Distancia Euclidiana y Mahalanobis

Persona Estatura Peso A-BA 2.00 100 20.00B 1.80 80 2.1396C 1.70 72 1.6850D 1.65 81

1.79 83.25VARIANZA 0.024 140.917

EUCLIDIANA ESTANDARIZADAMETROS CENTIMET MILI metros

P1P2 20.00 28.28 201.00 2.14P3 28.00 41.04 301.30 3.08P4 19.00 39.82 350.52 2.81

M= 0.02 0.000 140.90

A-C A-D Estatura Peso28.00 19.00 200.00 1003.08 2.81 180.00 802.36 1.60 170.00 72

165.00 81178.75 83.25239.58 140.92

ESTANDARIZADA MAHALANOBIScentime metros centime

2.12 1.72 1.723.05 2.37 2.372.77 2.39 2.39

MATRIZ ESTANDARIZADA1.37287385 1.41102150.08075729 -0.27378029

-0.565301 -0.94770101-0.88833014 -0.1895402

Persona Estatura en m Peso en kg Persona Estatura en cmA 2.00 100 A 200.00B 1.80 80 B 180.00C 1.70 72 C 170.00D 1.65 81 D 165.00

prom 1.79 83.25 promedio 178.75varianza 0.024 140.917 varianza 239.583

Distancia Euclidiana m Euclidiana cm Eucli m std Eucli cm std Maha mA-B 20.001 28.284 2.123 2.123 1.72A-C 28.002 41.037 3.053 3.053 2.37A-D 19.003 39.825 2.770 2.770 2.37B-C 8.001 12.806 0.934 0.934 0.68B-D 1.011 15.033 0.973 0.973 2.13C-D 9.000 10.296 0.824 0.824 2.15

2.12323392 8.34782609 0.14192785333.05288283 12.5217391 0.19869899473.05288283 12.5217391 0.19869899470.93357401 4.17391304 0.05677114130.97274191 6.26086957 -0.00709639270.82410899 2.08695652 -0.063867534

4.50812228 6.4783277196 6.4783277196 1.97020544 1.11024606 -0.85995937576.47832772 9.3200935901 9.3200935901 2.84176587 1.67956187 -1.16220399566.47832772 9.3200935901 9.3200935901 2.84176587 1.67956187 -1.16220399561.97020544 2.8417658705 2.8417658705 0.87156044 0.56931582 -0.30224461991.11024606 1.6795618749 1.6795618749 0.56931582 0.94622683 0.3769110123

-0.85995938 -1.1622039956 -1.1622039956 -0.30224462 0.37691101 0.6791556321

Peso en kg Mvarianzas= 0.024 0100 0 140.9178072 Inversa de Mvarianza81 41.7391 0.0000

83.25 0.0000 0.0071140.917

Maha cm Matriz covarianzas m Matriz covarianzas cm1.72 0.024 1.6042 239.58332.37 1.6042 140.9167 160.41672.390.68 Inversa de Mcova m Inversa Mcov cm2.14 174.28469743 -1.984062298 0.017553652.16 -1.984062298 0.0296830166 -0.01998272

Matriz de diferencias Matriz de diferenciasA-B 0.2 20.00 20.00A-C 0.3 28.00 30.00A-D 0.30 28.00 35.00B-C 0.10 8.00 10.00B-D 0.15 -1 15.00C-D 0.05 -9 5.00

Transpuesta de diferenciasA-B A-C A-D B-C B-D C-D0.2 0.3 0.3 0.1 0.15 0.0520 28 28 8 -1 -9

Maha mA-B -4.82430647 0.1968478714A-C -3.26833511 0.235905774A-D -3.26833511 0.235905774B-C 1.55597136 0.0390579026B-D 28.1267669 -0.327292361C-D 26.5707956 -0.366350264

Maha m A-B A-C A-D B-C B-DA-B 2.97209613 4.0644484581 4.0644484581 1.09235232 -0.92049384A-C 4.06444846 5.6248611391 5.6248611391 1.56041268 -0.72615604A-D 4.06444846 5.6248611391 5.6248611391 1.56041268 -0.72615604B-C 1.09235232 1.560412681 1.560412681 0.46806036 0.1943378B-D -0.92049384 -0.726156041 -0.726156041 0.1943378 4.5463074

C-D -2.01284617 -2.286568722 -2.286568722 -0.27372256 4.3519696

Matriz covarianzas cm160.4167140.9167

Inversa Mcov cm-0.019982720.02984431

Matriz de diferencias20.0028.0019.008.00-1-9

20 30 35 10 1520 28 19 8 -1

-0.04858136 0.19723185-0.0329066 0.236159150.23470617 -0.132353290.01567476 0.03892730.28328752 -0.329585140.26761276 -0.36851243

