PROCESAMIENTO E INTERPRETACIÓN DE DATOS MANUAL DE PROCEDIMIENTOS
UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO PROGRAMA DE MAESTRÍA Y DOCTORADO EN ARQUITECTURA IMPARTE: MTRO. EN ARQ. ARTURO VALERIANO FLORES ARQ. ÁLVARO BORBOA OSORIO JUNIO 2018
INTRODUCCIÓN Se realiza este manual de procedimientos como parte de los trabajos realizados en la materia de Procesamiento e Interpretación de Datos impartida en el campo de conocimiento de Tecnologías del Programa de Maestría y Doctorado en Arquitectura de la Universidad Nacional Autónoma de México por el Mtro. en Arq. Arturo Valeriano Flores. La intención del presente manual es asentar en un documento único el procedimiento que se llevó a cabo durante el semestre para la captura y procesamiento de los datos propios de las investigaciones realizadas por cada uno de los alumnos de la materia. Para efectos prácticos, se eligieron datos obtenidos previamente en la investigación Tecnología BIM en la Conformación de Bases de Datos Tridimensionales para su Integración a Sistemas de Información Geográfica. En esta investigación se tomó como caso de estudio al edificio que alberga a la Dirección General de Posgrados para su análisis espacial. Las variables por considerar en este manual son Capacidad, Ocupación y Superficie. • • •
Capacidad: máxima cantidad de personar para las que está diseñado un espacio Ocupación: cantidad real de personas que hacen uso de ese espacio. Este dato es arbitrario pues en la investigación aún no se cuenta con la información necesaria para dar fe de la veracidad de los datos que se levantaron en campo. Superficie: para el presente manual se tratará como Área, pues los datos están expresados en m².
La intención primordial de hacer esta comparación no es demostrar aspectos de funcionamiento del inmueble mismo, sino demostrar la factibilidad de ocupar los datos obtenidos por medio de la metodología propuesta en la investigación para facilitar la toma de decisiones y realizar análisis de datos tridimensionales de los edificios que conforman a la UNAM.
DATOS
S/I A-102 A-104 A-105 A-106 A-107 S/I A-108 A-110 A-111 A-109 A-103 A-101 A-201 A-202 A-203 A-204 A-205 A-206 A-208 A-209 A-210 A-211 A-212 A-213 B-001 B-002 B-003 B-004 B-005 B-104 B-105 B-106 B-107 B-108 S/I B-109 B-110 B-111 B-112 B-113 B-114 B-117 B-118 B-119 B-120 B-121 B-122 B-204 B-202 S/I B-209 B-213 B-207 B-215 B-219 B-220 B-205 B-216 B-218 B-223 B-203 B-201 B-224 B-222 B-221 B-208 B-212 B-206 B-301 B-302
5 3 3 3 3 3 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 16 16 20 16 10 0 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 4 4 4 4 4 4 6 3 3 4 3 24 24 4 4 4 4 6 49 25
0 21.91 1 8.54 0 8.55 1 8.54 1 8.54 1 17.26 5 119.8 1 15.92 0 15.75 1 16.2 1 15.76 1 8.54 1 8.32 1 8.53 1 8.53 1 8.53 1 8.53 1 8.53 1 8.53 1 7.8 1 7.72 1 7.72 1 7.76 1 7.76 1 7.72 2 98.32 2 100.09 1 99.67 4 41.23 10 24.92 0 19.28 0 9.41 1 19.28 1 19.27 1 18.89 2 7.28 1 7.28 1 7.14 1 7 1 7 1 7.15 1 7 1 7 0 7 1 7.16 1 6.98 1 7 1 7.15 1 6.96 1 15.19 1 36.16 0 21.56 0 8.06 0 15.19 0 16.49 4 8.06 4 8.06 4 15.19 1 6.96 1 6.96 0 6.96 1 7.5 0 59.99 12 56.29 0 8.06 0 8.06 1 7.31 0 23.47 4 14.93 22 74.74 0 41.85
B-303 B-304 B-305 B-306 B-307 B-308 S/I S/I C-107 C-109 C-112 C-111 C-106 C-105 C-108 C-110 D-101 D-102 D-103 D-104 D-105 D-106 D-116 D-114 D-112 S/I S/I D-109 D-107 D-115 D-113 D-111 D-110 D-108 D-201 D-203 D-202 D-204 D-205 D-206 D-207 D-208 D-209 S/I S/I D-301 D-302 D-303 D-304 D-305 D-306 D-307 D-308 S/I E-101 E-103 E-105 E-107 S/I E-110 E-111 E-112 E-113 E-102 E-104 E-106 E-109 E-201 S/I E-206 E-202
