DIMENSION 2 + -0.02 ! 20 ! -4 -0.04 ! 10 ! -8 -0.06 ! 11 ! -12 -0.08 ! 19 ! -16 -0.10 ! ! -20 -0.12 ! ! -24 -0.14 ! 18 ! -28 -0.16 ! ! -32 -0.18 ! ! -36 -0.20 ! 17 ! -40 -0.22 ! 12 ! -44 -0.24 ! ! -48 -0.27 ! ! -52 -0.29 ! ! -56 -0.31 ! 16 14 ! -60 -0.33 ! 13 ! -64 -0.35 ! 15 ! -68 -0.37 ! ! -72 -0.39 ! ! -76 -0.41 ! ! -80 -0.43 ! ! -84 -0.45 ! ! -88 -0.47 ! ! -92 -0.49 ! ! -96 -0.51 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -0.51-0.46-0.41-0.36-0.31-0.25-0.20-0.15-0.10-0.05 * 0.05 0.10 0.15 0.20 0.25 0.31 0.36 0.41 0.46 0.51 POINT 8 OVERLAYS POINT(S) 7 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 4 PLOTTED AGAINST DIMENSION 2 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 0.51 ! ! 100 0.49 ! ! 96 0.47 ! ! 92 0.45 ! ! 88 0.43 ! ! 84 0.41 ! ! 80 0.39 ! ! 76 0.37 ! ! 72 0.35 ! ! 68 0.33 ! 4 ! 64 0.31 ! 6 3 ! 60 0.29 ! ! 56 0.27 ! 8 ! 52 0.24 ! 5 ! 48 0.22 ! ! 44 0.20 ! ! 40 0.18 ! ! 36 0.16 ! 2 ! 32 0.14 ! ! 28 0.12 ! ! 24 0.10 ! ! 20 0.08 ! ! 16 0.06 ! 9 ! 12 0.04 ! 1 ! 8 0.02 ! ! 4 DIMENSION 2 + -0.02 ! 20 ! -4 -0.04 ! 10 ! -8 -0.06 ! 11 ! -12 -0.08 ! 19 ! -16 -0.10 ! ! -20 -0.12 ! ! -24 -0.14 ! 18 ! -28 -0.16 ! ! -32 -0.18 ! ! -36 -0.20 ! 17 ! -40 -0.22 ! 12 ! -44 -0.24 ! ! -48 -0.27 ! ! -52 -0.29 ! ! -56 -0.31 ! 14 16 ! -60 -0.33 ! 13 ! -64 -0.35 ! 15 ! -68 -0.37 ! ! -72 -0.39 ! ! -76 -0.41 ! ! -80 -0.43 ! ! -84 -0.45 ! ! -88 -0.47 ! ! -92 -0.49 ! ! -96 -0.51 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -0.51-0.46-0.41-0.36-0.31-0.25-0.20-0.15-0.10-0.05 * 0.05 0.10 0.15 0.20 0.25 0.31 0.36 0.41 0.46 0.51 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. INITIAL STIMULI CONFIGURATION DIMENSION 4 PLOTTED AGAINST DIMENSION 3 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 0.51 ! ! 100 0.49 ! ! 96 0.47 ! ! 92 0.45 ! ! 88 0.43 ! ! 84 0.41 ! ! 80 0.39 ! ! 76 0.37 ! ! 72 0.35 ! 5 ! 68 0.33 ! 1 ! 64 0.31 ! ! 60 0.29 ! 10 ! 56 0.27 ! 2 ! 52 0.24 ! ! 48 0.22 ! 12 ! 44 0.20 ! 9 ! 40 0.18 ! ! 36 0.16 ! ! 32 0.14 ! 6 13 ! 28 0.12 ! 14 ! 24 0.10 ! ! 20 0.08 ! ! 16 0.06 ! ! 12 0.04 ! 15 ! 8 0.02 ! ! 4 DIMENSION 3 + -0.02 ! ! -4 -0.04 ! ! -8 -0.06 ! ! -12 -0.08 ! 4 ! -16 -0.10 ! 7 ! -20 -0.12 ! 8 ! -24 -0.14 ! ! -28 -0.16 ! 19 16 ! -32 -0.18 ! ! -36 -0.20 ! ! -40 -0.22 ! ! -44 -0.24 ! 20 18 ! -48 -0.27 ! ! -52 -0.29 ! 17 ! -56 -0.31 ! 11 ! -60 -0.33 ! ! -64 -0.35 ! ! -68 -0.37 ! ! -72 -0.39 ! ! -76 -0.41 ! 3 ! -80 -0.43 ! ! -84 -0.45 ! ! -88 -0.47 ! ! -92 -0.49 ! ! -96 -0.51 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -0.51-0.46-0.41-0.36-0.31-0.25-0.20-0.15-0.10-0.05 * 0.05 0.10 0.15 0.20 0.25 0.31 0.36 0.41 0.46 0.51 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 1 PROPERTY NAME : PROPERTY NUMBER ONE. MOMENTS 1 2 3 4 0.566510E+04 0.656594E+06 -0.739582E+08 0.225714E+13 SKEWNESS= -0.139008 KURTOSIS= 1.745193 THE STANDARDIZED INDEX OF NONLINEAR CORRELATION Z= -5.77523 ZSQ= 33.35324 ORIGINAL VALUES ON PROPERTY NO : 1 PROPERTY NAME : PROPERTY NUMBER ONE. 