C-D Maha m A-B A-C A-D-2.01284617 A-B 2.9730098 4.065051 2.04705756-2.28656872 A-C 4.065051 5.62525821 3.33529291-2.28656872 A-D 2.04705756 3.33529291 5.70000332-0.27372256 B-C 1.0920412 1.56020721 1.28823535

4.3519696 B-D -0.92595225 -0.72975809 3.65294577

4.62569215 C-D -2.01799345 -2.2899653 2.36471041

5-9

B-C B-D C-D1.0920412 -0.92595225 -2.01799345

1.56020721 -0.72975809 -2.28996531.28823535 3.65294577 2.364710410.46816601 0.19619415 -0.271971860.19619415 4.57889801 4.38270386

-0.27197186 4.38270386 4.65467572

Persona Estatura en m Peso en kg Persona Estatura en cmA 2.00 100 A 200.00B 1.80 80 B 180.00C 1.70 72 C 170.00D 1.65 81 D 165.00

prom 1.79 83.25 promedio 178.75varianza 0.024 140.917 varianza 239.583

covarianza 1.6041666667 covarianza 160.4166666667

Distancia Euclidiana m Euclidiana cm Eucli m std Eucli cm std Maha mA-B 20.001 28.284 2.123 2.123 1.72A-C 28.002 41.037 3.053 3.053 2.37A-D 19.003 39.825 2.770 2.770 2.39B-C 8.001 12.806 0.934 0.934 0.68B-D 1.011 15.033 0.973 0.973 2.14C-D 9.000 10.296 0.824 0.824 2.16

Matrices

Eucli m std Eucli cm std Matriz covarianzas m2.123 2.123 0.02403.053 3.053 1.60422.770 2.7700.934 0.934 Inversa de covarianzas m0.973 0.973 175.540.824 0.824 -2.00

Dis Maha m (Dif x inv cova)-4.8581-3.290723.47061.5675

28.328726.7612

Distancia de Mahalanobis m2.9730103806 4.0650519031 2.04705882 1.09204152 -0.92595155714.0650519031 5.6252595156 3.33529412 1.56020761 -0.72975778552.0470588235 3.3352941176 5.7 1.28823529 3.65294117651.0920415225 1.5602076125 1.28823529 0.46816609 0.1961937716

-0.9259515571 -0.7297577855 3.65294118 0.19619377 4.5788927336-2.0179930796 -2.2899653979 2.36470588 -0.27197232 4.3826989619

Peso en kg Mvarianzas= 0.024 0100 0 140.9178072 Inversa de Mvarianza81 41.7391 0.0000

83.25 0.0000 0.0071140.917

Maha cm Matriz de diferencias mA-B 0.20 20.00A-C 0.30 28.00A-D 0.35 19.00B-C 0.10 8.00B-D 0.15 -1.00C-D 0.05 -9.00

Matriz covarianzas m Transpuesta de diferencias m1.6042 0.2 0.3 0.35 0.1

140.9167 20 28 19 8

Inversa de covarianzas m Transpuesta de diferencias cm-2.00 20 30 35 100.03 20 28 19 8

Dis Maha m (Dif x inv cova) Distancia estandarizada m (Dif x inv varianzas)0.1972 8.348 0.1420.2362 12.522 0.199-0.1324 14.609 0.1350.0389 4.174 0.057-0.3296 6.261 -0.007-0.3685 2.087 -0.064

Distancia estandarizada m (Dif x inv varianzas)(transpuesta de diferenciaa)-2.01799308 4.508 6.478 5.618 1.970

-2.2899654 6.478 9.320 8.158 2.8422.36470588 5.618 8.158 7.675 2.540

-0.27197232 1.970 2.842 2.540 0.8724.38269896 1.110 1.680 2.056 0.5694.65467128 -0.860 -1.162 -0.483 -0.302

Distancia estandarizada cm (Dif x inv varianzas)(transpuesta de diferenciaa) 4.508 6.478 5.618 1.970 6.478 9.320 8.158 2.842 5.618 8.158 7.675 2.540

1.970 2.842 2.540 0.872 1.110 1.680 2.056 0.569 - 0.860 - 1.162 - 0.483 - 0.302

M var cm 239.583 00 140.917

Inversa de Mvarianza0.0042 0.00000.0000 0.0071

Matriz de diferencias cmA-B 20.00 20.00A-C 30.00 28.00A-D 35.00 19.00B-C 10.00 8.00B-D 15.00 -1.00C-D 5.00 -9.00

0.15 0.05-1 -9

15 5-1 -9

Distancia estandarizada cm (Dif x inv varianzas)0.0835 0.14190.1252 0.19870.1461 0.13480.0417 0.05680.0626 -0.00710.0209 -0.0639

Distancia estandarizada m (Dif x inv varianzas)(transpuesta de diferenciaa)1.110 -0.8601.680 -1.1622.056 -0.4830.569 -0.3020.946 0.3770.377 0.679