19 19 25 25 19 57 5 5 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 2 4 3 3 3 3 3 3 3 56 24 18 24 8 12 56 37 37 3 4 57 19 25 25 19 19 37 37 12 3 3 3 3 8 3 3 3 3 3 3 3 3 34 4 3 3
10 25.83 9 25.84 20 41.87 0 41.88 0 25.82 20 73.23 3 57.9 2 62.11 1 8.54 1 8.54 1 16.03 1 15.75 1 15.81 1 16.29 0 8.54 0 8.55 1 19.3 1 19.27 0 19.28 1 19.29 1 19.28 1 18.89 1 7.3 1 7 1 7.15 2 7.37 0 183.07 1 7 1 7.15 1 7.16 1 7 1 7 1 7.15 1 6.99 36 75.12 12 41.75 0 25.74 0 41.76 4 12.72 0 12.51 13 74.38 0 82.4 5 82.4 0 20.25 0 20.3 30 75.12 0 25.84 0 41.86 0 41.85 10 25.94 12 74.09 20 82.4 30 82.4 0 22.87 1 8.55 1 8.54 1 8.54 1 8.54 0 120.15 1 16.03 1 15.76 1 15.76 1 16.34 1 8.54 1 8.54 1 8.54 1 8.54 0 98.95 0 70.86 0 32.11 0 8.53
E-203 E-204 F-008 F-001 F-007 F-006 F-009 F-010 F-102 F-103 F-104 F-105 F-106 F-108 F-110 F-112 S/I F-114 F-115 F-01 F-107 F-109 F-111 F-113 F-116 F-201 F-203 F-202 F-204 F-205 F-206 F-207 F-301 F-303 F-302 F-304 F-305 F-306 S/I S/I S/I H-122 H-120 H-115 H-113 H-111 H-109 H-107 H-126 H-127 H-128 H-129 H-130 H-123 H-121 H-116 H-114 H-112 H-110 H-108 H-201 H-202 H-203 H-204 H-205 H-206 H-207 H-209 H-210 H-212 H-213
3 3 3 3 3 3 19 19 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 56 24 18 24 12 12 56 57 25 19 25 19 57 10 16 10 3 3 3 3 3 3 3 20 20 12 28 28 3 3 3 3 3 3 3 56 18 24 24 12 12 18 56 56 24 12
0 8.52 0 8.54 1 16.12 1 7.57 1 7.56 1 9.51 0 39.07 0 34.08 1 19.28 1 19.28 0 19.29 1 19.28 1 19.28 1 7.26 1 7.11 1 7.11 1 7.25 1 7.11 1 7.11 1 18.9 1 7.38 1 7.11 1 7.26 1 7.11 1 7.27 0 74.37 13 41.75 0 25.95 12 41.76 0 12.61 10 12.43 36 75.13 0 74.37 0 41.86 5 25.95 23 41.87 0 25.82 32 75.12 5 22.29 0 252.45 0 18.53 1 7.72 1 7.42 1 7.73 1 7.73 1 7.74 1 7.72 1 7.36 12 41.77 0 41.77 12 25.84 0 74.54 15 73.5 1 7.71 1 7.72 1 7.41 1 7.71 1 7.72 1 7.71 1 7.72 0 74.37 0 26.24 0 41.75 0 41.77 10 13.06 5 12.58 5 26.22 0 75.12 0 75.56 20 41.85 12 12.78
H-214 H-216 H-217 H-218 H-219 H-220 H-221 H-301 H-303 H-302 H-304 H-305 H-307 H-306 H-308 H-309 H-310 H-311 H-312 H-313 H-314 H-315 H-316 S/I I-113 I-114 I-115 S/I I-217 I-220 I-219 I-218 I-216 I-215 S/I J-213 J-216 J-208 J-209 J-210 J-211 J-212 J-213 J-212 J-214 J-215 J-217 J-218 J-324 J-325 J-307 J-326 J-301 J-302 J-303 J-304 J-305 J-306 J-308 J-309 J-310 J-311 J-312 J-313 J-314 J-315 J-316 J-321 J-320 J-319 J-318 S/I S/I
12 18 24 24 12 12 56 57 25 19 25 19 25 19 57 57 25 19 19 25 25 19 57 4 3 3 3 4 3 3 3 3 3 3 4 5 3 3 3 3 3 3 3 3 3 3 3 3 6 26 3 8 57 19 25 25 19 57 3 3 3 3 3 3 3 3 3 3 3 12 12 184 184
0 12.59 5 25.95 0 41.85 0 41.87 0 12.78 0 12.58 25 74.09 0 74.09 0 41.86 0 25.83 0 41.87 0 25.93 0 41.86 10 25.94 0 75.12 0 75.56 25 41.87 0 25.93 0 25.92 0 41.88 0 41.87 0 25.93 25 74.09 4 52.18 1 8.13 1 8.44 1 8.44 1 48.14 1 10.21 1 9.79 1 15.79 1 10.3 1 10.36 1 10.37 2 73.3 1 27.15 1 8.39 1 8.76 1 8.76 1 8.76 1 8.76 1 8.76 1 8.76 1 8.77 1 8.75 1 8.41 1 8.75 1 8.75 0 46.36 0 53.32 1 26.78 0 79.59 0 75.14 0 25.92 0 41.89 0 41.89 0 25.93 0 74.1 1 8.75 1 8.76 1 8.76 1 8.76 1 8.76 1 8.76 1 8.76 1 8.76 1 8.41 1 10.1 1 9.95 0 31.06 0 31.05 0 227.06 0 226
RESUMEN ESTADÍSTICO
n = Cantidad de datos = VALOR MÍNIMO = VALOR MÁXIMO = PROMEDIO = ERROR ESTÁNDAR = VARIANZA = DESVIACIÓN ESTÁNDAR = MEDIANA = Valor al centro de la muestra = 25 PERCENTIL = Valor al 1/4 de la muestra = 75 PERCENTIL = Valor al 3/4 de la muestra =
286 0 184 12.9965 1.20864 417.793 20.44 3 3 19
286 0 36 2.73077 0.35871 36.8009 6.06638 1 0 1
286 6.96 252.45 28.195 1.9998 1143.7 33.819 15.75 8.405 41.75