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000 PROJECTIONS ON FITTED VECTORS 0.1234 0.2047 0.2181 0.2875 0.3359 0.3117 0.2403 0.1856 0.1066 0.0224 -0.1214 -0.1646 -0.2447 -0.2803 -0.3086 -0.3136 -0.2682 -0.2008 -0.1092 -0.0246 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 1 IS -0.798 , RSQ= 0.636 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 1 PROPERTY NAME : PROPERTY NUMBER ONE. OBTAINED VALUES ! 0.64 ! * 0.61 ! * ! 0.56 ! * ! ! ! 0.54 ! * 0.53 ! * 0.50 ! * ! 0.44 ! * ! ! ! ! 0.42 !* 0.34 ! * ! ! ! ! ! 0.29 ! * ! ! ! 0.21 ! * ! ! ! ! ! 0.20 ! * 0.16 ! * ! ! 0.12 ! * ! ! 0.08 ! * ! ! 0.05 ! * ! 0.04 ! * 0.01 ! * ! 0.01 ! * +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 2 PROPERTY NAME : PROPERTY NUMBER TWO. MOMENTS 1 2 3 4 0.566510E+04 0.656594E+06 -0.739582E+08 0.225714E+13 SKEWNESS= -0.139008 KURTOSIS= 1.745193 THE STANDARDIZED INDEX OF NONLINEAR CORRELATION Z= -3.97884 ZSQ= 15.83116 ORIGINAL VALUES ON PROPERTY NO : 2 PROPERTY NAME : PROPERTY NUMBER TWO. 1.8000 0.6000 0.2000 0.4000 0.9000 1.7000 1.1000 0.7000 2.0000 1.6000 1.2000 1.9000 0.5000 0.8000 1.0000 1.3000 1.5000 0.1000 1.4000 0.3000 PROJECTIONS ON FITTED VECTORS 0.3203 0.1965 -0.3234 -0.1830 0.2245 0.2794 -0.1790 0.2347 0.0361 0.2013 -0.3147 0.1979 0.0379 0.2795 0.0098 -0.2849 -0.0483 -0.2044 -0.1908 -0.2894 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 2 IS 0.399 , RSQ= 0.159 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 2 PROPERTY NAME : PROPERTY NUMBER TWO. OBTAINED VALUES 0.60 ! * ! ! ! 0.56 ! * * ! ! 0.55 ! * 0.53 ! * ! 0.37 ! * * * ! ! ! ! ! ! ! ! ! ! ! 0.34 ! * * ! 0.28 ! * ! ! ! ! 0.14 ! * ! ! ! ! ! ! ! ! ! 0.13 ! * * * 0.04 !* ! ! ! ! ! ! 0.01 ! * * ! 0.01 ! * +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 3 PROPERTY NAME : PROPERTY NUMBER THREE. MOMENTS 1 2 3 4 0.566510E+04 0.656594E+06 -0.739582E+08 0.225714E+13 SKEWNESS= -0.139008 KURTOSIS= 1.745193 THE STANDARDIZED INDEX OF NONLINEAR CORRELATION Z= -6.25406 ZSQ= 39.11326 ORIGINAL VALUES ON PROPERTY NO : 3 PROPERTY NAME : PROPERTY NUMBER THREE. 1.5000 0.1000 1.8000 0.4000 1.7000 1.1000 1.4000 0.2000 1.6000 0.3000 0.8000 1.0000 1.9000 0.7000 1.2000 1.3000 0.9000 0.5000 0.6000 2.0000 PROJECTIONS ON FITTED VECTORS 0.1391 -0.2635 0.3170 -0.2209 0.2592 -0.0390 0.0837 -0.2558 0.1938 -0.2352 -0.1391 -0.0742 0.3975 -0.1607 -0.0055 0.0338 -0.1127 -0.2076 -0.1851 0.4775 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 3 IS 0.969 , RSQ= 0.939 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 3 PROPERTY NAME : PROPERTY NUMBER THREE. OBTAINED VALUES ! 