Distancia estandarizada cm (Dif x inv varianzas)(transpuesta de diferenciaa) 1.110 - 0.860 1.680 - 1.162 2.056 - 0.483

0.569 - 0.302 0.946 0.377 0.377 0.679

cia1 general 126.974 4.224 173.2972 ford 96.933 3.835 160.8933 exxon 86.656 3.51 83.2194 IBM 63.438 3.758 77.7345 GENERAL ELE 55.264 3.939 128.3446 MOBIL 50.976 1.809 39.087 PHILIP 39.069 2.946 38.5288 CHRY 36.156 0.359 51.0389 DUPONT 35.209 2.48 34.715

10 TEXACO 32.416 2.413 25.636

MEDIA 62.3091 2.9273 81.2484VARIANZA 1000.50911 1.43002001 2980.48978

matriz de covarianzas1000.5 25.6 1511.8

25.6 1.4 45.71511.8 45.7 2980.5

0.00443858 -0.01535786 -0.0020159-0.01535786 1.4831777 -0.01495159

-0.0020159 -0.01495159 0.00158729

matriz inversa de

covarianzas

DISTANCIA EUCLID EUCLI STD mahalanobis Diferencias de Xi-Promedio112.499669 2.8632208536 2.087997631 64.664986.8498744 1.975506371 1.5383127567 34.623924.4334677 0.9117069376 1.5739404412 24.34693.78358098 0.6985500326 1.0598290218 1.128947.6303738 1.2286292039 2.3218233033 -7.045143.6790992 1.2647165915 1.2333715127 -11.333148.6326554 1.073498183 1.1528338734 -23.240140.0405928 2.3669577424 2.5882534566 -26.153153.8513956 1.2650946626 0.9562830397 -27.100163.1395357 1.4545685434 1.1124835668 -29.8931

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10

Diferencias de Xi-Promedio 1 2 31.2967 92.0486 64.6649 34.6239 24.34690.9077 79.6446 1.2967 0.9077 0.58270.5827 1.9706 92.0486 79.6446 1.97060.8307 -3.51441.0117 47.0956 Transpuesta de la diferencia de Xi-promedio

-1.1183 -42.16840.0187 -42.7204

-2.5683 -30.2104-0.4473 -46.5334-0.5143 -55.6124

Multi de M:14-0:23 x transpuesta de diferencias(Mult de L:2-N:11) matriz inversa de cova 1 2

0.081545 -0.44615066 -0.00363766 4.35973411 2.12871502-0.02081496 -0.37628188 0.0430494 2.12871502 2.366406140.09514412 0.46086783 -0.0546653 1.71822749 -0.64120607

-0.00066238 1.2672841 -0.02027442 -0.26577702 -0.48736818-0.14174784 0.90457445 0.0738302 -1.19718094 1.793396480.05187912 -0.85410089 -0.02736683 -0.2718331 -1.15863031

-0.01732016 1.02339145 -0.02123965 -1.74805467 -1.36238233-0.01573789 -2.95589622 0.04316947 -0.87691058 0.21024087-0.01960969 0.44852238 -0.01254318 -1.84104176 -1.27083659-0.01267531 0.52778945 -0.02032204 -2.00587854 -1.57833503

4 5 6 7 8 91.1289 -7.0451 -11.3331 -23.2401 -26.1531 -27.10010.8307 1.0117 -1.1183 0.0187 -2.5683 -0.4473

-3.5144 47.0956 -42.1684 -42.7204 -30.2104 -46.5334

Transpuesta de la diferencia de Xi-promedio

Multi de M:14-0:23 x transpuesta de diferencias3 4 5 6 7 8

1.71822749 -0.26577702 -1.19718094 -0.2718331 -1.74805467 -0.87691058-0.64120607 -0.48736818 1.79339648 -1.15863031 -1.36238233 0.210240872.47728851 0.68236683 -2.77853505 0.71148207 0.13278305 -2.020499760.68236683 1.12323756 0.33194199 -0.55475728 0.90522315 -2.62494427

-2.77853505 0.33194199 5.39086345 -2.51844482 0.15709354 -0.846513260.71148207 -0.55475728 -2.51844482 1.52120529 -0.05252561 1.663550450.13278305 0.90522315 0.15709354 -0.05252561 1.32902594 -1.53374207

-2.02049976 -2.62494427 -0.84651326 1.66355045 -1.53374207 6.69905596-0.24079885 0.39453189 0.00119392 0.24958173 0.99996813 -0.26015136-0.04110823 0.49554531 -0.3338153 0.41037158 1.17261087 -0.41008598

10-29.8931

-0.5143-55.6124

9 10-1.84104176 -2.00587854-1.27083659 -1.57833503-0.24079885 -0.041108230.39453189 0.495545310.00119392 -0.33381530.24958173 0.410371580.99996813 1.17261087

-0.26015136 -0.410085980.91447725 1.053075631.05307563 1.23761969