GRÁFICA DE CAJA Esta grafica permite identificar la distribución de los datos en la muestra, nos indica la ubicación proporcional de la mediana, el primero y el tercer cuartil, así como los datos atípicos en la muestra
HISTOGRAMAS
CORRELACIÓN DE VARIABLES Se usa para determinar la naturaleza de la telación entre dos cantidades. Se refiere a la cercanía a la línea generada por el modelo matemático representativo de la relación entre dos grupos de variables de cada una de las variables. COEFICIENTE DE CORRELACIÓN Se trata de un número sin unidades que permite comparar valores de unidades diferentes para identificar su relación, así mismo, nos permite identificar si la correlación de las variables es directa o inversamente proporcional en función de si su valor es positivo o negativo. 1. se calculan los puntajes z de cada variable:
2. el coeficiente de correlación (r) se refiere al promedio del producto de los puntajes z de las dos variables que se comparan:
s
-0.391218582 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.146599948 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 0.146942414 0.146942414 0.146942414 0.342637322 0.146942414 -0.146599948 -0.635837217 -0.489066036 -0.489066036 -0.489066036 -0.342294855 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.391218582 -0.391218582 -0.440142309 -0.440142309 -0.440142309 -0.440142309 -0.440142309 -0.440142309 -0.342294855 -0.489066036 -0.489066036 -0.440142309 -0.489066036 0.538332229 0.538332229 -0.440142309 -0.440142309 -0.440142309 -0.440142309 -0.342294855 1.761425403 0.587255956
-0.450148177 -0.285305169 -0.450148177 -0.285305169 -0.285305169 -0.285305169 0.374066865 -0.285305169 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.12046216 -0.12046216 -0.285305169 0.209223856 1.198281907 -0.450148177 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.12046216 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.450148177 -0.450148177 0.209223856 0.209223856 0.209223856 -0.285305169 -0.285305169 -0.450148177 -0.285305169 -0.450148177 1.527967924 -0.450148177 -0.450148177 -0.285305169 -0.450148177 0.209223856 3.176398009 -0.450148177
-0.185845813 -0.581184425 -0.580888734 -0.581184425 -0.581184425 -0.323342039 2.708671517 -0.362964608 -0.367991352 -0.354685265 -0.367695661 -0.581184425 -0.587689623 -0.581480116 -0.581480116 -0.581480116 -0.581480116 -0.581480116 -0.581480116 -0.603065545 -0.605431071 -0.605431071 -0.604248308 -0.604248308 -0.605431071 2.073527659 2.125864933 2.113445919 0.385428830 -0.096842880 -0.263612496 -0.555459325 -0.263612496 -0.263908187 -0.275144438 -0.618441467 -0.618441467 -0.622581138 -0.626720810 -0.626720810 -0.622285447 -0.626720810 -0.626720810 -0.626720810 -0.621989757 -0.627312191 -0.626720810 -0.622285447 -0.627903573 -0.384550037 0.235513590 -0.196194992 -0.595377584 -0.384550037 -0.346110232 -0.595377584 -0.595377584 -0.384550037 -0.627903573 -0.627903573 -0.627903573 -0.611936269 0.940144788 0.830739189 -0.595377584 -0.595377584 -0.617554395 -0.139718047 -0.392237998 1.376288731 0.403761660
0.293713595 0.293713595 0.587255956 0.587255956 0.293713595 2.152815218 -0.391218582 -0.391218582 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.244447402 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.537989763 -0.440142309 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 2.103891491 0.538332229 0.244789868 0.538332229 -0.244447402 -0.048752494 2.103891491 1.174340679 1.174340679 -0.489066036 -0.440142309 2.152815218 0.293713595 0.587255956 0.587255956 0.293713595 0.293713595 1.174340679 1.174340679 -0.048752494 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.244447402 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 1.027569499 -0.440142309 -0.489066036 -0.489066036