0.67 ! * ! ! ! ! 0.59 ! * ! ! ! ! 0.53 ! * ! ! ! 0.47 ! * ! ! ! 0.41 ! * ! ! ! 0.35 ! * ! ! ! 0.30 ! * ! ! 0.27 ! * ! 0.23 ! * ! ! 0.20 ! * ! 0.15 ! * ! ! 0.14 ! * 0.11 ! * ! 0.09 ! * 0.06 ! * ! 0.05 ! * 0.03 ! * 0.02 ! * 0.02 ! * +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. PROPERTY NO : 4 PROPERTY NAME : PROPERTY NUMBER FOUR. MOMENTS 1 2 3 4 0.566510E+04 0.656594E+06 -0.739582E+08 0.225714E+13 SKEWNESS= -0.139008 KURTOSIS= 1.745193 THE STANDARDIZED INDEX OF NONLINEAR CORRELATION Z= -6.32223 ZSQ= 39.97064 ORIGINAL VALUES ON PROPERTY NO : 4 PROPERTY NAME : PROPERTY NUMBER FOUR. 1.8000 1.3000 0.2000 0.6000 1.9000 0.9000 0.8000 0.1000 1.7000 1.5000 0.4000 1.6000 2.0000 1.2000 1.4000 1.1000 0.3000 0.5000 0.7000 1.0000 PROJECTIONS ON FITTED VECTORS 0.2933 0.0988 -0.3308 -0.1756 0.3309 -0.0536 -0.0982 -0.3625 0.2510 0.1757 -0.2548 0.2141 0.3663 0.0610 0.1344 0.0150 -0.2898 -0.2150 -0.1377 -0.0226 CORRELATION BETWEEN ORIGINAL AND FITTED VECTORS FOR PROPERTY NO. 4 IS 1.000 , RSQ= 1.000 PLOT OF ORIGINAL (X-AXIS) VERSUS OBTAINED (Y-AXIS)FOR PROPERTY VECTOR NO. 4 PROPERTY NAME : PROPERTY NUMBER FOUR. OBTAINED VALUES ! 0.70 ! * ! 0.67 ! * ! 0.62 ! * ! ! 0.58 ! * ! ! 0.55 ! * ! 0.51 ! * ! ! 0.48 ! * ! 0.43 ! * ! ! 0.39 ! * ! ! 0.34 ! * ! ! 0.31 ! * ! 0.27 ! * ! ! 0.24 ! * ! 0.19 ! * ! ! 0.15 ! * ! ! 0.12 ! * ! 0.07 ! * ! ! 0.04 ! * ! 0.01 ! * ! ! +-------------------------------------------------------------------------------- 0.10 0.34 0.57 0.81 1.05 1.29 1.52 1.76 ORIGINAL VALUES PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. ================================================ RESULTS OF THE NON-LINEAR REGESSION PROCEDURE ================================================ INDEX TYPE = CARROLL'S KAPPA ------------------------------- TABLE 1. THE SMALLEST EIGEN ROOT ASSOCIATED WITH EACH PROPERTY ROOT PROPERTY 1 51.8637 PROPERTY NUMBER ONE. 2 128.4754 PROPERTY NUMBER TWO. 3 31.4426 PROPERTY NUMBER THREE. 4 28.5352 PROPERTY NUMBER FOUR. TABLE 2. DIRECTION COSINES OF FITTED VECTORS IN NORMALIZED SPACE DIMENSION VECTOR 1 2 3 4 1 0.0786 0.9658 0.2453 0.0305 2 -0.1990 0.0426 0.8336 -0.5135 3 0.9999 0.0050 -0.0118 -0.0111 4 0.3890 -0.3078 0.8509 0.1731 TABLE 3. COSINE OF ANGLES BETWEEN VECTORS VECTOR 1 2 3 4 2 0.2143 3 0.0802 -0.2029 4 -0.0527 0.5300 0.3754 TABLE 4. DIRECTION COSINES OF FITTED VECTORS IN ORIGINAL SPACE DIMENSION VECTORS 1 2 3 4 1 0.9939 -0.0901 -0.0078 0.0630 2 0.0171 -0.9952 -0.0039 0.0961 3 0.0261 -0.0112 0.9986 0.0438 4 0.0014 -0.0206 0.0003 0.9998 STIMULUS SPACE IN 4 DIMENSIONS 1 0.3090 -0.4760 1.1269 0.7500 2 0.5880 -0.2940 -2.2501 0.2500 3 0.8090 0.4760 2.6949 -0.8500 4 0.9510 0.2940 -1.8631 -0.4500 5 1.0000 -0.2940 2.1189 0.8500 6 0.9510 -0.4760 -0.3511 -0.1500 7 0.8090 0.2940 0.6999 -0.2500 8 0.5880 -0.4760 -2.1341 -0.9500 9 0.3090 0.0000 1.5979 0.6500 10 0.0000 -0.2940 -2.0051 0.4500 11 -0.3090 0.4760 -1.1301 -0.6500 12 -0.5880 -0.2940 -0.6371 0.5500 13 -0.8090 0.0000 3.3309 0.9500 14 -0.9510 -0.4760 -1.3411 0.1500 15 -1.0000 0.0000 -0.0351 0.3500 16 -0.9510 0.4760 0.3139 0.0500 17 -0.8090 0.0000 -0.8951 -0.7500 18 -0.5880 0.2940 -1.7061 -0.5500 19 -0.3090 0.2940 -1.5331 -0.3500 20 0.0000 0.4760 4.0339 -0.0500 TABLE OF RESIDUALS ------------------ 1 2 3 4 1 -0.0234 1.4797 1.3609 1.5067 2 -0.0047 0.4035 0.3635 1.2012 3 0.0819 0.5234 1.4830 0.5308 4 0.1125 0.5830 0.6209 0.7756 5 0.1641 0.6755 1.4408 1.5691 6 0.2883 1.4206 1.1390 0.9536 7 0.4597 1.2790 1.3163 0.8982 8 0.6144 0.4653 0.4558 0.4625 9 0.7934 1.9639 1.4062 1.4490 10 0.9776 1.3987 0.5352 1.3243 11 1.2214 1.5147 0.9391 0.6548 12 1.3646 1.7021 1.0742 1.3859 13 1.5447 0.4621 1.5025 1.6337 14 1.6803 0.5205 0.8607 1.1390 15 1.8086 0.9902 1.2055 1.2656 16 1.9136 1.5849 1.2662 1.0850 17 1.9682 1.5483 1.0127 0.5898 18 2.0008 0.3044 0.7076 0.7150 19 2.0092 1.5908 0.7851 0.8377 20 2.0246 0.5894 1.5225 1.0226 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. HISTOGRAM OF LOG RESIDUALS FREQUENCY 20! *** 19! *** 18! *** 17! *** 16! *** 15! *** 14! *** 13! *** 12! *** 11! ****** 10! ****** 9! ********* 8! *** ************ 7! *** ************ 6! *** ****************** 5! *** ****************** 4! ************************ 3! ************************ 2! *** ************************ 1!*** *** *** *** *** ****************************** !!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=!!=! LOG -2.332 -1.877 -1.422 -0.968 -0.513 -0.058 0.397 ACTUAL 0.005 0.013 0.038 0.108 0.307 0.876 2.497 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 2 PLOTTED AGAINST DIMENSION 1 DIMENSION 2 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 5 21 ! 28 0.97 ! 6 7 3 ! 24 0.81 ! ! 20 0.65 ! 8 2 ! 16 0.48 ! ! 12 0.32 ! 1 9 ! 8 0.16 ! 22 10 24 20 ! 4 DIMENSION 1 + -0.16 ! ! -4 -0.32 ! 19 11 ! -8 -0.48 ! ! -12 -0.65 ! 12 18 ! -16 -0.81 ! ! -20 -0.97 ! 14 17 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 24 OVERLAYS POINT(S) 23 POINT 17 OVERLAYS POINT(S) 13 POINT 7 OVERLAYS POINT(S) 4 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 3 PLOTTED AGAINST DIMENSION 1 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 21 5 ! 28 0.97 ! 6 7 3 ! 24 0.81 ! ! 20 0.65 ! 2 8 ! 16 0.48 ! ! 12 0.32 ! 1 9 ! 8 0.16 ! 10 22 24 20 ! 4 DIMENSION 1 + -0.16 ! ! -4 -0.32 ! 19 11 ! -8 -0.48 ! ! -12 -0.65 ! 18 12 ! -16 -0.81 ! ! -20 -0.97 ! 14 17 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 4 PLOTTED AGAINST DIMENSION 1 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 21 5 ! 28 0.97 ! 