1.198281907 1.033438899 2.846711992 -0.450148177 -0.450148177 2.846711992 0.044380848 -0.12046216 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.285305169 -0.285305169 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.12046216 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 5.484200127 1.527967924 -0.450148177 -0.450148177 0.209223856 -0.450148177 1.692810933 -0.450148177 0.374066865 -0.450148177 -0.450148177 4.495142077 -0.450148177 -0.450148177 -0.450148177 1.198281907 1.527967924 2.846711992 4.495142077 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.450148177 -0.450148177
-0.069935016 -0.069639325 0.404353042 0.404648733 -0.070230707 1.331639419 0.878345409 1.002831239 -0.581184425 -0.581184425 -0.359712009 -0.367991352 -0.366217207 -0.352024048 -0.581184425 -0.580888734 -0.263021114 -0.263908187 -0.263612496 -0.263316805 -0.263612496 -0.275144438 -0.617850085 -0.626720810 -0.622285447 -0.615780250 4.579507267 -0.626720810 -0.622285447 -0.621989757 -0.626720810 -0.626720810 -0.622285447 -0.627016500 1.387524982 0.400804752 -0.072596233 0.401100443 -0.457585667 -0.463795174 1.365643862 1.602787891 1.602787891 -0.234930488 -0.233452033 1.387524982 -0.069639325 0.404057351 0.403761660 -0.066682417 1.357068829 1.602787891 1.602787891 -0.157459496 -0.580888734 -0.581184425 -0.581184425 -0.581184425 2.719020696 -0.359712009 -0.367695661 -0.367695661 -0.350545594 -0.581184425 -0.581184425 -0.581184425 -0.581184425 2.092156180 1.261560697 0.115758812 -0.581480116
-0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 0.293713595 0.293713595 -0.489066036 -0.489066036 -0.244447402 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 2.103891491 0.538332229 0.244789868 0.538332229 -0.048752494 -0.048752494 2.103891491 2.152815218 0.587255956 0.293713595 0.587255956 0.293713595 2.152815218 -0.146599948 0.146942414 -0.146599948 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 0.342637322 0.342637322 -0.048752494 0.734027137 0.734027137 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 2.103891491 0.244789868 0.538332229 0.538332229 -0.048752494 -0.048752494 0.244789868 2.103891491 2.103891491 0.538332229 -0.048752494
-0.450148177 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.285305169 -0.285305169 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 1.692810933 -0.450148177 1.527967924 -0.450148177 1.198281907 5.484200127 -0.450148177 -0.450148177 0.374066865 3.341241017 -0.450148177 4.824828093 0.374066865 -0.450148177 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 1.527967924 -0.450148177 1.527967924 -0.450148177 2.02249695 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.450148177 -0.450148177 1.198281907 0.374066865 0.374066865 -0.450148177 -0.450148177 2.846711992 1.527967924
-0.581775807 -0.581184425 -0.357050792 -0.609866434 -0.610162124 -0.552502417 0.321559615 0.174009902 -0.263612496 -0.263612496 -0.263316805 -0.263612496 -0.263612496 -0.619032849 -0.623468211 -0.623468211 -0.619328539 -0.623468211 -0.623468211 -0.274848747 -0.615484559 -0.623468211 -0.619032849 -0.623468211 -0.618737158 1.365348171 0.400804752 -0.066386726 0.401100443 -0.460838266 -0.466160700 1.387820673 1.365348171 0.404057351 -0.066386726 0.404353042 -0.070230707 1.387524982 -0.174609562 6.631010101 -0.285789307 -0.605431071 -0.614301796 -0.605135381 -0.605135381 -0.604839690 -0.605431071 -0.616075940 0.401396134 0.401396134 -0.069639325 1.370374915 1.339623071 -0.605726762 -0.605431071 -0.614597486 -0.605726762 -0.605431071 -0.605726762 -0.605431071 1.365348171 -0.057811693 0.400804752 0.401396134 -0.447532179 -0.461725338 -0.058403074 1.387524982 1.400535378 0.403761660 -0.455811522
-0.048752494 0.244789868 0.538332229 0.538332229 -0.048752494 -0.048752494 2.103891491 2.152815218 0.587255956 0.293713595 0.587255956 0.293713595 0.587255956 0.293713595 2.152815218 2.152815218 0.587255956 0.293713595 0.293713595 0.587255956 0.587255956 0.293713595 2.152815218 -0.440142309 -0.489066036 -0.489066036 -0.489066036 -0.440142309 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.440142309 -0.391218582 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.342294855 0.636179683 -0.489066036 -0.244447402 2.152815218 0.293713595 0.587255956 0.587255956 0.293713595 2.152815218 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.489066036 -0.048752494 -0.048752494 8.366128538 8.366128538
-0.450148177 0.374066865 -0.450148177 -0.450148177 -0.450148177 -0.450148177 3.670927034 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.450148177 1.198281907 -0.450148177 -0.450148177 3.670927034 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.450148177 3.670927034 0.209223856 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.12046216 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.285305169 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.450148177 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.285305169 -0.450148177 -0.450148177 -0.450148177 -0.450148177
-0.461429647 -0.066386726 0.403761660 0.404353042 -0.455811522 -0.461725338 1.357068829 1.357068829 0.404057351 -0.069935016 0.404353042 -0.066978108 0.404057351 -0.066682417 1.387524982 1.400535378 0.404353042 -0.066978108 -0.067273799 0.404648733 0.404353042 -0.066978108 1.357068829 0.709210266 -0.593307748 -0.584141333 -0.584141333 0.589751179 -0.531804060 -0.544223074 -0.366808588 -0.529142843 -0.527368698 -0.527073007 1.333709255 -0.030903829 -0.585619787 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.574383536 -0.574974918 -0.585028406 -0.574974918 -0.574974918 0.537118215 0.742919018 -0.041844389 1.519698774 1.388116364 -0.067273799 0.404944423 0.404944423 -0.066978108 1.357364520 -0.574974918 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.574679227 -0.585028406 -0.535056659 -0.539492021 0.084711277 0.084415586 5.880251136 5.848907910
GRÁFICAS DE DISPERSIÓN Sirven para resumir los datos multivariados cuando cada elemento consta de más de dos valores. Simplemente se construirías diagramas de dispersión distintos para cada par de valores. A continuación se muestran las graficas de dospersión sorrespondientes a los valores de CAPACIDAD-OCUPACIÓN y CAPACIDAD-ÁREA.
40 35
OCUPACIÓN Y1
30 25 20 15 10 5 0
0
50
100
150
200
150
200
CAPACIDAD X
300 250
ÁREA Y2
200 150 100 50 0
0
50
100
CAPACIDAD X
RECTA DE MÍNIMOS CUADRADOS Cuando dos cariables tienen una relación lineal, el diagrama de disperción tiende a estar agrupado alrededor de la recta de mínimos cuadrados. Se refiere al modelo lineal que resulta en la recta.
variable dependiente coeficientes de regresión intercepto pendiente variable independiente error El coeficiente ß1 representa la pendiente de la recta de mínimos cuadrados, es una estimación de la constante verdadera del valor de ß1. El coeficiente ß0 es el intercepto de la recta de mínimos cuadrados, significa una estimación de valor de ß0.