3 7 6 ! 24 0.81 ! ! 20 0.65 ! 8 2 ! 16 0.48 ! ! 12 0.32 ! 9 1 ! 8 0.16 ! 20 22 10 24 ! 4 DIMENSION 1 + -0.16 ! ! -4 -0.32 ! 11 19 ! -8 -0.48 ! ! -12 -0.65 ! 18 12 ! -16 -0.81 ! ! -20 -0.97 ! 17 16 ! -24 -1.13 ! 15 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 16 OVERLAYS POINT(S) 14 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 3 PLOTTED AGAINST DIMENSION 2 DIMENSION 3 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! ! 28 0.97 ! ! 24 0.81 ! ! 20 0.65 ! ! 16 0.48 ! 11 16 3 20 ! 12 0.32 ! 18 19 7 ! 8 0.16 ! 17 15 9 13 ! 4 DIMENSION 2 + -0.16 ! 21 24 23 ! -4 -0.32 ! 2 10 12 5 ! -8 -0.48 ! 8 14 6 1 ! -12 -0.65 ! ! -16 -0.81 ! ! -20 -0.97 ! ! -24 -1.13 ! 22 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 18 OVERLAYS POINT(S) 4 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 4 PLOTTED AGAINST DIMENSION 2 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! ! 28 0.97 ! ! 24 0.81 ! ! 20 0.65 ! ! 16 0.48 ! 3 11 20 16 ! 12 0.32 ! 18 19 ! 8 0.16 ! 17 15 9 13 ! 4 DIMENSION 2 + -0.16 ! 23 24 ! -4 -0.32 ! 10 12 5 ! -8 -0.48 ! 8 6 14 1 ! -12 -0.65 ! ! -16 -0.81 ! ! -20 -0.97 ! ! -24 -1.13 ! 22 ! -28 -1.29 ! ! -32 -1.45 ! ! -36 -1.61 ! ! -40 -1.77 ! ! -44 -1.94 ! ! -48 -2.10 ! ! -52 -2.26 ! ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 23 OVERLAYS POINT(S) 21 POINT 19 OVERLAYS POINT(S) 7 POINT 10 OVERLAYS POINT(S) 2 PROFIT TEST DATA. ARTIFICIAL DATA 20 POINTS 4 DIMENSIONS 4 PROPERTIES. STIMULUS POINTS AND DIRECTION COSINES OF FITTED PROPERTY VECTORS DIMENSION 4 PLOTTED AGAINST DIMENSION 3 DIMENSION 4 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 * 10 20 30 40 50 60 70 80 90 100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. 4.03 ! 20 ! 100 3.87 ! ! 96 3.71 ! ! 92 3.55 ! ! 88 3.39 ! 13 ! 84 3.23 ! ! 80 3.07 ! ! 76 2.90 ! ! 72 2.74 ! 3 ! 68 2.58 ! ! 64 2.42 ! ! 60 2.26 ! 5 ! 56 2.10 ! ! 52 1.94 ! ! 48 1.77 ! ! 44 1.61 ! 9 ! 40 1.45 ! ! 36 1.29 ! ! 32 1.13 ! 23 1 ! 28 0.97 ! ! 24 0.81 ! 7 ! 20 0.65 ! ! 16 0.48 ! ! 12 0.32 ! 16 ! 8 0.16 ! 24 ! 4 DIMENSION 3 + -0.16 ! 22 15 ! -4 -0.32 ! ! -8 -0.48 ! 6 ! -12 -0.65 ! 12 ! -16 -0.81 ! ! -20 -0.97 ! 17 ! -24 -1.13 ! ! -28 -1.29 ! 11 ! -32 -1.45 ! 14 ! -36 -1.61 ! 19 ! -40 -1.77 ! 18 ! -44 -1.94 ! 4 ! -48 -2.10 ! 10 ! -52 -2.26 ! 8 2 ! -56 -2.42 ! ! -60 -2.58 ! ! -64 -2.74 ! ! -68 -2.90 ! ! -72 -3.07 ! ! -76 -3.23 ! ! -80 -3.39 ! ! -84 -3.55 ! ! -88 -3.71 ! ! -92 -3.87 ! ! -96 -4.03 ! !-100 .+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+....+. -4.03-3.63-3.23-2.82-2.42-2.02-1.61-1.21-0.81-0.40 * 0.40 0.81 1.21 1.61 2.02 2.42 2.82 3.23 3.63 4.03 POINT 22 OVERLAYS POINT(S) 21 POINTS 1 TO 20 ARE STIMULI, POINTS 21 TO 24 ARE SUBJECT VECTORS 34. FINISH NORMAL END OF RUN. 34 CONTROL CARDS, 0 ERRORS, 0 WARNINGS.