21.83659 17.30163 27.29813 17.30163 17.30163 17.30163 -6.79975 17.30163 27.29813 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 -2.19486 -2.19486 -5.19836 8.88906 21.83314 8.18275 35.49044 17.30163 17.30163 17.30163 5.11283 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 27.29813 17.30163 17.30163 17.30163 17.30163 17.30163 13.84009 13.84009 24.56736 24.56736 24.56736 24.56736 -11.41864 -11.41864 -8.88017 17.30163 17.30163 24.56736 17.30163 -30.04802 101.99398 24.56736 24.56736 15.57086 24.56736 -8.88017 693.75976 -32.77879
50.25912201 196.482607 196.382642 196.482607 196.482607 109.313127 -274.493963 122.708437 124.407842 119.909417 124.307877 196.482607 198.681837 196.582572 196.582572 196.582572 196.582572 196.582572 196.582572 203.880017 204.679737 204.679737 204.279877 204.279877 204.679737 210.620017 215.936212 214.674742 91.28964201 -9.83688299 26.71421701 244.141072 89.12019701 89.22016201 93.01883201 146.332777 209.078197 210.477707 211.877217 211.877217 210.377742 211.877217 211.877217 211.877217 210.277777 212.077147 211.877217 210.377742 212.277077 103.995602 -63.69100299 59.69303701 181.145787 117.000742 105.305292 181.145787 181.145787 90.99046201 212.277077 212.277077 191.041937 206.878967 349.854742 309.141792 181.145787 181.145787 187.893162 42.50972201 92.80955201 1675.777867 163.906112
63.94401225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 8.97901225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 9.02101225 9.02101225 9.02101225 49.04901225 9.02101225 8.97901225 168.9090123 99.93001225 99.93001225 99.93001225 48.95101225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 63.94401225 63.94401225 80.93701225 80.93701225 80.93701225 80.93701225 80.93701225 80.93701225 48.95101225 99.93001225 99.93001225 80.93701225 99.93001225 121.0770123 121.0770123 80.93701225 80.93701225 80.93701225 80.93701225 48.95101225 1296.252012 144.0840123
43.64083 37.63733 207.29121 -32.77879 -16.39417 759.90661 -2.15291 5.84359 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 27.29813 27.29813 17.30163 17.30163 13.64429 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 8.03590 24.56736 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 1430.69338 101.99398 -13.66340 -30.04802 -6.34171 2.72121 441.61288 -65.54801 54.46949 27.29813 24.56736 1199.94161 -16.39417 -32.77879 -32.77879 43.64083 55.64783 414.52199 654.55699 2.72121 17.30163 17.30163 17.30163 17.30163 13.64429 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 -57.35571 24.56736 27.29813 27.29813
-14.19911799 -14.13908299 164.146182 164.266217 -14.25915299 1981.691462 -237.534913 -271.200178 196.482607 196.482607 121.608822 124.407842 123.808052 119.009732 196.482607 196.382642 88.92026701 89.22016201 44.54449701 89.02023201 89.12019701 93.01883201 208.878267 211.877217 210.377742 229.003652 -1393.331678 211.877217 210.377742 210.277777 211.877217 211.877217 210.377742 211.977182 2017.933217 149.150902 -12.28429299 149.260937 77.32153701 15.63024201 1986.110627 1301.106357 1301.106357 79.42359201 71.02862701 2064.858077 -14.13908299 164.026147 163.906112 -13.53873299 275.529792 1301.106357 1301.106357 5.30650201 196.382642 196.482607 196.482607 196.482607 -459.452458 121.608822 124.307877 124.307877 118.509907 196.482607 196.482607 196.482607 196.482607 1486.099702 -383.834413 -39.13489799 196.582572
36.04201225 36.04201225 144.0840123 144.0840123 36.04201225 1936.308012 63.94401225 63.94401225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 24.96501225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 120.9230123 80.93701225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 1849.301012 121.0770123 25.03501225 121.0770123 24.96501225 0.99301225 1849.301012 576.1680123 576.1680123 99.93001225 80.93701225 1936.308012 36.04201225 144.0840123 144.0840123 36.04201225 36.04201225 576.1680123 576.1680123 0.99301225 99.93001225 99.93001225 99.93001225 99.93001225 24.96501225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 441.1470123 80.93701225 99.93001225 99.93001225
27.29813 27.29813 17.30163 17.30163 17.30163 17.30163 -16.39417 -16.39417 17.30163 17.30163 13.64429 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 -117.43262 112.99748 -13.66340 101.99398 2.72121 -7.24379 1430.69338 -120.16339 -32.77879 13.62333 243.30171 -16.39417 1287.94861 -6.79975 -8.20186 8.18275 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 64.91706 -19.12494 -9.23679 -40.97109 184.08141 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 -117.43262 -13.66340 -30.04802 -30.04802 -7.24379 -2.26129 11.35410 -117.43262 -117.43262 190.02198 -9.23679
196.682537 196.482607 120.709137 206.179212 206.279177 186.786002 65.28722201 35.32975701 89.12019701 89.12019701 44.49453201 89.12019701 89.12019701 209.278127 210.777602 210.777602 209.378092 210.777602 210.777602 92.91886701 208.078547 210.777602 209.278127 210.777602 209.178162 1985.680592 149.150902 -11.23355799 149.260937 15.53059201 15.70996201 2018.363252 2031.855452 164.026147 -13.47869799 164.146182 -14.25915299 2064.858077 17.69475201 673.549472 28.96159201 204.679737 207.678687 204.579772 204.579772 204.479807 204.679737 208.278477 95.07153201 95.07153201 2.34689701 695.335107 679.731467 204.779702 204.679737 207.778652 204.779702 204.679737 204.779702 204.679737 1985.680592 -9.78254299 149.150902 149.370972 15.08216701 15.56048701 -9.88261299 2017.933217 2036.854757 150.251252 15.36118701
99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 36.04201225 36.04201225 99.93001225 99.93001225 24.96501225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 1849.301012 121.0770123 25.03501225 121.0770123 0.99301225 0.99301225 1849.301012 1936.308012 144.0840123 36.04201225 144.0840123 36.04201225 1936.308012 8.97901225 9.02101225 8.97901225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 49.04901225 49.04901225 0.99301225 225.1050123 225.1050123 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 1849.301012 25.03501225 121.0770123 121.0770123 0.99301225 0.99301225 25.03501225 1849.301012 1849.301012 121.0770123 0.99301225
2.72121 11.35410 -30.04802 -30.04802 2.72121 2.72121 957.65488 -120.16339 -32.77879 -16.39417 -32.77879 -16.39417 -32.77879 43.64083 -120.16339 -120.16339 267.30871 -16.39417 -16.39417 -32.77879 -32.77879 -16.39417 979.92411 -11.41864 17.30163 17.30163 17.30163 15.57086 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 6.57436 13.84009 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 19.10583 -35.50955 17.30163 13.64429 -120.16339 -16.39417 -32.77879 -32.77879 -16.39417 -120.16339 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 17.30163 2.72121 2.72121 -466.97106 -466.97106
15.55052201 -11.23355799 150.251252 150.471322 15.36118701 15.56048701 1973.639612 2019.534472 164.026147 -14.19911799 164.146182 -13.59876799 164.026147 -13.53873299 2064.858077 2084.219617 164.146182 -13.59876799 -13.65880299 164.266217 164.146182 -13.59876799 2019.534472 -215.779793 200.581172 197.482257 197.482257 -179.433933 179.788452 183.986982 124.007982 178.888767 178.288977 178.189012 -405.785873 8.35746201 197.982082 194.283377 194.283377 194.283377 194.283377 194.283377 194.283377 194.183412 194.383342 197.782152 194.383342 194.383342 -127.090443 326.711117 14.14644701 -256.794418 2065.738147 -13.65880299 164.386252 164.386252 -13.59876799 2019.974507 194.383342 194.283377 194.283377 194.283377 194.283377 194.283377 194.283377 194.283377 197.782152 180.888067 182.387542 -2.85483299 -2.84486799 34006.58709 33825.32338
0.99301225 25.03501225 121.0770123 121.0770123 0.99301225 0.99301225 1849.301012 1936.308012 144.0840123 36.04201225 144.0840123 36.04201225 144.0840123 36.04201225 1936.308012 1936.308012 144.0840123 36.04201225 36.04201225 144.0840123 144.0840123 36.04201225 1936.308012 80.93701225 99.93001225 99.93001225 99.93001225 80.93701225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 80.93701225 63.94401225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 48.95101225 169.0910123 99.93001225 24.96501225 1936.308012 36.04201225 144.0840123 144.0840123 36.04201225 1936.308012 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 99.93001225 0.99301225 0.99301225 29242.19701 29242.19701
1
1
1
1
40
y = 0.1017x + 1.4093
35
r = 0.342587
OCUPACIÓN Y1
30 25 20 15 10 5 0
0
50
100
150
200
CAPACIDAD X
300
y = 1.2267x + 12.252 r = 0.74143
250
ÁREA Y2
200 150 100 50 0
0
50
100
CAPACIDAD X
150
200
RAÍZ DEL ERROR MEDIO CUADRÁTICO Es un valor que determina la probabilidad error que tiene la variable dependiente obtenida por un modelo matemático, es decir, la variable ajustada con respecto a los valores de la misma variable de la muestra. Se ocupa para comparar la bondad o precisión de un modelo matemático. Se trata de un valor sin unidad que se encuentra entre 0 y 1, entre más alto es su valor, mayos probabilidad de error hay en el valor ajustado y por tanto el modelo matemático es menos preciso, por esta razón, se busca que la raís del error medio cuadrático sea lo más acercado a 0. Este valor se obtiene con la fórmula:
1.917712291 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 2.426095151 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 3.036154585 3.036154585 3.036154585 3.442860873 3.036154585 2.426095151 1.40932943 1.714359146 1.714359146 1.714359146 2.019388863 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.714359146 1.917712291 1.917712291 1.816035718 1.816035718 1.816035718 1.816035718 1.816035718 1.816035718 2.019388863 1.714359146 1.714359146 1.816035718 1.714359146 3.849567162 3.849567162 1.816035718 1.816035718 1.816035718 1.816035718 2.019388863 6.391481466 3.951243734
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26.97270162 34.33309329 41.69348496 41.69348496 26.97270162 26.97270162 80.9489072 82.17563914 42.9202169 35.55982523 42.9202169 35.55982523 42.9202169 35.55982523 82.17563914 82.17563914 42.9202169 35.55982523 35.55982523 42.9202169 42.9202169 35.55982523 82.17563914 17.15884606 15.93211411 15.93211411 15.93211411 17.15884606 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 17.15884606 18.385578 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 19.61230995 44.14694885 15.93211411 22.06577384 82.17563914 35.55982523 42.9202169 42.9202169 35.55982523 82.17563914 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 15.93211411 26.97270162 26.97270162 237.9705962 237.9705962
-14.3827016 -8.38309329 0.15651504 0.17651504 -14.1927016 -14.3927016 -6.8589072 -8.08563914 -1.0602169 -9.72982523 -1.0502169 -9.62982523 -1.0602169 -9.61982523 -7.05563914 -6.61563914 -1.0502169 -9.62982523 -9.63982523 -1.0402169 -1.0502169 -9.62982523 -8.08563914 35.0211539 -7.80211411 -7.49211411 -7.49211411 30.9811539 -5.72211411 -6.14211411 -0.14211411 -5.63211411 -5.57211411 -5.56211411 56.1411539 8.764422 -7.54211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.16211411 -7.18211411 -7.52211411 -7.18211411 -7.18211411 26.7476901 9.17305115 10.8478859 57.5242262 -7.03563914 -9.63982523 -1.0302169 -1.0302169 -9.62982523 -8.07563914 -7.18211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.17211411 -7.52211411 -5.83211411 -5.98211411 4.08729838 4.07729838 -10.9105962 -11.9705962
206.8621058 70.27625306 0.024496959 0.03115756 201.4327792 207.1498598 47.04460796 65.37756037 1.12405988 94.66949905 1.102955542 92.733534 1.12405988 92.5410375 49.78204373 43.76668128 1.102955542 92.733534 92.92623051 1.082051204 1.102955542 92.733534 65.37756037 1226.481224 60.87298461 56.13177386 56.13177386 959.8318997 32.7425899 37.72556576 0.020196421 31.72070936 31.04845567 30.93711339 3151.829166 76.81509297 56.88348527 51.43922083 51.43922083 51.43922083 51.43922083 51.43922083 51.43922083 51.29587854 51.58276311 56.5822007 51.58276311 51.58276311 715.4389232 84.14486745 117.6766283 3309.036596 49.50021817 92.92623051 1.061346866 1.061346866 92.733534 65.21594758 51.58276311 51.43922083 51.43922083 51.43922083 51.43922083 51.43922083 51.43922083 51.43922083 56.5822007 34.01355501 35.78568924 16.70600807 16.62436211 119.0411087 143.2951726
= 9257.30
= 2.083407 = 208.34%
= 146777.21
= 0.80347441 = 80.34%
Comparar la raĂz del error medio cuadrĂĄtico de los dos modelos presentados no tiene validez alguna, pues se trata de dos modelos lineales que representan una misma variable independiente, pero dos variables dependientes diferentes, este ejercicio se usa para comparar don modelos lineales obtenidos de dos o mĂĄs muestras pero con las mismas variables.
GRÁFICA DE RESIDUOS Se comparan los valores de los residuos e contra los valores de la variable dependiente ajustada. Esto determina de qué tamaño es el rango en el que se encuentran los residuos, entre más pequeño es el rango de residuos, mayos es la precición del modelo, pues significa que los valores de la muestra están uniformemente distribuidos con respecto a la recta de mínimos cuadrados.
GRÁFICA DE RESIDUOS 40 30 20
e
10 0 -10
0
5
10
15
20
25
200
250
-20 -30
y1 ajustada
GRÁFICA DE RESIDUOS 250 200
e
150 100 50 0 -50
0
50
100
150
y2 ajustada
Estas dos gráficas presentan una aglomeración evidente de residuos en una parte de la gráfica, esto quiere decir que los valores ajustados no están uniformemente distribuidos con respecto al modelo de la recta media cuadrática.
UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO PROGRAMA DE MAESTRÍA Y DOCTORADO EN ARQUITECTURA IMPARTE: MTRO. EN ARQ. ARTURO VALERIANO FLORES ARQ. ÁLVARO BORBOA OSORIO JUNIO 2018